# Questions: what has been asked here, what it got, and where the record is

*(GENERATED from the `<!-- ledger -->` blocks at the top of the notes; never
hand-edited. Regenerate with `node research/qc.js --index` or
`node research/gen-questions-index.js`. The block format and the gate that
enforces it are documented at the top of `qc/questions.js`.)*

**Before proposing an attack or briefing an agent:** find the TODO item in
section 1, search for the actual object, then read the relevant records and
their decisive dependencies. Use [OUTCOMES.md](OUTCOMES.md) for reuse and
revisit conditions. An item can span many unrelated attempts; loading every
linked note is not the required first step. Verify any conclusion that
determines the next move, including an ANSWERED or CLOSED entry.

**Status describes the question, not proof strength or review grade.**
OPEN: unresolved. PARTIAL: specified parts are resolved. ANSWERED: the bounded
question has an answer, which may be a negative finding, finite measurement
or completed specification. Its underlying arithmetic target may remain OPEN.
CLOSED: the stated premise or approach is closed at its recorded scope; this
does not refute every related conjecture. SUPERSEDED: another record replaces
this one. Consult the owning note and linked reviews for HELD or other grades.

**Multiple records:** conflicting statuses are shown as MIXED. The displayed
verdict comes from the last record in path order, not necessarily the newest
or most authoritative review. Read the linked records before resolving a
disagreement; the generator does not adjudicate it.

## 1. By TODO item: what has already run under each

| TODO item | question | status | verdict | records |
|---|---|---|---|---|
| C | `Q-agent-start` What must an incoming agent read and preserve before continuing the reviewed arithmetic campaign? | ANSWERED | Onboarding and document ownership only. The second dispatch is completed and independently reviewed on 2026-09-09. RESEARCH-EXECUTION.md owns current dispositions and candidate next obligations; RESEARCH-HANDOFF.md owns the updated exact contract. No assignment is started by that review. Twin-prime infinitude and required signed estimates remain OPEN. | [AGENT-START.md](AGENT-START.md) |
| C | `Q-bilinear-fold-first-attack` Does assigning each Mobius factor to its first fold, or applying a direct second-moment bound, establish the missing one-sided estimate? | ANSWERED | The first-fold identity yields no saving; a direct second moment has a negligible diagonal and an open two-prime off-diagonal. Fixed-fold covariance is an exact residue-imbalance square and the beta weights balance at each fixed modulus. Growing-depth joint control remains OPEN; B>=-C2*x+o(x) is not improved. | [bilinear-fold-attack.md](bilinear-fold-attack.md) |
| C | `Q-centered-discrepancy-estimate` Can the top of D_y be removed using ordinary prime distribution after an exact divisor flip, and what estimate remains? | PARTIAL | Equations (3)-(4), the exact split and flip, survive review and finite controls. A repair of the top-range bound T^top=O_(A,eps)(x/log^A x) is DERIVED in section 3a (2026-09-08) with the endpoint atom retained, odd square divisors, the corrected reciprocal-totient local factors with (m',g)=1, explicit truncation powers, a Cauchy multiplicity device, and a uniform Mobius mean proved from the q=1 Siegel-Walfisz statements; its inputs are the terminal-point BV of Tao Notes 3 Theorem 17 with the prefix form derived by rounding. The handler (lane V) read the derivation on 2026-09-08, reconstructed (BV*), (3a.9), (3a.14) and (3a.16), checked the limiting constant of (3a.9) numerically at eight (b,g) pairs and found no defect; it is accepted at its stated scope, with ineffective constants. The payoff is D_y=D^(e_1)+O_(A,eps)(x/log^A x) only, so the handoff consumer is equivalent to D^(e_1)>=-4x/25+o(x). The fixed-endpoint signed discrepancy, D_y>=-4x/25+o(x) and twin-prime infinitude remain OPEN. | [centered-discrepancy-estimate.md](centered-discrepancy-estimate.md) |
| C | `Q-centered-discrepancy-measurement` At reachable x, is the OPEN sufficient input D_y>=-4x/25 numerically violated, is the absolute form (13) numerically plausible, and does D_y carry structure beyond a random-sign model? | ANSWERED | MEASURED to x=2^38. Neither pre-registered falsifier fires. D_y/x stays within 0.0043 of zero for the measured j>=26. Over 30<=j<=38, D_y/x differs from -(T1/x-C2) by at most 2e-4, with maximum 1.84401e-4 at j=30; the classical term dominates this finite comparison. The data do not establish an asymptotic fluctuation scale, an impossibility of informative future measurements, or the sufficient signed estimate. No proof status changes. | [centered-discrepancy-measurement.md](centered-discrepancy-measurement.md) |
| C | `Q-chain-review-0906` Do the written derivations from S(x) down to E_dagger hold as stated, with every imported theorem used inside its hypotheses and every discarded term at the claimed O_H(x/log^H x) rate, and where does the chain remain unreviewed? | ANSWERED | Three independent adversarial passes found no defect in the six classical contributions from S(x) to E_>, none in the grouped moment (1)-(20) including the E_* to E_dagger step, and none in the residual-coverage link E_> to E_*, whose block-shape derivation was reconstructed and verified exactly. Every imported theorem was confirmed in its primary source except the Mobius Bombieri-Vinogradov citation, which points at an exercise sheet and needs a published replacement. Stale o(x) rates in three note bodies were replaced. A checked argument is not a refereed theorem; the OPEN signed margin is untouched. | [chain-review-0906.md](chain-review-0906.md) |
| C | `Q-chen-fold-benchmark` Can the fold framework reproduce a classical Chen lower bound on long intervals with every imported hypothesis and error budget stated? | ANSWERED | The classical implication is derived below using three explicitly imported theorem statements, with the combinatorial minorant proved and its integral margin certified by exact rational arithmetic. This is a benchmark, not a new prime theorem, and it does not prove twins or a short-zone result. | [chen-fold-benchmark.md](chen-fold-benchmark.md) |
| C | `Q-chen-opportunity` Does the signed Chen target identify an approachable proof mechanism, and what should the next research obligation be? | ANSWERED | The target is sufficient but subtracts an avoidable odd-composite penalty; even cancellation of its obvious signed components does not close the existing separate bounds. Select a prime-detecting weight against explicitly justified arithmetic input ranges before pursuing a new estimate. The opportunity is a research judgment, not a proved mechanism. | [chen-opportunity-audit.md](chen-opportunity-audit.md) |
| C | `Q-chen-signed-target` What exact additional arithmetic estimate would turn the completed Chen benchmark into a proof of infinitely many twin primes? | PARTIAL | An elementary prime minorant gives a conditional twin theorem with all weights, ranges, quantifiers and errors specified. The opportunity audit identifies an avoidable negative-weight penalty and a separate-estimate budget that fails even under component cancellation; this sufficient target remains OPEN and is not the sole next proof obligation. | [chen-signed-target.md](chen-signed-target.md) |
| C | `Q-coefficient-structure` Does the arithmetic structure of the aggregated coefficients reduce the endpoint estimate beyond the previous rectangle, and can smaller coefficient norms alone supply the remaining power saving? | ANSWERED | Exact classification gives a nonsquarefree L2 norm of size at most sqrt(D)*W^(1/4) times logarithms, while the squarefree top-band energy is at least a constant times D*W*log(W). At d~x^0.277, e~x^0.467 every endpoint sector except the squarefree-squarefree prime sum has a power saving. This reduces that rectangle to one explicit endpoint correlation; prime-dispersion.md supplies the remaining estimate and controls the full rectangle. Finite algebra, CRT sectors and archived prefixes are checked separately. | [coefficient-structure.md](coefficient-structure.md) |
| C | `Q-cofactor-progression-transfer` Can the corrected full-cofactor kernel be estimated on a growing cofactor range by representing its actual arithmetic on CRT progressions, and does the resulting bound reach the twin consumer? | PARTIAL | Derived from named imports: for some positive absolute kappa and d, all prime-r cofactor pairs s,t <= floor((log x)^kappa), including non-squarefree inputs and mixed transition/smoothed profiles, admit a dyadic scale-average O(log^(2-d) X) bound after division by x. The extension uses bounded multiplicative Euler modifications on the progression s\|n, t\|n-2 and keeps its density 1/lcm(s,t), so summing cofactors costs only O((log log X)^2). This goes beyond s=t=1 but remains short of o(x). The large-cofactor joint remainder, outside residual and twin margin remain OPEN; the attempted extension to power-sized cofactors fails on source modulus range and accumulated logarithmic cost. | [cofactor-progression-transfer.md](cofactor-progression-transfer.md) |
| C | `Q-consumer-comparison` How does the sufficient margin C_2 x + E_dagger(x) >= c_0 x/(log x)^K compare logically with the published sufficient routes to twin primes, and what does the literature already own of the corner object? | ANSWERED | The sufficient margin remains OPEN. The published conditional routes imply it where their hypotheses and stated lower bounds apply; reverse implications are not established. The dictionary is E_dagger(x)/x = C_2(2 delta_x - delta_{x/2} - 1) + o(1), with K>0 below that normalisation's resolution. Independent review corrects the comparison: cumulative and dyadic consumers on unbounded scales are equivalent at the same fixed K with possibly different positive constants. At K=0 an eventual cumulative lower bound also implies the unbounded-scale dyadic consumer. The nonnegative-weight corner identification applies only to the prime-cofactor subfamily; the full residual retains additional branches. Every surveyed route remains conditional. | [consumer-comparison.md](consumer-comparison.md) |
| C | `Q-corner-branch-diagnostic` Can future experiments enumerate the full coefficients C(n) and C'(n-2) branch by branch, without silently dropping proper prime powers, cofactors s>1, non-squarefree inputs or either gcd branch? | ANSWERED | The driver exists and its two independent constructions of each side agree exactly on 8192 retained sides and 1802 fixture sides; five deletion and reconstruction controls are ACTIVE in both runs. Its split by gcd(n,n-2) measures integer parity, not the per-term CRT gcd partition. The fixed-eta corner is empty on the retained prefix, and Elo exceeds E0 across the entire J_x, so the matrix is a proxy window. This is finite algebra and tool preparation, with no asymptotic estimate or twin margin. | [corner-branch-diagnostic.md](corner-branch-diagnostic.md) |
| C | `Q-corner-coefficient-energy` Can the full corner coefficients be studied before splitting their cofactor branches, and what do exact energy and classical smoothed sieve weights supply? | ANSWERED | The sharp coefficient energy is an explicit signed quadratic form in short cofactors plus O_epsilon(x^(1/2)K^2*x^epsilon), a power below x at the fixed corner. Logarithmically averaging the divisor cutoff gives Barban–Vehov weights and an O_eta(x log x) squared norm on each side and absolute shifted-product bound. The follow-up sharp-corner-transition.md gives sharp O_eta(x log^2 x) norms and proves a non-negligible norm transition for sufficiently small fixed eta. Signed transition saving and the global complement remain OPEN; no exact residual cut or twin margin changes. | [corner-coefficient-energy.md](corner-coefficient-energy.md) |
| C | `Q-corner-correlation` On the corner S_0 where both cofactors sit just above their own cutoffs, what exactly is the remaining endpoint sum, what does the sufficient consumer need there, and does any reviewed correlation theorem supply it? | PARTIAL | The full corner is exactly sum_n C(n)C'(n-2). Proper-prime-power terms above the cutoffs are negligible at fixed eta by §1.1; the remaining prime-r terms with s>1 or s'>1 and non-squarefree inputs remain OPEN. The s=s'=1 piece has a nonnegative Mobius-product weight with exact moving cuts. The multiplicative lift and round-review sampling give small continuous and dyadic scale-average log savings for that subfamily, with no o(x), full-corner control or twin margin. The complement is still open. | [corner-correlation.md](corner-correlation.md) |
| C | `Q-corner-log-average` What do logarithmically averaged correlation theorems and their quantitative successors actually supply for the prime-cofactor corner weight, with exact support, rates and scale quantifiers? | PARTIAL | The pure band is invariant under dilation by primes outside it; the exact cofactor window is not, but its support extends to x^(1-2eta) and need not leave the window under a fixed dilation. Uniform-prefix logarithmic bounds imply block bounds by Abel summation; a relative exponent above 3 is one sufficient route to o(x), not a universal necessary threshold. Pilatte's 1/(96e) calculation applies only to his displayed parameter choice. A bounded multiplicative Fourier lift now gives a small continuous scale-average log saving for the prime-cofactor subfamily via Tao-Teravainen v2; see prime-band-transfer.md. No o(x), dyadic pointwise estimate, full-corner estimate or positive twin margin follows. | [corner-log-average.md](corner-log-average.md) |
| C | `Q-corner-measurement` At finite dyadic x, how large is the corner two-point correlation K(x)=sum_{x/2<n<=x} mu(n)mu(n-2)L(n)L'(n-2) of corner-correlation (5) relative to C_2 x, to its own absolute mass, and to a matched random-sign control, and does \|K\|/mass fall with x? | PARTIAL | MEASURED, on the range and cutoffs recorded in the bound OUTPUT block of corner-measurement.js. The dominant finding is disconfirming for the measurement itself, not for the corner: at every reachable x the actual right cutoff Z=floor(x^(1/20)) admits at most one prime in its band and is empty at several j, so the actual-parameter rows are a one-prime object rather than the asymptotic corner, and the enlarged-cutoff rows are a model of the corner's shape and not the corner. On the rows that exist, \|K\|/mass falls with x at a rate that is not faster than the matched random-sign control's own decay, so the runs give no evidence of arithmetic cancellation beyond square-root-of-count. K stays many orders below C_2 x at every j measured and never falls below -C_2 x. No asymptotic rate, saving or cancellation is established, and nothing here changes the OPEN status of the corner or of the sufficient twin margin. | [corner-measurement.md](corner-measurement.md) |
| C | `Q-cross-campaign-synthesis` What can be recovered by comparing the fold, anchored, arithmetic and literature campaigns, including the proposed papers, against the actual twin-prime consumer? | ANSWERED | The full-coefficient viewpoint leads to an exact sharp energy quadratic form, a Graham/Barban–Vehov O_eta(x log x) bound for smoothed full coefficients, and a small-prime cutoff-difference identity. The follow-up sharp-corner-transition.md prices the full sharp norm and rules out negligible L2 transfer for sufficiently small fixed eta. The local proposals supply quantifier and dependency lessons; a reversed anchored inequality, overbroad Suen closure and stale proposal header are repaired. Signed transition correlations and the global margin remain OPEN. The subsequent global-cutoff-averaging.md gives the current complete global formulation and signed research priority; its one-point cancellation is not a shift-2 estimate. | [cross-campaign-synthesis.md](cross-campaign-synthesis.md) |
| C | `Q-data-reuse-audit` Do existing runs or their embedded inputs retain what the current determinant-2 sum needs, and can useful data be recovered without repeating the old campaigns? | ANSWERED | The fold CSV supplies a verified base-prime list and archived interval boundaries; three old rows are reproduced and their bounded prefixes reconstructed with full factorizations retained. Other inspected outputs are aggregate statistics or twin-gap records. These finite inputs support coefficient and grouping tests, not an asymptotic twin bound. | [data-reuse-audit.md](data-reuse-audit.md) |
| C | `Q-determinant-corollary` Does Bettin-Chandee Corollary 1, applied to d*k-e*t=2 after moving the non-smooth part of beta_V and beta_Z onto the coefficient side, control any part of the endpoint remainder that the current estimates do not? | ANSWERED | The transfer is legal and exact: the smoothness hypothesis the literature scout recorded as the blocker is removable, at the cost eta=x^kappa and a boundary error O(x^(1-kappa)log^C x). Priced, it adds nothing. Requiring all four pieces and all bands gives 22max(a,b)+17min(a,b)<20, whose supremum of delta+nu is 2869/3900 < 19/25, so the region is strictly inside the already controlled delta+nu<19/25; the added area is exactly 0. A split by the size of the moved prime power also adds nothing, because every per-band budget is nondecreasing in the band exponents and the top band reproduces the full box. The log-log piece alone is controlled on 12.97 percent of the domain outside the current region, which is one of four pieces and changes nothing for R. W_dagger does not shrink, E_dagger is unchanged, and the sufficient twin margin remains OPEN. | [determinant-corollary.md](determinant-corollary.md) |
| C | `Q-dispersion-range` How far do the dispersion and coefficient-sector estimates extend across divisor sizes, and does a better orientation or gcd budget enlarge their overlap? | ANSWERED | Averaging the nonzero gcd losses over the original divisor gives a different dispersion bound with cross-prime exponent (5/4)a+(1/2)b+3/50, where a=delta+6/25 and b=nu+1/20. Explicit diagonal, prime-cut and sparse-sector inequalities control a region of full rectangles, including d~x^0.282, e~x^0.522 at product scale x^0.804. Its cross-prime and left-sparse budgets are 0.9985 and 0.9988. The supremum of product exponents in this sufficient region is 5397/6700; it is not a uniform product cutoff. Balanced supports separately allow 12/25<s<94/175. The global remainder and twin margin remain OPEN. | [dispersion-range.md](dispersion-range.md) |
| C | `Q-endpoint-fourier` Does a complete Fourier truncation budget and a matched Kloosterman-fraction theorem control any further part of the actual endpoint sum when its small prime-power coefficients are combined first? | ANSWERED | A written classical-input derivation controls the rectangle d in (floor(x^(27/100)),2floor(x^(27/100))], e in (floor(x^(46/100)),2floor(x^(46/100))] to O_H(x/log^H x) for every fixed H. Its product is of order x^(73/100), outside the previously controlled region eventually. The aggregated Fourier exponent is 1989/2000; the full Vaaler tail and gcd=2 branch are included. This is a regional estimate, not a full residual bound or twin theorem; finite algebra and saved-factor checks are separate validation. | [endpoint-fourier.md](endpoint-fourier.md) |
| C | `Q-endpoint-pairing` Does retaining the difference of interval endpoints improve the complete Fourier budget, and are the lowest frequencies actually the next obstruction on the squarefree pilot rectangle? | ANSWERED | A written derivation controls the full rectangle d~x^(11/40), e~x^(93/200) to O_H(x/log^H x), with product of order x^(37/50). The sufficient first exponent becomes 3/20+(7/10)(a+b)+(1/4)max(a,b), equal to 3999/4000 there. On the a=b=517/1000 pilot, this transition-frequency budget is 20061/20000, not the separate-endpoint 20163/20000; prime-dispersion.md now controls that pilot with a different estimate. Finite identities and exact exponent checks validate the implementation, not the asymptotic theorem. No uniform product cutoff or twin lower bound follows. | [endpoint-pairing.md](endpoint-pairing.md) |
| C | `Q-endpoint-target-audit` Does the endpoint reduction require a fixed positive fraction of the expected twin count, and do recorded uniform-gap theorem failures exclude its weaker consumer? | ANSWERED | No fixed fraction is required: for every fixed H the reduction has error O_H(x/log^H x), so C2*x+E_>(x)>=c*x/log^K x on unbounded dyadic scales suffices, as does a stated logarithmically rescaled average. These implications are derived from named inputs; their endpoint hypotheses remain OPEN. The recorded uniform-gap theorem comparison has different quantifiers and does not establish an obstruction for this consumer. | [endpoint-target-audit.md](endpoint-target-audit.md) |
| C | `Q-fixed-endpoint-discrepancy` After the accepted truncation to odd moduli e<x^(1/2+eps), what exactly is the fixed-endpoint centered discrepancy D^(e_1) below and above the level x^(1/2-eps'), which piece does an existing theorem estimate, and what single input would close D^(e_1)>=-4x/25+o(x)? | PARTIAL | Reviewed 2026-09-09 after the coprimality repair: T_I^low=O_(A,eps')(x/log^A x), hence S=C_2x+B+O_A(x/log^A x), with B the exact Type II plus band sum (2.9). The untruncated modulus bound was false; g<=(log x)^(A+13), both tails, the coprime density and the weighted BV multiplicity now pay the estimate. Review corrects harmless log powers and the power-of-two atom over the full eps' range. D^(e_1)>=-4x/25+o(x) is equivalent to B+2C_2M>=-4x/25+o(x); it implies, but is not equivalent to, B>=-(C_2-1/200)x+o(x). The latter and H_B are sufficient OPEN margins. The absolute band statement (4.9) is one stronger sufficient input, not a necessary condition. No inspected source estimates the remaining actual signed B. Twin-prime infinitude remains OPEN. | [fixed-endpoint-discrepancy.md](fixed-endpoint-discrepancy.md) |
| C | `Q-fold-arithmetic-bridge` Does one parity-table bridge from the anchored fold ledger yield a sufficient twin lower bound with named arithmetic inputs? | PARTIAL | Exact identities retained. The one unread sieve input of the pricing, Bombieri--Vinogradov for k-fold X^(1/u)-rough products, is derived from Wu's Lemma 2.3 (section 3a); the same input, sieved in the composite variable, gives the contamination aggregate constant 4 for each fixed k,u, replacing the displayed 12.86 to 19.72. With these inputs, elementary bounds give Q_cov(u)<1 and c*_real(u)<4 for every u>4 (section 4a, independently reviewed 2026-09-09 with rational certificates), so neither sufficient ratio test succeeds at any depth. This closes the two tests, not the decorrelation hypotheses, and supplies no twin estimate. | [fold-arithmetic-bridge.md](fold-arithmetic-bridge.md) |
| C | `Q-full-coefficient-average` Can aggregating the complete coefficients before a correlation theorem remove the explicit cofactor count, and what additional estimate is needed? | PARTIAL | Exact factor and rounded-endpoint Fourier identities retained, with c_(i,0)=3/5 and an explicit composite-filtered weighted sum. The full family is not 1-bounded, but the sufficient phase condition admits at least k=0,+/-1 on the left and l=0,+/-1,...,+/-6 on the right for every Mellin twist; the earlier zero-only claim is corrected. Composite filtering and the required correlation rate remain unmatched. Proposition 6.5, independently reviewed including on 2026-09-09, proves coefficient norm at least (log x)^(2/5) for representations by 1-bounded functions on all smooth inputs. This does not exclude density-one representations, paid growing components or a jointly treated Fourier sum. No sufficient signed twin margin follows. | [full-coefficient-average.md](full-coefficient-average.md) |
| C | `Q-global-cutoff-averaging` Does the wider corpus suggest changing the global decomposition before extending the small-cofactor estimate, and can that change be made without an unpaid transition or outside term? | PARTIAL | Derived: independently averaging the two initial Mobius cutoffs over fixed exponent intervals gives S=C2*x+sum G_L(n)G_R(n-2)+O_A(x/log^A x), uniformly on dyadic scales, with all cofactor and prime-power branches included. Each full G has squared norm O(x log x). The existing sharp-corner lower norm then forces cancellation between the corner coefficient and the rest at the same input. This does not estimate their shifted product. The global signed residual was already O(x) by the sieve upper bound and positivity; the new norm representation is not an improved signed bound. Prefer a bounded attempt on this global coefficient pair and a one-sided consumer; the twin margin remains OPEN. | [global-cutoff-averaging.md](global-cutoff-averaging.md) |
| C | `Q-global-factor-signs` Which full factor configurations cause negative global products, can prime-power exceptions be paid, and does a pair-trigger upper bound control the negative part? | PARTIAL | Derived: G_i(n)=Lambda_(>W_i)(n)-F_i(s_i(n))*log t_i(n)-E_i(n), with all small-prime factors in s_i and all primes of t_i exceeding W_i. The correction is supported on a small-prime power exceeding W_i; its full shifted effect is O_epsilon(x^(39/40+epsilon)). After also paying proper prime powers, the residual is a composite-filtered signed smooth/rough cofactor sum. A ten-small-prime cell has F=-84 although every pair lies below a, refuting the proposed pair-trigger majorant. Prime filters contribute explicit terms when bounding the negative part; dropping them is an upper bound, not an identity. No scale-x signed improvement or twin margin follows. | [global-factor-signs.md](global-factor-signs.md) |
| C | `Q-global-smooth-majorant` Can a higher-order majorant control the complete global coefficient pair at scale x while retaining every factor configuration and the prime filters? | PARTIAL | Derived using the corrected Henriot upper theorem: a C3 probability average of the same admissible initial cutoffs gives a full residual with sum \|Ghat_L(n) Ghat_R(n-2)\|=O(x). The three-smallest-prime majorant has bounded harmonic mass and meets the source growth class uniformly, despite not being multiplicative. All prime-power exceptions are paid. This replaces the O(x log x) absolute budget for the earlier logarithmic profile by O(x) for a different admissible profile representing the same signed residual to arbitrary logarithmic precision. The implied constant is not compared with C2 and no improved signed lower bound or twin margin is supplied. | [global-smooth-majorant.md](global-smooth-majorant.md) |
| C | `Q-grouped-divisor-moment` Does the full gcd-normalized moment proposed by the literature audit hold, and what exact portion of the twin-prime remainder does it control? | ANSWERED | The proposed moment is derived from classical completion with all coefficient sectors and uniform twists included. Full rectangles are controlled when delta<19/25 and delta+3nu<161/100, in addition to the preceding region. A concrete extra cut d<=floor(x^(151/200)), de^3<=floor(x^(321/200)) controls the entire d~e~x^(2/5) benchmark and leaves an explicit smaller-domain endpoint remainder. The uniform product threshold stays below 19/25. At delta=8/25,nu=9/20, the next deficit is confined to small-common-divisor nonzero kernels; their required saving and the global twin margin remain OPEN. Finite validation does not prove asymptotic rates. | [grouped-divisor-moment.md](grouped-divisor-moment.md) |
| C | `Q-handoff-review-0906` Does the handed-back arithmetic campaign survive an independent check of its main regional estimate and the conclusions used to choose the next research direction? | ANSWERED | The bounded handoff audit is completed in reports 20 and 21: the checked local reduction and regional mechanisms survive, named source statements were verified, and the consumer, corner support, rate, shrinking-margin and identity-piece overclaims were corrected. Joint Cauchy is now priced and adds no region. The multiplicative band transfer has a separate PARTIAL owner with a weaker continuous-scale payoff. Imported deep theorems remain imports; this is not corpus-wide certification or a twin margin. | [handoff-review-0906.md](handoff-review-0906.md) |
| C | `Q-heath-brown-edges` Does the a=1 edge, and hence the corner S_0, come from the particular two-cutoff Vaughan identity in prime-detection-spec.md and shifted-prime-decomposition.md, or does an equivalent edge reappear under Heath-Brown's identity and the other standard decompositions of Lambda? | ANSWERED | The exact identities and exponent simplex leave a=1 in separately bounded formal pieces, including Heath-Brown's balanced j=K configuration. This does not prove an intrinsic edge after identity-piece cancellation. The bounded-cofactor object has affine dilations, not literally F(n)F(n-2). Linnik's fixed truncation has a large term-wise absolute tail by an elementary counting proof; its signed tail is not thereby bounded below. Heath-Brown K=3 narrows the classical split band, with coefficient and Type I normalization obligations retained. No full alternative reduction, new region or twin margin follows. | [heath-brown-edges.md](heath-brown-edges.md) |
| C | `Q-joint-correction-source-audit` Does completing the supported prime-partner correction yield cancellation beyond the existing Vaughan reduction, and which literature inputs actually justify that completion? | ANSWERED | CHECKED prior-art matches for subset convolution, complementary sieve sums and signed smooth-number distribution. DERIVED reconstruction identifies the unrestricted factor weight with an existing short divisor approximant, up to the paid prime-power error. Its supports are x^(12/25) and x^(1/10). Reassembling the entire joint correction returns the already-open Vaughan remainder and supplies no new signed bound. A formal factor-vector control distinguishes the unrestricted logarithmic weight from the selected prime-cofactor branch. The matched general sieve theorems require inputs not supplied here. Literature novelty is unestablished; twin infinitude remains OPEN. | [joint-correction-source-audit.md](joint-correction-source-audit.md) |
| C | `Q-joint-factor-estimate` Can an additional estimate for actual factor configurations control the full signed balance of the C3 residual? | ANSWERED | DERIVED: for the single-large-prime delta-rough family F, the residual splits exactly as R_F = C2*x*H_delta - Z_F^p + o(x), where the Type I part C2*x*H_delta is evaluated by ordinary prime BV on each cofactor interval and the twisted Mobius constant 2C2 (corrected 2026-09-08 after V2: Wu Lemma 2.3 is squarefree-only and did not cover the non-squarefree b_R moduli; prime BV covers all moduli), and Z_F^p is the signed prime-partner sum. The complement carries the opposite Type I part -C2*x*H_delta, so grouping by factor configuration transfers Type I mass and leaves the twisted prime correlation B_L unchanged. With the matched upper sieve the family bound is C2*x(1+H_delta-(40/9)H^+), certified below -2/5 C2*x: INSUFFICIENT BOUND. Even a sieve constant 2 in place of 40/9 needs H^abs<1 and leaves the complement unpaid. Independently reviewed 2026-09-09 with the uniform delta-range and complement corrections below. Twin infinitude and every sufficient margin remain OPEN. | [joint-factor-estimate.md](joint-factor-estimate.md) |
| C | `Q-kernel-sign-control` At delta=8/25, nu=9/20, is the moment Mfrak and its small-common-divisor kernel X_small measurably smaller with the actual coefficient b_u=A_right(gu) than with \|b_u\| or with \|b_u\| times an independent seeded random sign, and does the actual/random ratio decrease with x over the feasible dyadic range? | ANSWERED | MEASURED, negative. Over seven dyadic scales j=18..30 and four boxes, the pre-registered slope of log2(actual/random) for X_small has mean + sd >= 0 in all four families, so the run gives no heuristic support for extra Mobius-sign cancellation in the small-j kernel. The actual coefficient's \|X_small\| ranks like one more random draw. The measurement is weak where it matters: the finite moment is 97.66-102.58 percent equal-frequency class, X_small carries 0.02-2.88 percent, J0=floor(x^(1/20)) is 1 at j=18 and 2 at j=20..30, and Z=2 collapses the prime-power sector of (13) to r=2. Equation (21) and the global twin margin remain OPEN and untouched. | [kernel-sign-control.md](kernel-sign-control.md) |
| C | `Q-left-divisor-signs` Can the Möbius structure of the left coefficient A_left(gm) replace the first Cauchy inequality, so that its sqrt(M) loss is not paid, and what does that buy at the target box (delta,nu)=(8/25,9/20) and at the corner a=b=1? | PARTIAL | Partly, and not where it is needed. Two lemmas are derived: a Type I bound with no zero-frequency budget, usable at the target box whenever the arbitrary block is shorter than x^(1/4), and a Type II bound that is uniform in the Perron twist heights. Applied to the actual coefficient they confine the target-box deficit to sectors with left prime power r>=x^(43/200) and right prime power q>x^(3/100), and lower the worst block exponent there from 103/100 to 41/40. The corner a=b=1 is untouched: grouped, Type I, Type II, Bettin-Chandee/Wright and even a hypothetical per-block square-root bound all exceed 1 there. No region is added, E_dagger and the consumer (20) are unchanged, and the global twin margin remains OPEN. | [left-divisor-signs.md](left-divisor-signs.md) |
| C | `Q-mobius-bv-derivation` Is there a published theorem statement of Bombieri-Vinogradov for the Mobius function at level T^(1/2)/log^B T with a maximum over coprime classes, and if not, does that estimate follow from published theorems by a derivation whose every hypothesis is checked? | ANSWERED | No published theorem statement was located in five channels searched in the owning convention named in research/SEARCH-CONVENTIONS.md; the closest is Granville-Shao's published assertion that the result is known, which carries no proof locator for the Mobius case. The estimate is derived here from four numbered results of Koukoulopoulos, GSM 203 (Corollary 13.4, Theorem 26.2, Theorem 26.6, equation (26.3)) plus Vaughan's identity for mu, with B(A)=A+6 and an ineffective constant. This is a derivation from published theorems, not a refereed theorem, and it is read from the author's preliminary version of that book. | [mobius-bv-derivation.md](mobius-bv-derivation.md) |
| C | `Q-moving-cutoff-parity` Does a proof-level reading of the shifted-Mobius sieve give a valid, explicit error-tolerant arithmetic target, and does its divisor switching preserve the moving boundary? | ANSWERED | CHECKED prior art: Murty--Vatwani already supplies the conditional squarefree/parity mechanism and fixed-residue reduction. Its printed p. 654 swap omits n+h>ey; an exact finite counterexample verifies failure of that equality. DERIVED dyadic repair keeps the boundary and gives S=C2*x-2*C2*M+D_y+O_A(x/log^A x). A one-sided D_y>=-4*x/25+o(x) on unbounded dyadic scales is sufficient, using the certified margin C2*(1-A2)>33/200. That discrepancy estimate remains OPEN. Vatwani's recovered author preprint clarifies the one-odd-exponent cases and unfilled near-level-one hypotheses. No new signed bound is obtained; literature novelty is unestablished. | [moving-cutoff-parity.md](moving-cutoff-parity.md) |
| C | `Q-next-correlation-source-map` Is there a primary-source statement with stronger scale or coefficient quantifiers than the ones the prime-band transfer actually consumed? | ANSWERED | Scoped negative for the inspected statements: function-class and rate mismatches remain. The coordinating review withdraws the all-scales/dyadic-omitting requirement as a necessary gate, since bounded-interval stability yields a weak dyadic scale average from the existing input. No sufficient rate or full-coefficient theorem is matched. Proper-prime-power terms are already negligible on the fixed corner; other prime-r cofactor branches remain open. | [next-correlation-source-map.md](next-correlation-source-map.md) |
| C | `Q-next-transfer-review` Does prime-band-transfer.md (1)-(6) follow at exactly its stated scope, and does any step fail against an adversarial reading of its hypotheses? | ANSWERED | The derivation (1)-(6) survives at its stated continuous-average scope. The coordinating round review corrects check l: interval stability additionally gives a dyadic scale average, with a further exponent loss. There is no every-dyadic estimate, o(N), full-corner control or twin margin. Proper-prime-power branches have a separate negligible fixed-corner bound. | [next-transfer-review.md](next-transfer-review.md) |
| C | `Q-paired-factor-budget` Does averaging the proposed two-small-prime loss and three-small-prime gain using existing distribution theorems make their net contribution sufficient for the current twin consumer? | ANSWERED | DERIVED from the matched classical inputs, with finite rational enclosures VERIFIED: the explicit positive family has liminf P3/(C2*x)>1, but liminf (N2-P3)/(C2*x)>11/10. Keeping only these families and the main term therefore fails at the current cutoffs. Pan--Ding supplies aggregate level x^(9/20), stronger than the earlier per-cofactor application; the complete signed margin remains OPEN. The aggregation machinery is prior art and literature novelty of this application is unestablished. | [paired-factor-budget.md](paired-factor-budget.md) |
| C | `Q-polylog-fold-transfer` Can the fixed-fold calculation be made uniform at growing depth, and transferred to the actual bilinear remainder with an adequate error? | ANSWERED | The local bilinear model is O_H(x/log^H x) uniformly for polylogarithmic squarefree moduli. Its absolute reconstruction error is at least (1/2+o(1))*x. The needed signed reconstruction bound remains OPEN, so this model does not establish the twin-prime lower bound. | [polylog-fold-transfer.md](polylog-fold-transfer.md) |
| C | `Q-prime-band-completion` Can the remaining squarefree correlation be localized to simpler prime and harmonic bands, and does completion then permit a direct general bilinear Kloosterman estimate? | ANSWERED | The pilot reduces, with power-saving endpoint errors, to p in (x^0.235,x^0.24], q in (x^0.045,x^0.05] and positive h in (x^0.029,T], with T=O(x^0.0342). Both primes exceed 2h eventually. Completion is exact but produces coupled h-dependent coefficients on every dual residue modulo q. Its full-frequency Kloosterman matrix has norm exactly q, so a uniform power saving by an arbitrary-coefficient operator bound is impossible at that scope. This completion alone leaves the 61/20000 budget deficit; prime-dispersion.md controls the pilot using a different second moment. No twin lower bound is established. | [prime-band-completion.md](prime-band-completion.md) |
| C | `Q-prime-band-transfer` Can the nonmultiplicative prime-band weight be represented by bounded multiplicative functions, and what does an available quantitative correlation theorem actually give after all scale and normalization costs? | PARTIAL | A smooth Fourier superposition represents mu(n)L_B(n)/log X exactly on n<=2X+2. The quantitative non-pretentious input and a mesh give a continuous scale-average saving for the exact s=s'=1 windows. The round review additionally derives a dyadic scale-average saving by bounded-interval stability, with exponent c_*/2. Neither estimate gives an every-dyadic bound, o(N), full-corner control or a twin margin. The extension in cofactor-progression-transfer.md now estimates a growing polylogarithmic cofactor family; the full remainder remains open. Proper-prime-power branches have the separate bound in corner-correlation §1.1. | [prime-band-transfer.md](prime-band-transfer.md) |
| C | `Q-prime-detection-inputs` Can we give a locally correct positive comparison sequence, justify the ordinary arithmetic inputs, and prove exactly what one additional estimate would buy? | ANSWERED | Yes: the comparison sequence and Type I estimates are derived, and a classical Vaughan decomposition gives S(x)=C2*x+B(x)+O_H(x/log^H x) for every fixed H. A fixed one-sided saving over B>=-C2*x+o(x) implies twins on unbounded scales. This is a fully specified classical reduction, not a new cancellation estimate or proof mechanism. | [prime-detection-spec.md](prime-detection-spec.md) |
| C | `Q-prime-dispersion` Can a second moment retaining two right primes control the remaining localized squarefree pilot after its actual conductor and coefficient costs are included? | ANSWERED | Yes at this rectangle: aggregation in m=dp before Cauchy gives a logarithmically bounded coefficient on a long interval. The only zero-phase pairs are identical (q,h). Distinct primes give modulus e*q1*q2 with gcd loss at most O(A*Z); completion and Weil bound all off-diagonal terms. The diagonal has exponent 1989/2000 and the largest off-diagonal exponent is 1173/1250 before an arbitrarily small loss. The remaining high-frequency polynomial is O(x^(199/200)); consuming the previous reductions gives R_IJ=O_H(x/log^H x) at D=x^0.277, E=x^0.467. This is a full rectangle at product scale x^0.744, not a uniform product cutoff or a twin lower bound. | [prime-dispersion.md](prime-dispersion.md) |
| C | `Q-prime-power-dispersion` Does the repeated-prime structure control the BB contribution beyond its two-norm bound, and can a prime-power moment include every harmonic uniformly? | ANSWERED | The decomposition leaves an exceptional coefficient with norm at most sqrt(D) times logarithms; its odd prime-power core has a derived all-harmonic dispersion bound. The same bound for first powers removes the former left-prime cutoff and unpaired diagonal constraint. Two strict inequalities control a region including d~x^0.247, e~x^0.612 at product scale x^0.859. Their product-exponent supremum is 5757/6700, not a uniform product cutoff or a twin lower bound. Exact finite checks run separately from this classical-input derivation. | [prime-power-dispersion.md](prime-power-dispersion.md) |
| C | `Q-reachability-coverage` Which part of the original divisor domain can no improvement to the grouped moment's nonzero kernel reach, in either orientation, and what would a uniform saving on that kernel actually buy? | ANSWERED | For a prescribed fixed exponent margin eta0, the zero budgets leave S_0={p<2eta0,q<2eta0} below that required margin regardless of the nonzero-kernel saving. Uniform gamma=2 covers its complement at that prescribed margin. Smaller positive margins can reach fixed interior points of S_0; only p=q=0 remains at zero budget one for every margin. The proposed eta0~loglog x/log x substitution is not justified by estimates carrying x^epsilon losses; its box count is geometry only. The sufficient twin margin remains OPEN. Independent review F3 and F5 correct the quantifiers and the prime-power tail proof; round-review-0906 corrects the diagonal scope, fixed-margin bulk claim and six-cut separation. | [reachability-coverage.md](reachability-coverage.md) |
| C | `Q-research-execution` How should agents use the integrated returns, avoid repeated work and select the next bounded research obligation? | ANSWERED | The second dispatch from 1285d47 closed at 46fa948 and was independently reviewed on 2026-09-09. A/A2/B/C/D/E and V/W returns are present and integrated at their owning scopes. A2's corrected Type I estimate is accepted; D's fourth residual cut is retained and its remaining moment saving corrected to 7/200. C's low nonzero modes and E's aggregate scope are corrected. No new assignment is started by this integration; next obligations are candidates, not running work. Twin-prime infinitude and every sufficient signed margin remain OPEN. | [RESEARCH-EXECUTION.md](RESEARCH-EXECUTION.md) |
| C | `Q-research-handoff` What must an incoming research agent understand, verify and return before its work can advance the current twin-prime argument? | ANSWERED | Current handoff after the 2026-09-09 independent review of the dispatch ending at 46fa948. The full residual has four simultaneous complement conditions after D's regional estimate. A's centered truncation and A2's repaired low Type I estimate give the alternative S=C2*x+B+O_A(x/log^A x). B and all sufficient signed margins remain OPEN. The C3 absolute bound, family identities and scoped C/E failures retain their owning hypotheses. Execution is owned by RESEARCH-EXECUTION.md. | [RESEARCH-HANDOFF.md](RESEARCH-HANDOFF.md) |
| C | `Q-research-round-validation` Which submitted results from lanes A, A2, B, C, D, E, V and W survive direct review, and what can be integrated or used to choose the next attempt? | ANSWERED | Reviewed incoming commits 07ab47f through 46fa948 on 2026-09-09. A's truncation and A2's repaired low Type I estimate are accepted with bookkeeping corrections. B's ordinary-BV family identity survives; its uniform Dickman constant and complement condition are repaired. C's norm obstruction survives on all smooth inputs, but low nonzero Fourier modes are also 1-bounded. D's block estimate and fourth residual cut survive; its next moment saving is 7/200, not 17/200. E's rough-product distribution and aggregate constant 4 are accepted at the stated Wu uniformity reading; rational certificates close the two displayed tests for every fixed u>4. W remains OCR-only at the original 1974 theorem page. All sufficient twin-prime margins remain OPEN. | [research-round-validation.md](research-round-validation.md) |
| C | `Q-residual-coverage` What portion of the full residual is controlled with uniform margins, and can the exceptional first branch improve that coverage rather than just a regional corner? | ANSWERED | The first-branch and prime-free moments remove the exceptional norm condition. Full rectangles are controlled when delta+nu<19/25 or 5delta+2nu<123/50. Uniform twists justify exact coupled cuts: every fixed de<=x^theta with theta<19/25, and d^5*e^2<=x^lambda with lambda<123/50, as well as their union, have arbitrary fixed logarithmic savings. A concrete remaining endpoint sum has de>floor(x^(3/4)) and d^5*e^2>floor(x^(49/20)). Its twin margin is OPEN. The right zero-frequency budget, after an extra Cauchy inequality, limits the uniform product range; the left cross moment limits the other edge. Finite checks validate identities and masks, not asymptotic rates. | [residual-coverage.md](residual-coverage.md) |
| C | `Q-review-request-0906` Which claims of the arithmetic campaign should an independent reviewer check, in what order, against which records, and what must the review return? | ANSWERED | Completed review specification at the bounded scope recorded in handoff-review-0906.md and reports 20 and 21, with the subsequent round reviewed in round-review-0906.md. The dependency list records questions at dispatch, not current unfinished assignments. Imported proofs retain their review limits and the twin margin remains OPEN. Current assignments are in RESEARCH-EXECUTION.md. | [REVIEW-REQUEST.md](REVIEW-REQUEST.md) |
| C | `Q-round-review-0906` Which conclusions of the completed agent round survive review, and which corrections change the next research specification? | ANSWERED | The fixed-band lift and continuous moving-window estimate survive the checked source interface. Interval stability additionally gives a dyadic scale-average logarithmic saving, so the blanket scale exclusion was too strong. The rate and missing prime-cofactor terms with s>1 or s'>1 still prevent a twin margin. Proper-prime-power branches already have a negligible bound on the fixed corner. The driver computes integer parity, not the CRT gcd partition; its total coefficient identities survive. Diagonal lower-bound, reachability and six-cut bookkeeping overclaims are corrected. No region, exact residual cut or twin lower bound changes. | [round-review-0906.md](round-review-0906.md) |
| C | `Q-sharp-corner-transition` What is the energy of the complete sharp corner coefficient, and can the smoothed estimate be transferred through a negligible L2 transition? | ANSWERED | DERIVED using named analytic inputs: for each fixed 0<eta<1/400 the full sharp squared norms and absolute shifted product are O_eta(x log^2 x). For every sufficiently small fixed eta>0 both sharp squared norms and sharp-minus-smoothed squared norms are Theta_eta(x log^2 x) on the actual dyadic intervals. Thus an O_eta(x log x) sharp squared norm or negligible L2 transition fails in that range. Signed transition correlations and the global complement remain OPEN. No region, exact residual cut or twin margin changes. | [sharp-corner-transition.md](sharp-corner-transition.md) |
| C | `Q-shifted-prime-decomposition` Does decomposing Lambda(dk-2) give a provable saving on any part of the actual shifted-prime sum, and what exact arithmetic remains outside the imported hypotheses? | ANSWERED | Both second Type I terms are O_H(x/log^H x) by classical Mobius BV. The residual is an explicit weighted sum over dk-ev=2, equivalently an average of two-linear-form Mobius correlations with growing coefficients and possibly one-point intervals. Its required one-sided improvement is OPEN. No twin lower bound or novelty is claimed. | [shifted-prime-decomposition.md](shifted-prime-decomposition.md) |
| C | `Q-shifted-prime-mobius-sums` At reachable x, do the shifted-prime Mobius and Liouville sums, the cleanest instance of the parity input the twin reduction lacks, show any size or sign structure that a random-sign model does not, and how loose is the trivial bound on M(x) used for the centered tolerance? | ANSWERED | MEASURED to x=2^38 (10.9e9 primes). All four sums sit at random-sign size: \|U\|/control rms at most 2.8 at any j, slopes 0.28 to 0.65 against the control's 0.43 to 0.47 with per-draw spread 0.19 to 0.30; the pre-registered structure falsifier did not fire. M(x)/x is at most 8.8e-5 in magnitude for j>=29 against the trivial bound 0.374, so the -4x/25 tolerance in moving-cutoff-parity is loose by four orders at these scales; a proof still needs a bound on M, which is the same parity object. The squarefree density of p+2 among primes is 0.747911 at 2^38 against 2*Artin = 0.7479116. pi(2^j) matches OEIS A007053 at every j. Nothing here bears on the asymptotic conjecture. | [shifted-prime-mobius-sums.md](shifted-prime-mobius-sums.md) |
| C | `Q-signed-divisor-grouping` Can grouping different fibers while retaining their Mobius signs control an explicit part of R, and what signed error remains after that grouping? | ANSWERED | For every fixed H>0 the actual remainder restricted to de<=x^(7/10) is O_H(x/log^H x), although each sign's mass there is at least c*x*log(x) eventually. This follows from a written classical-input derivation, with finite algebra and archived-factor checks. The remaining de>x^(7/10) contribution reduces to an explicit weighted CRT endpoint discrepancy whose required one-sided improvement is OPEN. | [signed-divisor-grouping.md](signed-divisor-grouping.md) |
| C | `Q-signed-moment` Is there an argument for the block that does not pay sqrt(M) at the first Cauchy inequality or that extracts cancellation from the R=0 class, and what are its budgets at the corner a=b=1 and at the target box (delta,nu)=(8/25,9/20)? | PARTIAL | The true diagonal has an upper bound x^(1+o(1)) on the transition band, not a uniform nonzero lower bound. Lemma A controls only u1=u2,h1=h2; unequal proportional R=0 pairs remain outside it. Lemma B and the now-priced joint Cauchy arrangement add no region. The former general Holder floor is valid only under additional coefficient assumptions, not for arbitrary sparse coefficients. Conditional off-diagonal budgets and the random-matrix ceiling remain conditional and heuristic. No necessity of using both signs, full-corner estimate or sufficient twin margin is established. | [signed-moment.md](signed-moment.md) |
| C | `Q-singleton-fiber-audit` Can the one-point fibers of the coupled remainder be discarded or controlled in absolute value at scale x, and what do the actual weights and archived intervals show? | ANSWERED | The grouped coefficient is zero whenever either integer is prime. Each sign's ungrouped singleton mass is at least c*x*log(x) eventually for an absolute c>0, by a written derivation from named classical inputs. Finite full-interval and archived-prefix checks validate the partition. The signed singleton and longer-fiber contributions remain OPEN; no twin lower bound or novelty is claimed. | [singleton-fiber-audit.md](singleton-fiber-audit.md) |
| C | `Q-small-divisor-kernel` Does reciprocity separate the j<=x^(1/20) kernel of grouped-divisor-moment (21) at delta=8/25, nu=9/20, and do the Duke-Friedlander-Iwaniec / Bettin-Chandee and Kuznetsov interfaces then supply the required saving? | ANSWERED | The separation is exact and cheap: reciprocity splits index by index, the correction phase has sup norm and total variation O(A/(MN))=O(1/x) at this box, and Mellin separation of the endpoint weight costs x^epsilon with L1 mass min(1,Ax/(MN)), so the whole block reduces to a pure trilinear Kloosterman fraction with unimodular twists. The interfaces then fail by explicit amounts: Bettin-Chandee Theorem 1 gives block exponent 129/125, above the required 1 by 4/125 and above the classical 103/100; DFI (1.1) gives 1267/1200; every box Bettin-Chandee controls is already controlled, verified on 19005 rational boxes; the audit's spectral diagnostic factor is trivial for all common divisors up to x^(19/50). Closing this box inside the same interface needs the (M+N) exponent below 27/140 or the (AMN) exponent below 9/28. Target (21) and the global twin margin remain OPEN; nothing is added to the controlled region. | [small-divisor-kernel.md](small-divisor-kernel.md) |
| C | `Q-smooth-sieve-literature` Which nearby published results should be imported instead of rediscovered, and do their methods give a more focused next question for the complete global remainder? | PARTIAL | Existing sources supply the finite-difference mechanism, one-point concentration and quadratic profile optimization; shifted divisor-sum estimates admit fixed shift two under their own support and smoothness conditions. A derived application of corrected Henriot bounds gives small-prime mass O_sigma(delta^sigma x)+O_epsilon(x^(39/40+epsilon)), uniformly in delta for fixed 0<sigma<1. This permits approximation by bounded-factor configurations at fixed delta, but their joint signed estimate, usable constants and the twin margin remain open. Fixed delta alone cannot absorb a shrinking logarithmic margin. The unrestricted ordered-prime formula in GKM Lemma 10.5 is refuted without the symmetry used in its proof and subsequent application. | [smooth-sieve-literature.md](smooth-sieve-literature.md) |
| C | `Q-sparse-dispersion` Can the opposite dispersion orientation control the left nonsquarefree sector beyond the previous sparse-norm boundary, and what signed second moment remains at the resulting boundary? | ANSWERED | A paired second-moment bound controls the left B/right Q sector with all harmonics, including distinct-prime zero numerators. Combined with the existing left-prime dispersion and sparse bounds for other sectors, it controls d~x^0.275, e~x^0.541 at product scale x^0.816. The product-exponent supremum of the stated sufficient inequalities is 1368/1675. The remaining tight budgets are BB and the left-prime cross moment; neither a uniform product cutoff nor a twin lower bound follows. | [sparse-dispersion.md](sparse-dispersion.md) |
| C | `Q-structural-literature-audit` Which established mathematical structures match the current endpoint remainder, and which concrete next estimate is justified by a broad literature audit? | ANSWERED | Exact gcd/lcm normalization identifies dispersion coefficients, classifies equal frequencies and cancels the common-factor Mobius sign on the squarefree sector. The reviewed spectral, bilinear, trace-function, graph and correlation theorems do not directly close the residual. In the natural level diagnostic the structured spectral improvement disappears for common factors at most x^0.27. The grouped-divisor follow-up derives the proposed full moment using classical completion and controls the benchmark; its next small-common-divisor kernel and the global twin margin remain OPEN. | [structural-literature-audit.md](structural-literature-audit.md) |
| C | `Q-structured-dispersion-estimate` Can the actual coefficient structure of b_u=A_right(gu), preserved through one further factorization, improve the small-common-divisor cross term at (delta,nu)=(8/25,9/20) beyond the arbitrary-coefficient moment, and what does it buy regionally? | PARTIAL | Derived 2026-09-08; read by the handler (research-round-validation section 10) and independently by reader V3, both verifying Lemma H and (D1) within stated scope, with grouped-divisor-moment (7) and the required separate-coefficient upstream block shape rechecked on 2026-09-09; one correction applied (the regional cut is a fourth simultaneous condition of W_dagger, not a substitute for the third). Writing u=eq and applying Cauchy over (m,q) instead of over m keeps every pair of the moment inside a common prime-power factor, so the completed modulus grows by q while the pair count is that of e; one elementary harmonic gcd lemma prices the fixed factor. The block bound (D1) saves x^(min(sigma,alpha)/4) on the cross term and costs x^(sigma/2), x^sigma on the zero and period terms. At the target box the worst sector exponent falls from 41/40 to 407/400 and the box is not controlled. (D1) controls the strip delta<71/100, delta+3nu<327/200 outside the existing region (245 of 36481 grid boxes); section 6 adds the concrete cut d<=floor(x^(141/200)), de^3<=floor(x^(1631/1000)), de>floor(x^(77/100)) as a fourth simultaneous condition of W_dagger through the Perron machinery, changing only the summation domain of E_dagger. The target box (407/400), the corner, the uniform product threshold 19/25, the sign of E_dagger and the global twin margin are unchanged; the margin remains OPEN. | [structured-dispersion-estimate.md](structured-dispersion-estimate.md) |
| C | `Q-supported-coefficient-dickman` Can the whole supported coefficient be priced using existing literature before enumerating its factor cells, and does the resulting separate-sign sieve estimate supply a positive twin margin? | ANSWERED | DERIVED from classical inputs: at delta=1/100 the harmonic limit is H_delta=D(25/12)-1+E_delta with 0<=E_delta<=24/22!, hence -1<H_delta<-2/3. The elementary separate-sign lower-bound constant is less than -80/9 and cannot supply positivity after adding only the main term. This is an INSUFFICIENT BOUND, not a negative upper bound on the regional residual. Existing integration and Dickman machinery is prior art; literature novelty of this application is unestablished. The joint prime-partner/complement estimate and twin infinitude remain OPEN. | [supported-coefficient-dickman.md](supported-coefficient-dickman.md) |
| C | `Q-switching-negative-mass` Can existing switching and rough-number estimates price an actual opposed-sign factor family, and can a bound on the negative part alone close the current twin consumer? | ANSWERED | DERIVED from classical inputs: liminf Nhat/(C2*x) is at least kappa=(10*log(3)-36/5)*I>3/2, where I is the explicit ordered two-factor integral below. A three-prime left input and rough composite right input suffice; prime partners are subtracted using an upper sieve. The witness survives every fixed delta<1/50 and every averaging profile with the same plateaus. Consequently the negative-only consumer is false, and liminf Phat/(C2*x)>1/2. The signed twin margin remains OPEN; literature novelty is unestablished. | [switching-negative-mass.md](switching-negative-mass.md) |
| C | `Q-transition-energy-review` Does the sharp-energy chain in sharp-corner-transition.md survive an adversarial check, and do the upper norm, the small-fixed-eta lower norm and the failed negligible transition each stand at their stated scope? | ANSWERED | All ten assigned rows survive at their stated scope; no counterexample or decisive contradiction was found. The upper norm, the small-fixed-eta lower norm and the refuted negligible L2 transition each stand separately. Two repairs are citation-level only: the integer Barban-Vehov input is Graham 1978 quoted by Chen An, and the note should record why the k=Q constant is absolute. The de la Breteche-Dress-Tenenbaum PDF was refetched and its SHA-256 matches the pinned hash; its (1.5) and Theorem 1.1 supply exactly the imported (3) and (4). eta_0 remains positive and unextracted, and the signed sums, E_out and the twin margin remain OPEN. | [transition-energy-review.md](transition-energy-review.md) |
| C | `Q-transition-energy-review-spec` What independent checks are required before the sharp-energy and non-negligible-transition conclusions can guide the next signed research attempt? | ANSWERED | Bounded review assignment with explicit source, algebra, interval, error and quantifier checks; per-claim verdicts and dependency consequences are required. The assignment is specified, not executed. | [transition-energy-review-spec.md](transition-energy-review-spec.md) |
| C | `Q-transition-joint-budget` Can the mixed and smoothed terms be handled jointly with the transition pair, and what complete inequality would make such an estimate useful for the twin consumer? | PARTIAL | The exact split, cutoff-average identities and separate upper budgets survive. Averaging cutoff norms after triangle and Cauchy is saturated for sufficiently small fixed eta, but signed cutoff arguments and joint cancellation are not closed. R_00 need not be estimated separately under every grouping. The short-window constraint is corrected with a bounded majorant and a safely reduced lower constant. No consumer input or signed improvement is supplied; E_out and the sufficient twin margin remain OPEN. | [transition-joint-budget.md](transition-joint-budget.md) |
| C | `Q-transition-joint-budget-spec` Can the mixed and smoothed terms be handled jointly with the transition pair, and what complete inequality would make such an estimate useful for the twin consumer? | ANSWERED | Bounded assignment to audit the exact four-term decomposition, price a concrete joint treatment, and return a sufficient one-sided or common-scale inequality with all open terms explicit. The decomposition and existing norm budgets are inputs, not new findings. | [transition-joint-budget-spec.md](transition-joint-budget-spec.md) |
| C | `Q-transition-research-execution` How should the core research handler execute and integrate the three bounded transition assignments while retaining the central signed estimate? | ANSWERED | Prepared execution contract with a fixed mathematical baseline, three independently assignable specs, handler-owned signed research, dependency checks, shared-file ownership, reporting requirements and stopping rules. Execution is complete; the corrected results are in transition-round-review.md and transition-round-audit.md. The specification itself supplies no arithmetic estimate. | [TRANSITION-RESEARCH-EXECUTION.md](TRANSITION-RESEARCH-EXECUTION.md) |
| C | `Q-transition-round-audit` Which conclusions of the completed transition round survive direct review, which require correction, and what research decisions remain justified? | ANSWERED | The sharp upper norms and sufficiently-small-fixed-eta lower norms survive. The integration contained substantive errors: an omitted lower cutoff, an incorrect Mellin formula for the transition, a conflation of singleton divisor fibers with long cofactor fibers, an unpriced source representation and overbroad closures of joint or cutoff arguments. Owning notes and current records are corrected. No signed improvement or sufficient twin margin is established; the corrected cofactor and joint-correlation interfaces remain open. | [transition-round-audit.md](transition-round-audit.md) |
| C | `Q-transition-round-review` What survives the executed transition round after direct review, and what combined estimate is still missing? | ANSWERED | The energy chain survives at its original scope; the integration's missing cutoff, Mellin representation, fiber identification, normalization and general closure claims are corrected. The exact cofactor and joint-cutoff formulations remain useful. No signed estimate, controlled region, exact cut or sufficient twin margin changed. Only the stated norm-only procedure and the arbitrary-factor fixed-shift relaxation are refuted at their specified scopes. | [transition-round-review.md](transition-round-review.md) |
| C | `Q-transition-signed-estimate` Can the signed transition kernel (E1) be estimated beyond its absolute norm budget, and if not, what exact input does the consumer need? | PARTIAL | No signed improvement. Derived: the proper-prime-power part of R_11 is O(x^(39/40+epsilon)); the prime part is an exact beta-weighted sum over pairs of linear forms of two-point Mobius correlations with coefficients up to x^(6/25+2eta) and x^(1/20+2eta); the Cauchy budget is at most 2B*eta*x*log^2(x)(1+o(1)) and the fiber triangle budget 4*eta^4*x*log^4(x)(1+o(1)), so every existing inequality loses one of the two signs. The cutoff-difference identity converts T at pn into a sharp-window coefficient times log(p)/L plus two boundary windows; the entropy-decrement route then needs bounded coefficients, a short-interval one-point input for T and a log-weighted consumer, none available. The required one-sided input is stated exactly in section 5. The twin margin remains OPEN. | [transition-signed-estimate.md](transition-signed-estimate.md) |
| C | `Q-transition-source-match` Do the inspected divisor-correlation, shifted-convolution and averaged-Chowla statements directly supply a usable estimate for the exact transition kernel? | ANSWERED | No direct supplier was established among the inspected statements. The cofactor exchange and Theta identity are exact, but their scalar coefficient mass is not a full bounded-class representation for T. The transition Mellin kernel requires a sharp subtraction with a 1/s tail. Fixed-divisor singleton fibers differ from potentially long cofactor fibers. The fixed-shift arbitrary-factor relaxation is refuted; broader signed and cutoff methods remain open. | [transition-source-match.md](transition-source-match.md) |
| C | `Q-transition-source-match-spec` What bounded source investigation could supply a usable signed estimate for the transition kernel, and how must its hypotheses and losses be priced? | ANSWERED | Specification for up to three detailed source-interface assessments, including coefficient representation, scale quantifiers, normalization, separation errors and exact downstream payoff. No new theorem match or literature-absence result is claimed. | [transition-source-match-spec.md](transition-source-match-spec.md) |
| C | `Q-twin-reduction` What has the arithmetic campaign of 2026-09-05 and 2026-09-06 actually established about the twin sum, at what calibration, what exactly remains, and what would suffice? | ANSWERED | Consolidates the checked regional reduction S=C2*x+E_dagger+O_H(x/log^H x), its sufficient unbounded-scale margins, coefficient definitions and source dependencies. Later complete smooth and centered formulations are owned by RESEARCH-HANDOFF.md and their linked derivations. No new arithmetic estimate is supplied. Imported theorem proofs retain their stated review limits; every sufficient twin margin remains OPEN. | [TWIN-REDUCTION.md](TWIN-REDUCTION.md) |
| 9 | `Q-applied-0828-varE` Were the Var/E red team's corrections applied to the four HELD notes? | ANSWERED | Every WEAKENED and REFUTED verdict in redteam-0828-varE.md is applied to its target note in the present tense; four ledger verdicts are rewritten, the theta=1 row is raised to PROVEN, and seven live-doc sentences plus one producer reading stay open and are drafted here. | [applied-0828-varE.md](history/staging/applied-0828-varE.md) |
| 9 | `Q-lit-scourfield-2008` Does Scourfield, Smooth divisors of polynomials (LMS Lect. Note Ser. 352, CUP 2008, 286-311), supply the divisor-distribution estimate that varE-theta2-proof.md section 6 leaves open? | ANSWERED | DOES NOT DELIVER, at SECOND-HAND rung, and the chapter is still UNREAD at the page: ten channels were attempted, nine answered, and every one that answered is closed, degraded or paywalled, but the author's own restatement of the 2008 theorem, read at the page image of Scourfield, Funct. Approx. 55.1 (2016) 84 eq. (1.1), counts divisors m <= x of f(n) for n <= x with weight 1, for f a product of pairwise coprime irreducible factors each of degree at least 2, and the open step needs divisors n > 2L above the window, carrying a branch-dependent weight of total mass 4^omega, for the product of three LINEAR factors C(C-2)(C+2). Two gaps each independently fatal, plus a third that is AMBIGUOUS between two author-sourced statements and does not carry the verdict. One correction to lit-smooth-divisors.md is earned: the precision register of the owning convention is not uniformly (log y)^{o(1)} or order-of-magnitude, since (1.1) is an asymptotic with relative error O(1/log x), which is the right register and one epsilon short of the o(1/ln y) the open step needs. Step 1 of Var/E does NOT become conditional on a citation, and no absence may be written, since the chapter's interior lemmas were not read. | [lit-scourfield-2008.md](history/staging/lit-scourfield-2008.md) |
| 9 | `Q-paper-iii-restructure` Is Paper III restructured around the proven model theorem? | ANSWERED | Yes. paper/variance-note.md now carries four new sections in place of its fit narrative: sec.8 the proven spectral form (Var/E = delta X, delta ln^2 W -> 16 C_2 e^{-2gamma}/3 = 1.109905, the Montgomery-Soundararajan main term exactly L prime by prime, so all of Var/E is discrepancy), sec.9 the decoupled model with Theorems 7 and 8 and Lemmas 9-11 written out with proofs and the closed form lambda_2(2) = 1 - e^{-2gamma}(9/2 - 4 ln 2) = 0.45546 plus the theta = 1 identity with Gorodetsky, sec.10 Conjecture 1 (delta(X - X_dec) -> 0) with eight exact ratios, two of three lag groups closed and the third named as a divisor-distribution statement not yet searched, and sec.11 the 0.611 refutation as a short calibration paragraph; sections 1-5 are untouched, the abstract and section 6's open question are rewritten to match, and the "u = 2 exactly" defect in section 7 is corrected. | [paper-iii-restructure.md](history/staging/paper-iii-restructure.md) |
| 9 | `Q-recon-0830-smooth-aps` Does any theorem on y-friable integers in arithmetic progressions (Granville, Fouvry-Tenenbaum, Soundararajan, Harper, Drappeau, Drappeau-Granville-Shao) supply the uniform o(1) equidistribution that attack-0830-varE-identification.md section 4 leaves open, for moduli up to y^(4/5) with the lam1 weight and the squarefree restriction? | PARTIAL | NONE APPLIES AS STATED, and the step stays open; lim Var/E = 0.45546 stays HEURISTIC. Read at the page (eleven sources, arXiv text layers and the Acta Math. page image): every pointwise asymptotic is O(log q / log y)-precise (Granville 1993 Thm 1) or hypothesises log x / log q -> infinity, and every beyond-square-root level (Fouvry-Tenenbaum 1996, Drappeau 2015, Drappeau-Granville-Shao 2017, Pascadi 2023/2025) hypothesises y <= x^delta, i.e. u -> infinity, against our u in (1.2, 2]. NEAREST: Harper arXiv:1208.5992 (2012, a preprint with no journal version found) Theorem 2, the Barban-Davenport-Halberstam form, whose range (log^K x <= y <= x, Q <= Psi/log^A x, bounded u in the ineffective form) covers d up to L^(1/2)/log and whose weight (1 on all friable n, no squarefree restriction, no max over x' <= x) is unmet. The record's quantifier is also refined: the cell needs the lam0-weighted AVERAGE over d, not uniformity. PROVEN given the weighted form (H_w) of that theorem, derivation mine and unreviewed, with its two identities checked numerically in the producer: every two-branch cell of Xmix, both mirror cases, all bands, balanced blocks included, is o(ln^2 y), so the Bettin-Chandee kernel separation is not on this route; the reduction of (H_w) to Harper's theorem is OUTLINED and not written, and the three-branch type (measured -0.0002 at x = 19, trivial bound O(ln^3 y)) is untouched. Not TPC-strength. | [recon-0830-smooth-aps.md](history/staging/recon-0830-smooth-aps.md) |
| 9 | `Q-redteam-0828-varE` Does the 2026-08-28 chain from the exact comb variance to lim Var/E = Pr[GD(2) > 2] = 0.45546 survive an adversarial re-derivation, and does the refutation of the 0.611 reading hold? | ANSWERED | The constant survives at HEURISTIC and the 0.611 refutation is CONFIRMED and strengthened (the frozen out-of-sample half of the protocol also fails on the control); the correction is that TWO steps are open, not one, and that the theta=1 branch is an exact identity with a read theorem rather than a second-hand numerical match. | [redteam-0828-varE.md](history/staging/redteam-0828-varE.md) |
| 9 | `Q-redteam-0830-imports` Do the six lighter notes of 2026-08-30 (varE-identification, smooth-aps, rec-killrun, skeleton-door, at43-bigint, coherence) survive an adversarial pass on independent code and at the source pages, and which of their load-bearing claims are wrong? | ANSWERED | No note is refuted whole and no exponent moves. Every decisive measurement reproduces on code sharing nothing with the producers: the varE mixed remainder and its 0.844 / 0.826 share below 2L and 94.4 / 98.7 percent unbalanced share at x = 13, 17; the Buchstab deviations and all three crossing levels log10 z* = 33.53, 68.80, 33.62; the skeleton door's 9.2 / -0.9 percent, G30_agg 0.1113 / 0.1011 and the 0.0102 cap at @13, @17, by a path that also verifies cap-36 Theorem A; the @43 parity exactness on all 26,157,448 scour classes with 0 above 2^54 and a constructed @47 counterexample; and the five recon-0828 verdict counts summing to 75, which REFUTES rec-killrun's brief-error clause and confirms the orchestrator's rider. Seven claims WEAKEN. The load-bearing one is smooth-aps's "the weight is unmet in print": Harper's J. London Math. Soc. 112 (2025) e70293 proves a Barban-Davenport-Halberstam asymptotic for an ARBITRARY sequence on exactly that dyadic all-classes object, and his own footnote says the missing max over x' can be incorporated, so the NEAREST citation changes even though the step still does not close (the 2025 range is sqrt(2x) < Q <= x and its Theorem 2 route bars sieved sets by name). Also: Henriot Corollary 2 applies, but to the ERRATUM's statement and under two hypotheses the note leaves unstated (eps < alpha/600, not "every eps"; F at prime powers); varE section 4's display (*) carries an unfilled placeholder and is vacuous by a factor L/d; the skeleton door's "would tighten" is wrong in sign at @17, where the closable block is negative and removing it RAISES G30_agg to 0.1020; Halasz-Montgomery is not applicable for the reason given (it is an abstract inner-product inequality); FGKT's heuristic quote is on p. 4, not p. 3; and the "~13x had no source" is a corpus miss, the retired G2-walk figure at CHANGELOG.md:5716. Not TPC-strength; nothing here opens a route. | [redteam-0830-imports.md](history/staging/redteam-0830-imports.md) |
| 9 | `Q-redteam-0830-slack` Do attack-0830-head-remainder.md, attack-0830-tail-derivation.md and verify-0830-record-defects.md survive an adversarial re-derivation on independent code, and do the five riders the verification put on live notes stand as written? | ANSWERED | Arithmetically they survive: every figure of the three notes that this pass could recompute reproduced to the printed digit on code written from the definitions, 0 assertion failures over 58 assertion call sites (most inside per-level loops), including every figure of the verification's three claims and the half-decade Delta_HL it quoted rather than recomputed. Four sentences do not survive. (1) verify-0830-record-defects.md:316, a replacement queued for head-residual-hl3.md sec.0, says the pooled value sits "0.038 to 0.052 below the sub-window mean at all three decades"; measured, the two lower decades run to 0.076 and 0.066, and the same note's own falsifier row says 0.038 to 0.076, so the wrong half is the one queued to land. (2) verify-0830-record-defects.md:379's un-measured "+0.005" residual inside the eighths is +0.0004 measured at sixteenths, so the de-pooled top-decade value is converged and the caution can be dropped. (3) the ruling that the class null is "the matched figure" for the tail is matched on residue class only: p'^2 is coprime to every q <= p', and the ensemble's rough-class offset is E_rc - R = 5.6714 -> 7.5357 over x = 7..29 against the class null's 5.6000 -> 6.0336, giving t/(R_shell + 7.5357) = 1.0123 against t/classNull = 1.0157. (4) attack-0830-head-remainder.md sec.3's top row is not gap-scale matched: E[g] 244.0 against 235.9, y_match capped at 19997, and on the note's own six ensemble points Delta_ens ~ E[g]^-0.312, so meas/ens reads 0.9640 not 0.9539 and the headline "0.954 to 0.995" reads 0.964 to 0.995. Three levels the notes recorded as out of reach are run here: the X2 group at x = 23, the tile identities and conditionals at x = 29, and the ensemble ladder at y = 29 (pipe/ens 0.9535, 40 s, against the head note's "about fifteen minutes"). No route opens or closes and nothing here touches Z2. | [redteam-0830-slack.md](history/staging/redteam-0830-slack.md) |
| 9 | `Q-var41` What does the stable law predict for Var(41), and what can the tenth Var/E point pin? | OPEN | Pre-registration only, sealed and committed alone before any Var(41) engine exists: it freezes the prediction, a band taken from the law's own residuals at z <= 37, the derived z(41) prediction, and the honest statement that one more point cannot separate a limit from a drift. | [var41-prereg.md](history/staging/var41-prereg.md) |
| 9 | `Q-varE-identification-0830` Can either open step behind lim Var/E = 0.45546 (the identification delta*(X - X_dec) -> 0, or the theta = 2 mean-coefficient replacement) be proven, and if not, which single inequality does not close? | PARTIAL | Neither closes, and the two named steps are one statement (Conjecture 1 of variance-note sec.10; the model half is PROVEN in varE-limit-theorem.md). The remainder is re-split exactly at five levels: the corpus's X2 column doubles the positive half of one shift pattern (X2c = 2.66 against the group sum 0.09 at x = 19, PROVEN by rebuild), so its Xmix is overstated 2.3x; the true mixed remainder is MEASURED at -0.49 ln y and 82 % of it sits BELOW 2L, in the two-branch type, in the unbalanced range min(d,e) <= L^(2/5) (99.7 % of that cell at x = 19), outside the range of every bilinear Kloosterman-fraction bound; the divisor-distribution estimate the record names (n > 2L only) is therefore not the whole open step. Henriot's Corollary 2 (read at the page, erratum read) applies as stated and cuts the moduli to n <= L ln^(2+o(1)) y, PROVEN given that theorem; the one inequality left is the uniform o(1) equidistribution of y-friable squarefree integers in progressions to moduli up to y^(4/5), NOT SEARCHED at the page. The limit 0.45546 stays HEURISTIC. Not TPC-strength. | [attack-0830-varE-identification.md](history/staging/attack-0830-varE-identification.md) |
| 9 | `Q-varE-limit` Does lim Var/E on the diagonal window exist, and what is it? | PARTIAL | The theta=2 mean-coefficient step is neither proven nor refuted: the replacement error is exactly a sum over shifts of W(h) - V(h), it splits into a c=0 group (needs no decoupling) and CRT-mixed lags (open); measured ratios true/model 1.0098, 1.0039, 1.0014, 1.0013 at x = 13..23 with delta(X - X_dec) ln y falling rather than settling, so the error is O(1/ln y) or better MEASURED on four levels that exclude growth and nothing finer, and the limit 0.45546 stays HEURISTIC with varE-spectral's second step, its own limit theorem, still open. | [lit-dickman-variance.md](history/staging/lit-dickman-variance.md), [lit-smooth-divisors.md](history/staging/lit-smooth-divisors.md), [varE-asymptotic.md](history/staging/varE-asymptotic.md), [varE-exact-ladder-01.md](history/staging/varE-exact-ladder-01.md), [varE-limit-theorem.md](history/staging/varE-limit-theorem.md), [varE-spectral.md](history/staging/varE-spectral.md), [varE-theta2-proof.md](history/staging/varE-theta2-proof.md), [varE-theta2-step.md](history/staging/varE-theta2-step.md) |
| 9 | `Q-verify-record-defects-0830` Do the three defect claims of 2026-08-30 (attack-0830-varE-identification.md sec.8 on the doubled X2 column; attack-0830-tail-derivation.md sec.7 on the corpus's "R + 1/2"; attack-0830-head-remainder.md sec.1 on the decade-pooled Delta = 0.6214) reproduce on independent code from the definitions, and which of the corrections they list apply? | ANSWERED | Claim 1 CONFIRMED: the corpus delta*X2 column is the positive half of the p \| h-2 pattern doubled, that pattern's mirror is the p \| h+2 pattern (W-(-h) = W+(h) exactly, W-(h) != W-(-h) at 9 to 900,679 shifts), the group sum 2X2 reads -0.5603 .. 0.1846 at x = 7..19 against 5.7147 .. 5.3266, and Xmix is overstated 2.305x at x = 19 (6.9x at x = 7); X, X1 untouched. Claim 2 AMENDED: R + 5/2 and R + 3 are exact for the tail convention (all and odd origins, asserted at x = 7..23) and t/(R + 3) = 1.0228, but head-residual-factor.md:70 is the HEAD's forward convention where R + 1/2 and R + 1 are exact, so that correction does not apply; and p'^2 is 1 mod 6, where the tail constant is 5 (t/(R + 5) = 1.0181), with the class null (1.0157) the matched figure, so 1.0228 is one unmatched convention replacing another. Claim 3 CONFIRMED as an artefact, AMENDED on mechanism and on the half-decade reading: 0.6214 pooled against 0.6592, 0.6705, 0.6736 at 2, 4, 8 sub-windows; the between-slope (Simpson) piece the note derives is half of the pooling term (0.0187 of 0.0378 at halves, 0.0261 of 0.0522 at eighths), the other half is the within slope's own fall with height weighted by Var(g); and re-reading the halves from their eighths puts HL BELOW the measurement at 5 of 6 half-decades by 2.5 to 3.4 percent at the top decade, so "within 1.6 s.e., sign alternating" is itself a pooled statement. | [verify-0830-record-defects.md](history/staging/verify-0830-record-defects.md) |
| Z2 | `Q-X-upper-0829n` Can the rough-pair census X(K) on the stretch window be bounded above, unconditionally and with an explicit error term, by a dimension-2 upper-bound sieve, and how loose is the bound against exact X(K)? | PARTIAL | Yes, as a theorem with nothing open (Selberg's Λ² inequality with a remainder bounded by the interval structure alone, VERIFIED at all 10908 anchor-depth pairs), but it is loose by 7.82 to 10.13 against exact X(K) at the band depths, decomposed as a sieve loss 1.78 to 2.53 times a structural loss 4.01 to 4.39 that no upper-bound sieve can remove, the window holds the level below z² (s_max 1.81 to 1.96) so the bound stops improving past p_K = 31 to 61, its main term is the sifting function's and not the census's, and the drift is a crossing quantity outside the legal half and is not evaluated. | [attack-0829n-X-upper.md](history/staging/attack-0829n-X-upper.md) |
| Z2 | `Q-applied-0828-quadpoint` Were the quadpoint red team's corrections applied to the four HELD notes? | ANSWERED | Applied: the nine REFUTED and WEAKENED verdicts that target the four notes are written into them in present tense, with ledger blocks added; the tenth targets the sealed prereg, outside the fence, and is recorded in attack-quadpoint-02.md instead; three corrections owed by TODO.md Z2 and one by Z0 are listed here and are NOT applied. | [applied-0828-quadpoint.md](history/staging/applied-0828-quadpoint.md) |
| Z2 | `Q-capture-identity` Does the transplanted cap family collapse onto a classical object, and what does the collapse say about the depth law and the wall? | ANSWERED | PROVEN, elementary: floor_K = T − X(K) on the half-open window with both members in [Q², Q′²), a convention that is load-bearing; the wall is renamed, not weakened; Σ capU counts each member against its own threshold, not against a uniform p_K, the two differing 11% to 37% at K*. | [quadpoint-identity-01.md](history/staging/quadpoint-identity-01.md) |
| Z2 | `Q-derive-0904-r0-extension` Which pieces of the R0 decomposition (the tile form, the zone form, head, tail, Z2, and the composites R0/R1/R2/stretch) carry the parity obstruction's forbidden extension, and is any single piece both legal on the TPC-strength axis and exempt from it? | ANSWERED | No piece of R0 is both legal and exempt with content: the criterion reduces to a coordinate count (Proposition A) under which every statement forcing a twin pair into a range where roughness implies primality is covered, and the exempt residue is exactly the statements that assert no such forcing (R0's identity, lower bounds, boundary artefacts) plus the tile form, whose exemption is a property of the statement and provably does not close under deduction (Proposition B), so it survives only for routes with no sieve weight anywhere. | [derive-0904-r0-extension.md](history/staging/derive-0904-r0-extension.md) |
| Z2 | `Q-parity-adversary` Does a parity adversary built on our own stretches survive at every level, and what precision class does a certificate need? | ANSWERED | It does NOT survive: the exact-data adversary dies at D* about Q^1.18 (MEASURED, exact arithmetic, 43 anchors Q <= 200), and the certificate that kills it is itself destroyed by 0.30 of one count per modulus, so Z2's precision class is now measured rather than described; it is PROVEN not to be a proof ingredient. | [attack-parity-adversary.md](history/staging/attack-parity-adversary.md) |
| Z2 | `Q-parity-dstar-law-0829n` Does the exact-data parity adversary's killing level D*(Q) follow D* ~ Q^c with a stable c on the decades past Q = 200, and is c distinguishable from the independent-thinning null's? | CLOSED | No law in Q and CLOSED by the sealed kill rule (score 5 HIT, 1 MISS): MEASURED on 271 anchors 211 <= Q <= 13679, the Q-slope moves 1.446 to 1.204 to 0.575 across ranges while ln D* on ln width holds slope 1.097 +- 0.012 with a quarter of the scatter, D*/width about 0.5, and the independent-thinning null reproduces the width law within 0.025 in slope; the mechanism is that D* is where a modulus first reads a single position of the window, which is the wall survey's remainder statement in the stretch coordinate and names nothing new. | [attack-0829n-parity-dstar.md](history/staging/attack-0829n-parity-dstar.md) |
| Z2 | `Q-quadpoint-blind-31607-0830` Does the zero-parameter depth law y*(Q), stated on the set where T(Q) >= 1 and on both the 1/(2e^gamma) = 0.280730 and the u*omega(u) = 2 (1/u* = 0.280438) forms with and without the finite-size Mertens factor, survive a sealed blind test on the bands past Q = 10007, and can that decade tell the two asymptotes apart? | ANSWERED | MEASURED, blind, and it decides nothing asymptotic: on 8363 new anchors 10009 <= Q <= 100003 the 76 sealed rows score 64 HIT and 12 MISS with every MISS on the two naked asymptotes as pre-declared, the two finite-size zero-parameter comparators HIT every row at every band (residual on ln y*/ln h -0.00022 to -0.00002 against C2), K*/pool falls 0.032 -> 0.026 -> 0.020 -> 0.016 -> 0.013 with no bend and a quiet sup, and the band means sit 0.0017 to 0.0037 below both asymptotes, six to twelve times their 0.000291 difference, so which limit the deficit tends to is set by the comparator and not by the data. | [blind-0830-quadpoint-31607.md](history/staging/blind-0830-quadpoint-31607.md) |
| Z2 | `Q-quadpoint-c1c2-0830` Does the fourth decade's post-hoc, unsealed preference for the omega-form comparator C2 over the exact-Mertens comparator C1 (C1 above the data by 3.46 and 8.83 se at B11 and B12, C2 within 2.82 se) survive a sealed blind test at the fifth decade, Q in (100003, 316243], and what does that say about which mechanism explains the depth law's drift? | ANSWERED | MEASURED, sealed before the run and scored blind on 17702 new anchors, and it decides nothing asymptotic: the sealed D1 row HITs at both B13 and B14 (C1 above the data by 13.33 and 23.82 se, C2 within 1.26 and 1.82 se), so by the sealed rule the omega-at-finite-u crossing of import-rough-anatomy.md §2.1 is CONFIRMED over the exact-Mertens product of u2-engine-depth.md §5 as the depth law's main term at the sampling scale, while both still HIT every ±0.0015 row, the kill rows on C2 all HIT, K*/pool falls 0.013 -> 0.010 -> 0.008 with no bend, and the band means sit 0.0012 to 0.0018 below both asymptotes, so the two constants 0.280438 and 0.280730 stay unseparated by the pre-declared rule and the run separates two mechanisms, not two limits. | [blind-0830-quadpoint-c1c2.md](history/staging/blind-0830-quadpoint-c1c2.md) |
| Z2 | `Q-quadpoint-prior-art` In the owning conventions, who holds the rough-pair census, the capture identity and the crossing law, and is any of it ours? | ANSWERED | The object and the identity are standard (the dimension-2 twin sifting function plus Buchstab's identity; ADJACENT-STANDARD, no verbatim carrier, no novelty language); only the comparison X(y) < T and the crossing law stay ABSENT-PER-CONVENTION, and the Buchstab correction is 6.6% of the top-band residual, not 2%. | [quadpoint-prior-art.md](history/staging/quadpoint-prior-art.md) |
| Z2 | `Q-quadpoint-transplant` Does the anchored-cap family transplanted onto the stretch window S_Q certify every anchor, and what does the depth cost do with height? | ANSWERED | Pre-registration for the decade extension, committed ALONE before the segmented producer existed: it fixes the FALL trend line, the registered band readings, the kill rule and a digit-exact calibration gate that must abort before any new figure prints, and states that a falling K*/pool over two decades would still be only a measurement. | [attack-quadpoint-01.md](history/staging/attack-quadpoint-01.md), [attack-quadpoint-02.md](history/staging/attack-quadpoint-02.md), [quadpoint-decade-prereg.md](history/staging/quadpoint-decade-prereg.md) |
| Z2 | `Q-recon-0828-rough` Does the 2000-2026 literature on y-rough numbers, sifted sets and short intervals hold any theorem that lowers Z2 or G2, meaning any control on the largest gap or the minimum count of a sifted set in EVERY short interval, or any structure of rough numbers a gap bound could use? | ANSWERED | No. Ten angles examined, ten killed for this purpose; the strongest every-interval statement in print for one-class rough numbers is Iwaniec's S(x,y,z) >= (4y/log^2 y)(log(y/z^2) - O(1)) for y >> z^2, uniform in x, giving J(P(z)) << z^2, and it is the linear sieve run exactly at its sifting limit beta_1 = 2 with no slack outside it; no two-class analogue exists in print at any exponent, the corpus's own x^4.2665 is beta_2 by the same mechanism, and every remaining branch of the field (Matomaki-Radziwill, Gorodetsky, Friedlander-Iwaniec Cor 6.28, Gafni-Tao) carries the almost-all quantifier, which a second-moment statement can never convert into a bound on one empty window. | [recon-0828-rough.md](history/staging/recon-0828-rough.md) |
| Z2 | `Q-recon-0828-sieve` Is there anything in the 2008-2026 sieve literature, or in the parity-breaking literature, that lowers beta_2 = 4.26645 or supplies a consumer for a level theta > 1 on the two-class comb? | ANSWERED | No route. Twenty-one angles examined, nineteen dead on arrival, nothing in print beats 4.26645 at kappa = 2 at any level on four calibrated channels; the two survivors are an owning-convention row and one unresolved hypothesis in a five-page 1990 announcement whose stated requirement beta < 3 excludes beta_2 = 4.26645. | [recon-0828-sieve.md](history/staging/recon-0828-sieve.md) |
| Z2 | `Q-redteam-0828-quadpoint` Do the four HELD quadpoint notes of 2026-08-22 survive an adversarial pass: the capture identity's proof line by line, the depth law and its asymptote, the sealed prereg scoring, and the prior-art citations at page level? | ANSWERED | The identity is PROVEN once its window convention is written down and holds at every K of 50 anchors under an independent implementation; four load-bearing sentences are wrong (section 4's gloss on Sum capU, v1 section 2's limit, the prior-art note's 2%, and the note's unconditional y* sentences), and none of the four defects opens or closes a route. | [redteam-0828-quadpoint.md](history/staging/redteam-0828-quadpoint.md) |
| Z2 | `Q-redteam-0830-records` Do attack-0829n-parity-dstar.md (CLOSED, HELD) and attack-0830-record-mechanism.md (PARTIAL, HELD) survive an adversarial pass on independent code, does REFUTED row 95 stand as worded, and is TODO Z5's new title supported? | ANSWERED | Both notes' measurements reproduce on independent code and neither headline is refuted: D* is confirmed EXACTLY, by a BigInt rational simplex written here, at 299 of 376 anchors with 0 contradictions (the other 77 exceed the exact solver's size cap), the old range's 172-figure gate is re-derived exactly at all 43 anchors with 0 disagreements, and an independent 30-wheel sieve to 1e11 reproduces note (b)'s seven decade gap counts, CV^2 and far-tail slopes to every printed digit, with the counts also matching the published pi_2(10^k). Four sentences are wrong or over-stated and are replaced here: REFUTED row 95, note (a)'s ledger, its section 6 and TODO Z5 all attribute the null's 0.025 agreement to the WIDTH law when 0.025 is the ln Q slope difference (the width-slope difference on the same 84 matched anchors is 0.031); note (a) section 3's "the threshold sits in a gap of at least 0.25 at every anchor" is scoped in its own producer to the true arm and the null arm's exact gap is 0.1212; P6's HIT rests entirely on the decade-2 collapse that section 5 discounts as a sampler artefact when it discounts kill clause (a); and note (b)'s "d b_z = 1.0806 +- 0.0014" carries only the Monte Carlo pairing error, while moving the far-tail slope by 0.02 (against a spread of 0.0174 across six fit windows on the same decade and 0.1196 across decades) moves d b_z from 0.9888 to 1.1720, and continuing the law at slope 1 above the last resolved point still gives 0.7752. REFUTED row 95's CLOSED verdict stands on kill clause (b), which is better powered than the note presents it (paired s.e. 0.0401 against a 0.15 band), and the row needs two clauses reworded; TODO Z5's title is supported for "measured and not derived", and the resolved part of the law carries 72 per cent of the residual on its own with the extrapolation carrying the rest. | [redteam-0830-records.md](history/staging/redteam-0830-records.md) |
| Z2 | `Q-redteam-0830-zone` Do attack-0829n-X-upper.md, blind-0830-quadpoint-31607.md and blind-0830-quadpoint-c1c2.md survive an adversarial re-derivation and an independent re-implementation of their producers, and at what rung does the corpus carry each of their headline claims? | ANSWERED | They survive on the numbers and mostly on the wording. On independent code every band sum, tier ratio, sealed forecast, band statistic and z of all three notes reproduces to the printed digit (X-upper 7.82 to 10.13 and the flat 378100.0; the fourth decade's 76 rows at 64 HIT and 12 MISS with the same twelve MISSes; the fifth decade's class A at both bands), and three attacks failed to break them (the paired-se attack on the D rows, a search for a fitted constant in C1, and gap-selection at the band edges). Four defects stand: the X-upper note's "s_max 1.81 to 1.96" is wrong in its own arrow convention, which means B3 to B8, since s_max peaks at B4 and reads 1.85 at B8; the c1c2 note's OLD R2 row at B14 is a boundary call that my 1-in-8 subsample scores the other way; the c1c2 note's custody line "three tails, one code-sha256" is a tautology of tailfmt.js and is not evidence of a seal; and the unscored y* check carries a Jensen bias of about +0.44 in y, which is the whole size of the C2 gap it is read as corroborating. Nothing here moves 4.2665 to 2, no rung rises, and all three notes stay HELD. | [redteam-0830-zone.md](history/staging/redteam-0830-zone.md) |
| Z2 | `Q-redteam-0904-r0-extension` Do the seven load-bearing claims of derive-0904-r0-extension.md survive an adversarial re-derivation against Tao's own text, and do its proposed live-layer changes survive? | ANSWERED | Six of seven survive at their stated rung and one is refuted: Proposition A, the scope slip, row e'' and the equivariance transfer are CONFIRMED (the slip is strengthened, since Tao's own Example 2 is the target note's missing one-coordinate witness), Propositions B and D are WEAKENED (B's stated mechanism proves too much and its proposed insertion drops the qualifier that saves it; D's "same trigger" is near-definitional and its causal reading of the exponent band does not hold), and the claim that no corpus artifact certifies the window-count variance at width p'^2 is REFUTED by research/06-variance-theorem.js, which computes exactly that, brute-force verified at two levels; separately, EXEMPT throughout means "Claim 1's H5 fails", which is not the parity statement wall-note Face 1 is priced against, and the note's proposed live-layer text carries no H6 conditional. | [redteam-0904-r0-extension.md](history/staging/redteam-0904-r0-extension.md) |
| Z2 | `Q-roughpair-error` How big is the empirical error of the rough-pair census, and is Z2 dead on the numbers? | PARTIAL | Not dead on the numbers - the error sits below T at every one of 1,206 anchors, its scatter is sub-Poisson, its systematic part is 0.1% at the top band with the favourable sign and its exponent is 0.40 below the twin count's - but the same run moves the wall off the error term onto the depth, where the slack at the crossing is 1.056 and falling and the main term alone is 5.6 times the twin count at the sifting limit. | [attack-roughpair-error.md](history/staging/attack-roughpair-error.md) |
| Z2 | `Q-roughpair-null` Does the independent-thinning null named in attack-roughpair-error.md's defects list return chi2/df = 1, and is the measured sub-Poisson dispersion of the rough-pair census error real or a normalisation artefact? | ANSWERED | MEASURED, null-side, label (i), no bearing on the certificate: the independent-thinning null is binomial and returns 1 - p (0.8164 to 0.9808), not 1, so attack-roughpair-error.md's "below 1 everywhere: sub-Poisson" is WEAKENED and the registered F1 fires at u = 5; the deficit against the mean-matched null survives at pooled z = -5.87, -7.09, -11.39; and a CRT-exact null that only makes each prime's kill count exact in the window predicts 0.33 to 0.56, which the measured value EXCEEDS by 1.26 to 1.40, so D8 is interval-level in form, elementary in content, and not wall-relevant. | [measure-roughpair-null-0829.md](history/staging/measure-roughpair-null-0829.md) |
| Z4 | `Q-applied-0828-census` Were the census red team's corrections applied to the three HELD notes? | ANSWERED | Every WEAKENED and REFUTED verdict in redteam-0828-census.md is applied to its target note in the present tense; two producer defects and four live-doc corrections stay open and are listed here. | [applied-0828-census.md](history/staging/applied-0828-census.md) |
| Z4 | `Q-applied-0828-head` Were the head red team's corrections applied to the three HELD notes? | ANSWERED | Applied. Every WEAKENED and REFUTED row of redteam-0828-head.md lands in the note it targets as 42 prose edits, and all three ledger verdict lines now carry the surviving chain; four corrections fall outside the fence and are owed elsewhere, the load-bearing one being destroyer-census-01 §6(b)'s R and its h/R = 1.09 -> 1.03. | [applied-0828-head.md](history/staging/applied-0828-head.md) |
| Z4 | `Q-applied-0828-live` Which engine and head red-team corrections reached the live layer? | ANSWERED | Nineteen edits across four documents: the glossary's cap_K dimension count with its mandatory sifted-versus-assumed clause plus three new entries (twin opener, head, tail); the survey's one-class density factor, S1's restored pi(q-1) terms and r in N_x hypothesis, the dropped Chen absorption, Theorem C with its emptiness, dimension 1 for q_i < q, the comb-conditioning qualifier and the inverted shallow-band bullet; the certificate engine's equidistribution status cell, the q = T^{o(1)} second hypothesis and the Comb Discrepancy scope cell; and the census's R as the continuum functional with its three comparators; paper/staircase-note.md, TODO.md and QUESTIONS.md are owed and untouched. | [applied-0828-live.md](history/staging/applied-0828-live.md) |
| Z4 | `Q-destroyer-census` Who destroys each channel pair, what does the zone kill budget certify, and where does the counting certificate die? | ANSWERED | The census reproduces digit-exactly on an independent engine; the destroyer rule is positional, not temporal, the certificate holds at 15 zones and dies at p = 67 where B/C first crosses 1, and no first-mover excess survives the derived null. | [destroyer-census-01.md](history/staging/destroyer-census-01.md) |
| Z4 | `Q-head-remainder-0830` Does the 5.3 percent remainder that Hardy-Littlewood leaves in the head's endpoint deficit Delta = 2 - beta derive by a route that is not HL: the frozen-sieve first-survivor object, a level-of-distribution correction, or the exact tile-ensemble head? | PARTIAL | No route that is not HL closes it, and the remainder as recorded is not what it was taken to be. The record's Delta_meas = 0.6214 at [1e7,1e8) pools a decade over which the prime density falls ten percent, and the OLS intercept absorbs the gradient (a Simpson-type effect, sign derived): the two half-decades read 0.6848 and 0.6500, the four quarter-decades 0.7203 to 0.6565, and pooled minus the gap-weighted mean of the halves is -0.0378, -0.0455, -0.0524 at the three decades, so the same-sign 5.3 percent miss is the pooling. At half-decade resolution HL's pipeline prices Delta to 1.2 and 0.4 percent at the top two windows, inside one standard error, and the sign of the miss alternates. That agreement is a near-cancellation of two four-percent effects: the pipeline under-predicts its own rotation ensemble by 3.6 to 4.9 percent (pipe/ens 0.951 to 0.964 across y = 313 to 19997, MEASURED by exact CRT sampling; 1.049 to 0.958 at y = 11 to 23 by full enumeration), an ensemble quantity that derives by finite count with no prime input and whose sign is opposite to hl3 section 2's guess; and the anchored window's deficit sits 2 to 5 percent below its gap-scale-matched ensemble (Delta_meas/Delta_ens 0.878 to 0.995 over six half-decades, 0.954 to 0.995 on the four with more than 13,000 gaps), the anchoring part, which is a three-point prime correlation in a short window and is HL-strength by every route named. The head is a slack field and nothing here touches Z2. | [attack-0830-head-remainder.md](history/staging/attack-0830-head-remainder.md) |
| Z4 | `Q-head-residual` What is the head's residual prime-origin factor h/R = 1.09 -> 1.03, and does it derive? | PARTIAL | h - R decomposes exactly and A_forced derives; h/R -> 1 follows from beta CV^2 being bounded, beta CV^2 -> 2 controlling the RATE and not the limit (under it h - R -> D = -0.95, so +8.4661/ln^2 p cannot be the limit law); R is the continuum functional and the integer-origin null sees R + 1/2 exactly, so h - R = 5.679 depends on the unstated null population, reading 5.179 discrete-uniform and 2.925 coprime-to-30; the mod-30 answer is NO by a valid route, class term -0.0001; Delta = 2 - beta is priced by HL to 5.3 percent with nothing fitted and HL's own 1/ln x term absorbs the miss, so the 5.5 s.e. framing is dropped; the asymmetry-as-mechanism claim and the [0.289, 0.361] bracket are refuted, hl3's 16 percent standing; beta_null is 1.898 for the discrete-consistent null and 2 in the continuum; the 72/28 split reads 81/19 in the other exact order; c = 0.844 is 0.722 on a subset, pinned to 15 percent; Delta_HL ln p/lnln p = 4.02 is a property of the prediction; and the N4 plateau is not OPEN, needing beta CV^2 = 2.71 rising to 6.63. | [head-residual-factor.md](history/staging/head-residual-factor.md), [head-residual-hl3.md](history/staging/head-residual-hl3.md), [head-residual-null.md](history/staging/head-residual-null.md) |
| Z4 | `Q-redteam-0828-census` Do destroyer-census-01.md, stretch-01.md and records-placement-01.md survive an independent re-derivation of every load-bearing claim, and may they leave HELD? | ANSWERED | All three survive on arithmetic, every decisive number reproducing exactly on an independent engine; one sealed reading (records READ-3) is REFUTED as vacuous and four sentences need correcting before integration. | [redteam-0828-census.md](history/staging/redteam-0828-census.md) |
| Z4 | `Q-redteam-0828-head` Do the three 2026-08-28 head-residual notes survive an adversarial re-derivation of every load-bearing claim on independent code? | ANSWERED | Mostly yes on the numbers and no on two framings: "h/R -> 1 iff beta CV^2 -> 2" is REFUTED (the limit needs only boundedness, the product controls the RATE), and 9 to 59 percent of the quoted h - R is the choice of comparator, since R is the continuum functional and a discrete uniform origin sees R + 1/2 exactly. | [redteam-0828-head.md](history/staging/redteam-0828-head.md) |
| Z4 | `Q-redteam-0830-slack` Do attack-0830-head-remainder.md, attack-0830-tail-derivation.md and verify-0830-record-defects.md survive an adversarial re-derivation on independent code, and do the five riders the verification put on live notes stand as written? | ANSWERED | Arithmetically they survive: every figure of the three notes that this pass could recompute reproduced to the printed digit on code written from the definitions, 0 assertion failures over 58 assertion call sites (most inside per-level loops), including every figure of the verification's three claims and the half-decade Delta_HL it quoted rather than recomputed. Four sentences do not survive. (1) verify-0830-record-defects.md:316, a replacement queued for head-residual-hl3.md sec.0, says the pooled value sits "0.038 to 0.052 below the sub-window mean at all three decades"; measured, the two lower decades run to 0.076 and 0.066, and the same note's own falsifier row says 0.038 to 0.076, so the wrong half is the one queued to land. (2) verify-0830-record-defects.md:379's un-measured "+0.005" residual inside the eighths is +0.0004 measured at sixteenths, so the de-pooled top-decade value is converged and the caution can be dropped. (3) the ruling that the class null is "the matched figure" for the tail is matched on residue class only: p'^2 is coprime to every q <= p', and the ensemble's rough-class offset is E_rc - R = 5.6714 -> 7.5357 over x = 7..29 against the class null's 5.6000 -> 6.0336, giving t/(R_shell + 7.5357) = 1.0123 against t/classNull = 1.0157. (4) attack-0830-head-remainder.md sec.3's top row is not gap-scale matched: E[g] 244.0 against 235.9, y_match capped at 19997, and on the note's own six ensemble points Delta_ens ~ E[g]^-0.312, so meas/ens reads 0.9640 not 0.9539 and the headline "0.954 to 0.995" reads 0.964 to 0.995. Three levels the notes recorded as out of reach are run here: the X2 group at x = 23, the tile identities and conditionals at x = 29, and the ensemble ladder at y = 29 (pipe/ens 0.9535, 40 s, against the head note's "about fifteen minutes"). No route opens or closes and nothing here touches Z2. | [redteam-0830-slack.md](history/staging/redteam-0830-slack.md) |
| Z4 | `Q-tail-derivation-0830` Does the tail's measured law c = 0.7522 ln^2(p'^2) and its surplus derive, and which part of the coefficient is the tile's own (no prime input) against which part needs Hardy-Littlewood? | PARTIAL | PARTIAL, kill clause fired on the coefficient: the ensemble object (the same functional averaged over all p# translates) derives exactly, E_all = R + 5/2 and E_odd = R + 3 with R = Sum g^2/2W, computed exact at x = 7..29 with every conditional the rough-origin candidate needs, and its Mertens constant e^{2gamma}/(8 C2) = 0.6007 is 1/(2 C2) times rho(2) = e^{2gamma}/4 by construction; every route from there to the anchored 0.7574 passes through rho(2)'s limit (the sharp form of Assumption A, algebraically equivalent to HL) and through the zone's gap shape CV^2 -> 1 (an HL statement), so the anchored coefficient is HL in disguise and nothing beyond HL is derived; the tile's own (1 + CV^2)/2 is 0.6306 -> 0.7532 over x = 7..29 and not settled; the record's 0.7522 = HL x 0.9644 x 1.0298 is two non-HL-sized factors cancelling at this height; the rough-origin candidate has an exact ensemble counterpart E_rc/E_cls = 1.0050 -> 1.0523, right sign, wrong size and trend against the anchored 1.0157, not identified; one number derives that the record measured: the class-null offset E_cls - R = 5.600 -> 6.034 exact against the record's 6.05, replacing both the prereg's 0.5 and the note's 7.5; and the corpus's "R + 1/2" is the other convention, under the tail's own the constants are 5/2 and 3. | [attack-0830-tail-derivation.md](history/staging/attack-0830-tail-derivation.md) |
| Z4 | `Q-verify-record-defects-0830` Do the three defect claims of 2026-08-30 (attack-0830-varE-identification.md sec.8 on the doubled X2 column; attack-0830-tail-derivation.md sec.7 on the corpus's "R + 1/2"; attack-0830-head-remainder.md sec.1 on the decade-pooled Delta = 0.6214) reproduce on independent code from the definitions, and which of the corrections they list apply? | ANSWERED | Claim 1 CONFIRMED: the corpus delta*X2 column is the positive half of the p \| h-2 pattern doubled, that pattern's mirror is the p \| h+2 pattern (W-(-h) = W+(h) exactly, W-(h) != W-(-h) at 9 to 900,679 shifts), the group sum 2X2 reads -0.5603 .. 0.1846 at x = 7..19 against 5.7147 .. 5.3266, and Xmix is overstated 2.305x at x = 19 (6.9x at x = 7); X, X1 untouched. Claim 2 AMENDED: R + 5/2 and R + 3 are exact for the tail convention (all and odd origins, asserted at x = 7..23) and t/(R + 3) = 1.0228, but head-residual-factor.md:70 is the HEAD's forward convention where R + 1/2 and R + 1 are exact, so that correction does not apply; and p'^2 is 1 mod 6, where the tail constant is 5 (t/(R + 5) = 1.0181), with the class null (1.0157) the matched figure, so 1.0228 is one unmatched convention replacing another. Claim 3 CONFIRMED as an artefact, AMENDED on mechanism and on the half-decade reading: 0.6214 pooled against 0.6592, 0.6705, 0.6736 at 2, 4, 8 sub-windows; the between-slope (Simpson) piece the note derives is half of the pooling term (0.0187 of 0.0378 at halves, 0.0261 of 0.0522 at eighths), the other half is the within slope's own fall with height weighted by Var(g); and re-reading the halves from their eighths puts HL BELOW the measurement at 5 of 6 half-decades by 2.5 to 3.4 percent at the top decade, so "within 1.6 s.e., sign alternating" is itself a pooled statement. | [verify-0830-record-defects.md](history/staging/verify-0830-record-defects.md) |
| Z4 | `Q-zone-tail` What is the tail field of the zone (p, p'^2) - its law against ln^2, its worst case, its share of the R0 width, and is it the frozen-sieve last survivor below p'^2 at the rate the head is the frozen sqrt(p)-level first survivor above p? | PARTIAL | The field exists now, 1,225 zones, and nothing in it is derived. The tail is the head's own renewal functional read at height p'^2 rather than p: c_tail = 0.7771 ln^2(p'^2) at [3163,1e4) against the head's 0.6693 ln^2 p on the same zones and the same estimator, both referenced to HL's 0.7574, and the apparent factor of four is the unit ln^2(p'^2) = 4 ln^2 p and nothing else. The band drift does not settle (0.7518, 0.7288, 0.7771; the pre-registered 0.03 step is missed), so this is band composition on two decades and not a measured convergence. The frozen-sieve mirror is 100% at the zone's own level p, but that is the Zone Restriction Lemma restated and not a rate comparable to the head's 96.65%; the non-vacuous mirror is one fold back, where the tail survives at 98.69% with the residual priced exactly (88 extra lpf(n) = p survivors, 18.18% of them biting), and the head's own frozen level sqrt(p) identifies the tail in only 22.86%, refuting this note's own pre-registered [0,5] zones. The renewal surplus t/R = 1.0619 at B4 is NOT RESOLVED, its bootstrap [0.9937, 1.1321] containing 1, and an exhaustive class-matched origin null over 5,962,057 origins gives the same 1.0619; three matched non-square endpoints see no difference at all, sign tests z = 0.14, -0.54, 0.66 with six paired intervals all containing zero, so nothing here is a property of the endpoint being a prime square. R0 is asserted at all 1,225 zones and the shares are 1.82% head, 89.72% Z2, 8.46% tail at B4 with the tail's share FALLING, so filling the tail row moves the decomposition's difficulty nowhere: Z2 was the obstruction before and is more of it after. | [zone-tail-01.md](history/staging/zone-tail-01.md) |
| Z4 | `Q-zone-tail-02` On the full zonegap-01 range to 1e11, what is the per-zone tail law in both units, is the renewal surplus t/R real at 27,292 zones, and do the head and the tail of a zone have a joint law? | ANSWERED | Resolved DOWN and nothing is derived: zone-tail-01's unresolved t/R = 1.0619 at 782 zones reads 1.0298 on a height-matched comparator at 17,700 zones (bootstrap [1.0156, 1.0443], excluding 1) and 1.0157 against the exactly matched discrete class null (bootstrap [1.0013, 1.0308], clearing 1 by 0.0013), so part of the original figure was the comparator and the pre-registered rule returns MATCH by two parts in ten thousand; c_local = 0.7522 at the top band with bootstrap [0.7410, 0.7630] now CONTAINING HL's 0.7574 and the band drift inside the registered 0.03 per step for the first time but still non-monotone (0.7518, 0.7664, 0.7416, 0.7522), so no convergence is measured; global worst tail/ln^2(p'^2) = 6.840 at p = 15107 with max/mean no longer flat (4.40, 5.36, 8.59, 8.43); Q5 is answered in the negative, head and tail showing no dependence at 27,292 zones (detrended r = -0.0009 against null s.e. 0.0061, permutation p = 0.8920, variance ratio 0.9990, no KS rejection, no chi-square near threshold), so the R0 pieces are a product structure to first and second moments and in the sum's whole law while independence is NOT proven and the simultaneous-extremes regime is untouched; a candidate rough-origin mechanism for the surplus is HEURISTIC and does not fit the head's own excess band by band; the head field's effective sample size is measured at 1,910 distinct a_first among 17,700 top-band zones, so this note's own head interval is priced over draws the field does not hold, a cluster bootstrap over distinct a_first (producer SEC I(a), seed 613009117) measuring the inflation at 4.10 rather than the 3.04 the redundancy alone implies and moving the top-band interval to [0.6848, 0.7692], still inside the registered [0.68, 0.78] (correction originating with redteam-0829-measure-b.md section 1c C15); the scope of that defect is that one interval and not the corpus, since destroyer-census-01.md publishes no bootstrap, head-residual-factor.js bootstraps over gaps, zonegap-01.js has none and zone-tail-01.js bootstraps only tail quantities; ten of ten predictions hit, which is a criticism of the pre-registration; and the R0 shares read 1.40% / 92.80% / 5.81% with the tail's share still falling, so Z2 is more of the obstruction after this pass than before it. | [zone-tail-02-0829.md](history/staging/zone-tail-02-0829.md) |
| Z5 | `Q-applied-0828-litimports` Were the lit/imports red team's corrections applied to the six HELD notes? | ANSWERED | Applied, 64 substantive edits across the six notes: the Saffari-Vaughan range exponent is 6/11 in both import notes, the fixed-M THEOREM in import-fracparts is struck and the cap-36 MEASURED to PROVEN upgrade withdrawn, row 15 loses its theorem column and row 16 is regraded stale, and the six weakened sentences in the four literature notes now read as the audit requires; four claims are declined with reasons, and nine live documents plus two fenced staging notes are recorded here as owing corrections that this pass did not apply. | [applied-0828-litimports.md](history/staging/applied-0828-litimports.md) |
| Z5 | `Q-applied-0828-registries` Which lit/imports corrections reached the registries? | ANSWERED | 13 edits across six files, plus one appended changelog section: IMPORT-MAP gains rows 15 (no THEOREM, the column struck), 16 (STALE) and 17 (CLOSURE, two-sided) with its three counts recounted to seventeen rows; SEARCH-CONVENTIONS gains the Kourbatov-b, generalized-Dickman and VC-of-multiples rows with each channel's calibration state; import-map-construction's determinantal cell, natal-cap-36's separate-census sentence, one REFUTED row and one PRIOR-ART block are corrected; GLOSSARY, TODO, QUESTIONS, the five loose hyperuniformity documents and two staging notes are left for their holders and listed here. | [applied-0828-registries.md](history/staging/applied-0828-registries.md) |
| Z5 | `Q-record-deficit` Does the 6.0 percent record-location deficit survive the corrected null, and what is it? | MIXED (lit-kourbatov-shortfall.md: ANSWERED; record-location-null.md: PARTIAL) | Survives (z = -3.3, five window cuts); Z5's premises on 'location' and on n_eff were wrong; corrected-null formula in §4. | [lit-kourbatov-shortfall.md](history/staging/lit-kourbatov-shortfall.md), [record-location-null.md](history/staging/record-location-null.md) |
| Z5 | `Q-record-mechanism-0830` Which of three candidate mechanisms (sub-Poisson gap dispersion, the tile's exact gap law, Kourbatov's k = 1 conspiracy heuristic transported to k = 2) carries the residual 0.78 to 0.97 of Kourbatov's b, at what derived size, and what fraction of b is left? | PARTIAL | The residual is carried by the twin-prime gap law AT HEIGHT and by nothing else tried: a new sieve to 1e11 measures that law under-dispersed (CV^2 rising 0.7276 to 0.9295 over seven decades) with a far tail steeper than exponential (log-slope 1.0638 at the top decade), and fed into the record null it carries 95.7 to 99.8 percent of the residual (d b_z = 1.0370 and 1.0806 +- 0.0014 against 1.0833, MEASURED on a model, paired, 2000 replicates); the tile's period-wide law (d b_z = 8.10) and Kourbatov-Wolf's k = 1 bin-count heuristic (4.20) overshoot by 4 to 7x and are closed as posed; the transport of a bare CV^2 is family-dependent (0.62 against 1.06 at CV^2 = 0.93), so "computable from Var/E" is false as stated; Kourbatov-Wolf's second-order scale a_c/abar tracks the measured CV^2 to within 0.04 at every decade with no parameter and is an ansatz, not a derivation; the shape statistic moves a third of the way toward the data (z_D from -1.64 to -0.97); what is left with no derivation is the gap law itself, and the top height band's b (0.937 measured against 1.69 to 1.98 predicted on 17 records) is the open falsifier. | [attack-0830-record-mechanism.md](history/staging/attack-0830-record-mechanism.md) |
| Z5 | `Q-record-null2` How much of Kourbatov's shortfall coefficient b does an inhomogeneous-intensity record null carry, how much does a 6Z-latticed null carry, and what is the residual? | ANSWERED | The inhomogeneous null carries essentially none of b (d b_z = -0.0012 +- 0.0001, MEASURED); the 6Z lattice's share is LAW-DEPENDENT, +0.1113 +- 0.0003 under the memoryless rounding-up law against -0.0060 +- 0.0003 under rounding to nearest, so the null side is a bracket of 16.1 to 25.1 percent of b and three quarters or more stays a residual with no mechanism; record-location-null.md section 8's argued 1.7e-4 lattice bound is wrong but no single number replaces it; the 15 percent estimator disagreement is pinned as an exact weighting identity; and the shape assumption behind every b reading is measured at 1.6 sigma and stays open. | [measure-record-null2-0829.md](history/staging/measure-record-null2-0829.md) |
| Z5 | `Q-redteam-0828-litimports` Do the six notes of 2026-08-28 survive an adversarial pass, and which of their load-bearing claims are wrong? | ANSWERED | Every measured number reproduces on independent code; Saffari-Vaughan Theorem 10's range exponent is 6/11 not 1/11, which voids import-fracparts's one banked THEOREM at fixed M and corrects row 15 twice; four further weakenings, one refuted verdict line, no note refuted whole. | [redteam-0828-litimports.md](history/staging/redteam-0828-litimports.md) |
| Z5 | `Q-redteam-0830-records` Do attack-0829n-parity-dstar.md (CLOSED, HELD) and attack-0830-record-mechanism.md (PARTIAL, HELD) survive an adversarial pass on independent code, does REFUTED row 95 stand as worded, and is TODO Z5's new title supported? | ANSWERED | Both notes' measurements reproduce on independent code and neither headline is refuted: D* is confirmed EXACTLY, by a BigInt rational simplex written here, at 299 of 376 anchors with 0 contradictions (the other 77 exceed the exact solver's size cap), the old range's 172-figure gate is re-derived exactly at all 43 anchors with 0 disagreements, and an independent 30-wheel sieve to 1e11 reproduces note (b)'s seven decade gap counts, CV^2 and far-tail slopes to every printed digit, with the counts also matching the published pi_2(10^k). Four sentences are wrong or over-stated and are replaced here: REFUTED row 95, note (a)'s ledger, its section 6 and TODO Z5 all attribute the null's 0.025 agreement to the WIDTH law when 0.025 is the ln Q slope difference (the width-slope difference on the same 84 matched anchors is 0.031); note (a) section 3's "the threshold sits in a gap of at least 0.25 at every anchor" is scoped in its own producer to the true arm and the null arm's exact gap is 0.1212; P6's HIT rests entirely on the decade-2 collapse that section 5 discounts as a sampler artefact when it discounts kill clause (a); and note (b)'s "d b_z = 1.0806 +- 0.0014" carries only the Monte Carlo pairing error, while moving the far-tail slope by 0.02 (against a spread of 0.0174 across six fit windows on the same decade and 0.1196 across decades) moves d b_z from 0.9888 to 1.1720, and continuing the law at slope 1 above the last resolved point still gives 0.7752. REFUTED row 95's CLOSED verdict stands on kill clause (b), which is better powered than the note presents it (paired s.e. 0.0401 against a 0.15 band), and the row needs two clauses reworded; TODO Z5's title is supported for "measured and not derived", and the resolved part of the law carries 72 per cent of the residual on its own with the extrapolation carrying the rest. | [redteam-0830-records.md](history/staging/redteam-0830-records.md) |
| D | `Q-doubling-C2` Does the doubling inequality hold on the base-2 chain, and can a bridging certificate prove it? | PARTIAL | Not proven and not refuted: the exact C2 table has sup 5.2727 at s = 16, eleven proven finite-level bounds C2 <= K*+1 tight to a factor <= 2.91, two closures refuted outright, and the alarm is that K* drifts up (slope 0.6881 +/- 0.1328) while C2 does not (0.2018 +/- 0.1412). | [attack-doubling-01.md](history/staging/attack-doubling-01.md) |
| D | `Q-doubling-bridge-0829n` Can a bridging certificate carry Ghat(2s) <= 8 Ghat(s) from level s to level 2s uniformly in s, all s, on the base-2 chain? | PARTIAL | Not by any proven mechanism: the K*-product bridge is CLOSED at every C2 by the cited run floor K* >= pi(2s)-pi(s) (K* = 17 at s = 16 by exact walk, VERIFIED, so the certificate reads 18 against 8 on the chain itself; it exits the whole legal band at s = 128, PROVEN); the sharper maxsum bridge Ghat(2s) <= maxsum_{K*+1}(T_s) is PROVEN and holds under 8 at all fourteen enumerable steps (VERIFIED), but its all-s form needs an upper bound on K* against the entering primes' two-class covering that nothing proven supplies; the doubling inequality itself is untouched. | [attack-0829n-doubling-bridge.md](history/staging/attack-0829n-doubling-bridge.md) |
| D | `Q-doubling-killrun-0830` Can the exact per-fold L bounds of the pi(2s) - pi(s) folds inside one doubling step compose to an upper bound on the weighted kill-run below the allowance 8 Ghat(s)/gbar(s), for all s, without passing through K*? | PARTIAL | No, and the composition is closed as a route, not merely unproven: the folds compose as a PRODUCT, K*+1 <= prod_j (1+L_j) (PROVEN here, exact at fourteen steps, 540 against 18 at s = 16), the composed certificate never sits below yesterday's maxsum certificate (PROVEN by monotonicity), it exceeds the allowance at 8 of 14 enumerable steps starting at s = 9 (VERIFIED), and since every fold kills a slot the composed index is at least 2^N, whose floor 2^N gbar(s) alone exceeds 8 Ghat(s) at the chain rungs 16, 32, 64 and beats the cited polynomial ceiling on Ghat for all large s (PROVEN given the ceiling); the sum form is false at seven steps and the max form is a floor; the weighted run itself, computed exactly, sits at 0.83 of its allowance at s = 16 and (M8) is exactly where yesterday left it, OPEN. | [attack-0830-doubling-killrun.md](history/staging/attack-0830-doubling-killrun.md) |
| D | `Q-kstar-prereg` What is K* at the three next doubling steps, predicted before any period walk? | OPEN | Pre-registration only, committed alone: the predictions, the scoring rule and the growth-type verdict thresholds are fixed in advance, with the inclusion-exclusion engine validated against an independent scan engine on all eleven known steps first. | [attack-kstar-01-prereg.md](history/staging/attack-kstar-01-prereg.md) |
| D | `Q-recon-0830-rec-killrun` Does the literature hold, in its own conventions, a theorem whose hypotheses REC(s, u0) (the sup-versus-rms recovery of the level-D signed remainder over all positions, attack-0829n-rml-proof.md section 3) or the weighted kill-run K*(s) (the longest run of level-s slots the primes in (s, 2s] can kill, attack-0829n-doubling-bridge.md sections 0 and 3) satisfies as stated, or a Maier-type theorem that makes REC false for two-class sifted sets at some u0 below beta_2? | ANSWERED | No theorem applies to either object as stated, on four calibrated channels searched in the owning conventions; every neighbour is graded NEAREST with its unmet hypothesis named, and neither object is on any refuted row. On the Maier question the answer is negative for REC as stated (the Maier family bounds the COUNT, i.e. the full-level remainder, never a level-D truncation) but carries one calibration: at one class and full level the REC-shaped inequality is FALSE asymptotically, by Buchstab's origin ratio against the Montgomery-Vaughan full-period variance ceiling, and the embedded arithmetic puts the level where that falsity first shows at log10 z between 16 and 141 depending on u0 and epsilon, so a finite-z margin of the kind the corpus measures cannot see a failure of this type; at two classes the same full-level statement is HL-conditional at u0 = 2 and unlocated in print at any u0. No exponent moved. | [recon-0830-rec-killrun.md](history/staging/recon-0830-rec-killrun.md) |
| D | `Q-redteam-0830-doubling` Do attack-0829n-doubling-bridge.md and attack-0830-doubling-killrun.md survive an adversarial re-derivation on an engine sharing nothing with their producers, and do REFUTED rows 94 and 98 stand as worded? | ANSWERED | The mathematics survives: the maxsum certificate Ghat(2s) <= maxsum_{K*+1}(T_s) and the product composition K*+1 <= prod(1+L_j) are each re-derived here and hold, the second at 21,641,346 nesting links over 6,012,804 killed runs with zero failures including the zero-kill fold, and every quoted figure reproduces digit for digit on a fresh engine (K*(16) = 17; G2(31#) = 348 @ 8813641451 x4 from both base tiles; sup msc 6.6364; the diagonal cells; the 2^N ratios 1.226/1.481/41.348). Row 94 STANDS and is if anything under-claimed, but its attribution is wrong in one direction: Lemma 1 at s = 128 alone clears the whole band, so the s = 16 walk corroborates rather than carries it. One statement is falsified: the bridge note's NOT-REACHED line puts 19#->37# out of reach, but column-major it returns here, reproducing the ladder row x = 37 and adding a FIFTEENTH step at s = 19, 20 (K* = 13, N = 4, C2 3.5200, certificate 3.8000), so the enumerable range ends at s = 20, not s = 18. Row 98 STANDS on its mathematics and is WEAKENED on one clause: "the truth sits under it everywhere (sup w/a = 0.8295)" attaches the CERTIFICATE's ratio to the word truth; the truth's sup is 0.6591. | [redteam-0830-doubling.md](history/staging/redteam-0830-doubling.md) |
| D | `Q-redteam-0830-imports` Do the six lighter notes of 2026-08-30 (varE-identification, smooth-aps, rec-killrun, skeleton-door, at43-bigint, coherence) survive an adversarial pass on independent code and at the source pages, and which of their load-bearing claims are wrong? | ANSWERED | No note is refuted whole and no exponent moves. Every decisive measurement reproduces on code sharing nothing with the producers: the varE mixed remainder and its 0.844 / 0.826 share below 2L and 94.4 / 98.7 percent unbalanced share at x = 13, 17; the Buchstab deviations and all three crossing levels log10 z* = 33.53, 68.80, 33.62; the skeleton door's 9.2 / -0.9 percent, G30_agg 0.1113 / 0.1011 and the 0.0102 cap at @13, @17, by a path that also verifies cap-36 Theorem A; the @43 parity exactness on all 26,157,448 scour classes with 0 above 2^54 and a constructed @47 counterexample; and the five recon-0828 verdict counts summing to 75, which REFUTES rec-killrun's brief-error clause and confirms the orchestrator's rider. Seven claims WEAKEN. The load-bearing one is smooth-aps's "the weight is unmet in print": Harper's J. London Math. Soc. 112 (2025) e70293 proves a Barban-Davenport-Halberstam asymptotic for an ARBITRARY sequence on exactly that dyadic all-classes object, and his own footnote says the missing max over x' can be incorporated, so the NEAREST citation changes even though the step still does not close (the 2025 range is sqrt(2x) < Q <= x and its Theorem 2 route bars sieved sets by name). Also: Henriot Corollary 2 applies, but to the ERRATUM's statement and under two hypotheses the note leaves unstated (eps < alpha/600, not "every eps"; F at prime powers); varE section 4's display (*) carries an unfilled placeholder and is vacuous by a factor L/d; the skeleton door's "would tighten" is wrong in sign at @17, where the closable block is negative and removing it RAISES G30_agg to 0.1020; Halasz-Montgomery is not applicable for the reason given (it is an abstract inner-product inequality); FGKT's heuristic quote is on p. 4, not p. 3; and the "~13x had no source" is a corpus miss, the retired G2-walk figure at CHANGELOG.md:5716. Not TPC-strength; nothing here opens a route. | [redteam-0830-imports.md](history/staging/redteam-0830-imports.md) |
| 0 | `Q-applied-0828-closures` Were the closures red team's corrections applied to the five HELD notes? | ANSWERED | Applied. 47 prose corrections across the five notes; c2prime-refit-22 drops from CLOSED to PARTIAL and three ledger verdicts are rewritten; four producer READINGS blocks and eleven live-document lines carry the same defects and are listed here uncorrected, behind the fence. | [applied-0828-closures.md](history/staging/applied-0828-closures.md) |
| 0 | `Q-barrier-kappa2` Does Granville's exceptional-character construction, which makes the Jurkat-Richert f and F attained by interval sieving problems at kappa = 1, transfer to kappa = 2 and supply the missing barrier on wall-note Face 4, so that no class-blind argument can beat beta_2 = 4.26645 on intervals? | CLOSED | No. Verdict (b): the transfer runs, fixes the axiom obstruction that sift-limit-attack.md section 2 blamed for the mixed-sign sketch's death, and then hits a hard ceiling at u = 2, because the character's only gift is the one-point identity lambda = chi on z-rough integers and a sign pattern with a +1 coordinate is empty exactly when z^2 >= x; above u = 2 the surviving question is the shifted intersection of two positive-density lambda-classes, which is Chowla-strength, so the section 2 verdict stands with a corrected reason; the band (2, 4.26645] is untouched, and the hypothesis itself implies the target by Heath-Brown 1983. | [attack-barrier-kappa2.md](history/staging/attack-barrier-kappa2.md) |
| 0 | `Q-derive-0904-L7-transfer` Is the legal open-set target L7, G2(x#) << g(x#) (ln x)^A for a fixed A (which would give exponent 2 + o(1) from Iwaniec's one-class bound, below beta2 and above the TPC line), reachable by a TRANSFER from the one-class Jacobsthal bound, and if not, what does each transfer mechanism reduce to? | PARTIAL | No transfer mechanism in the corpus reaches L7, DERIVED: the union-bound transfer is vacuous already in the period average from x = 11 (the exact CRT budget sum of 1/(p - 1) over 3 <= p <= x passes 1 at x = 11), and the sieve-on-holes transfer is the Bruedern-Fouvry vector sieve, whose coupled unconditional form lands at 2(1 + sqrt e) = 5.2974 above beta2 and whose decoupled form needs the sup-over-positions remainder law that item 0 ruled a truth gap; L7 stays a legal OPEN statement with no mechanism, and the conjectural A = 1 is truth-side evidence only. | [derive-0904-L7-transfer.md](history/staging/derive-0904-L7-transfer.md) |
| 0 | `Q-g2-provenance-x37` Does the headline G2 exponent depend on the eight terms this repository has never reproduced, and does any instrument without G2(37#) inside it flag x = 37? | ANSWERED | MEASURED, both largely negative: the custody-only refit lands at 1.533 against the headline 1.498 and no provenance-block drop moves the corrected central by more than 0.035 (Ghat(64) alone moves it 0.002), while no G2-free instrument flags 37 in the high direction, the one \|z\| past 2 being h(37#) at -2.20 in the low direction and range-dependent; the blind extreme-value forecast of G2(37#) does overshoot at z = +6.58, unexplained. | [measure-g2-provenance-0829.md](history/staging/measure-g2-provenance-0829.md) |
| 0 | `Q-gap-spectrum` What is the full gap-length distribution of twin slots over one period of the tile, what does the excess functional \|B_N\| = sum_{g>N}(g-N) read on an x^s grid, and where does the empirical minimum window count leave zero? | ANSWERED | The distribution is exact at nine levels to x = 31 and the pre-registered renewal null FAILS in the light direction at every one: the tail is uniformly steeper than exponential (body slope -1.3302 against -1), no power law survives (the power-law slope moves by a factor 17), the maximum is 2.087 to 2.241 BELOW the renewal maximum, and \|B_N\| sits at 0.0245 to 0.7436 of the null and is exactly zero at s = 1.75 where the null predicts 6.5262e+5 empty windows; so no heavy-tail mechanism for a super-linear G2 exponent exists at any computable level, the identity G2 <= N + \|B_N\| is proven but degenerates to G2 <= N on this grid, and the sifting onset is flat at 1.63 to 1.70 against a sieve bound f2 that is zero everywhere the grid reaches. | [gap-spectrum-01.md](history/staging/gap-spectrum-01.md) |
| 0 | `Q-lit-siebert` Is Siebert's 1983 result stated for general sieve dimension kappa, or for kappa = 1 only, and does it therefore already contain the kappa = 2 extremal example that SEARCH-CONVENTIONS section 3 records as not found? | ANSWERED | kappa = 1 ONLY, on three independent statements of the theorem (the chapter's own publisher abstract, Granville 2020 section 1, Friedlander-Iwaniec 2022 page 20), all naming the LINEAR sieve and the Jurkat-Richert f and F; the chapter's full text was NOT reached, so this is testimony not primary reading, and the SEARCH-CONVENTIONS section 3 "no published kappa = 2 extremal example" row needs no correction. | [lit-siebert-1983.md](history/staging/lit-siebert-1983.md) |
| 0 | `Q-maximal-law-tpc` Is the SIEVE Gaussian maximal law TPC-implying? | ANSWERED | YES in the only form that would deliver anything: stated for the operative remainder R_H, need/z^2 runs 0.49 to 0.61, flat and below the zone budget at every z from 13 to 43, which is the Gap Reformulation, hence the Zone Postulate, hence TPC, so no soft argument can prove it; the published above-2 theta column is not the maximal law's verdict but the law plus two lossy steps. | [phase1-T4-maximal-law.md](history/staging/phase1-T4-maximal-law.md) |
| 0 | `Q-measure-g2-generic` Where does G2(x#) sit in the distribution of the same maximum gap taken over other two-class configurations with the same census, and is the constant-shift family generic inside the free-pair family? | ANSWERED | G2 is GENERIC in this coordinate on the registered rule, MEASURED: the midrank percentile of G2 in the census-matched two-class ensemble reads 20.00, 18.06, 26.35, 17.14 exhaustively at x = 11..19 and 13.70 sampled at x = 23, all inside the registered [5, 95] band so the falsifier does not fire, while sitting about one ensemble sd below the mean at all five levels; and the free-pair and constant-shift ensembles are PROVEN identical up to translation, so killer 1 gains no target in the class positions at these levels. | [measure-g2-generic-0829.md](history/staging/measure-g2-generic-0829.md) |
| 0 | `Q-omega-floor-blind-0830` Does the local log-slope of the pointwise floor Omega(z) of attack-0830-rec-cheapest.md (exact to z = 73, certified 2+4-chain family to z = 5e5), extended blind to new levels under a sealed forecast, behave as the DERIVED growth law Omega >> z^{16s/9}/ln^8 z predicts at s = 2.698721, and at what z would the test be decisive? | ANSWERED | MEASURED, blind, on the derived law only: 18 of 22 sealed rows HIT; the certified 2+4-chain family at p* = (47, 43) runs 5e5 -> 1e9 (A1A2 = 8.863e17 -> 9.351e32, exact integers) with its step slope falling 4.85 -> 4.38 through every sealed band onto the law's log-corrected slope, the decisive decade 1e8 -> 1e9 reading 4.410 against 16s/9 - 8/ln z = 4.389 (HIT, kill rule not triggered at 4.452 +/- 0.011); the 4 MISSes are the ratio to z^{16s/9}/ln^8 z sitting at 2.00-2.14 above the sealed cap of 2 at z >= 1e8, the pre-declared non-adverse direction; the exact floor is extended 73 -> 113 (251 -> 1980, equal to the hill-climb floors at 89 and 101), where the law predicts nothing; no exponent moves and the law stays DERIVED and HELD. | [blind-0830-omega-floor.md](history/staging/blind-0830-omega-floor.md) |
| 0 | `Q-rec-cheapest-0830` At the cheapest legal point of REC(s, u0), s -> 1+sqrt(e) and u0 -> beta_2, where the saving asked over the triangle inequality is only z^{1.031}, does any of the five dead routes close, does a mixed mean-square-plus-cap strategy close, and is the failure a proof gap or a truth gap? | PARTIAL | No route closes and the failing step is yesterday's statement, so PARTIAL on the routes; but the step is located as a TRUTH gap, not a proof gap, asymptotically: the certificate's own value at a CRT-planted doubly-smooth window is cc(r) = -(A1A2 + A1B2 + B1A2) with every term a count of exit chains of the Rosser supports (PROVEN, checked exhaustively at z <= 73), the window bound T <= cc(r) + H - 1 is exact, and the exit-chain count is DERIVED (held) to grow like z^{16s/9 - o(1)} at four primes and z^{2s - o(1)} in the limit, so REC(s, u0) is false for every u0 < 16s/9 = 4.7088 at s -> 1+sqrt(e), the whole legal band (2, beta_2] included, and RML(alpha) with it; at every computable z it is a proof gap (Omega(z) exact to z = 73 reads 251 against z^{u0} = 1.05e6, and a certified lower bound 8.86e17 at z = 5e5 sits a factor 1.2e6 under z^{u0}); no exponent moved. | [attack-0830-rec-cheapest.md](history/staging/attack-0830-rec-cheapest.md) |
| 0 | `Q-recon-0828-covering` Does the interval-covering, automated-proof or extremal-combinatorics literature hold a method that bounds the length of an interval covered by two residue classes per prime, or that turns the exact G₂ ladder into a statement at all x? | ANSWERED | No route. Fifteen angles examined, fourteen dead on arrival or already closed here; the best interval-covering bound in print is Crittenden-Vanden Eynden's own Lemma 2, which reads 1.02e12 against G₂(79#) = 1710 and is 8181x weaker than the corpus's own 4.2665 sieve bound at the same level; the one survivor, transplanting Costello-Watts's recurrent certificate to two classes, is a computation that certifies finitely many levels and whose analytic half is Erdős #970 at one class. | [recon-0828-covering.md](history/staging/recon-0828-covering.md) |
| 0 | `Q-recon-0828-farfields` Do any of the fields still absent from IMPORT-MAP.md hold a theorem whose hypothesis the tile satisfies exactly and whose conclusion is a lower bound on a periodic set's count in every window, a maximal-gap bound for a product-structured periodic set, or a positivity statement at a distinguished point? | ANSWERED | No route from any of the sixteen candidates priced; two reach STRONG-ANALOGY or better and CLEAN and both bank only a closure or a wall address, the Fourier one by a one-line non-vanishing proof that empties the Donoho-Stark/Tao/Meshulam family on this object, and Janson's lower tail by saturating at exp(-1/c) >= 0.0805 against the 1/W a position union bound needs, short by 3.6e2 at x = 11 and 2.8e13 at x = 41. | [recon-0828-farfields.md](history/staging/recon-0828-farfields.md) |
| 0 | `Q-recon-0828-rough` Does the 2000-2026 literature on y-rough numbers, sifted sets and short intervals hold any theorem that lowers Z2 or G2, meaning any control on the largest gap or the minimum count of a sifted set in EVERY short interval, or any structure of rough numbers a gap bound could use? | ANSWERED | No. Ten angles examined, ten killed for this purpose; the strongest every-interval statement in print for one-class rough numbers is Iwaniec's S(x,y,z) >= (4y/log^2 y)(log(y/z^2) - O(1)) for y >> z^2, uniform in x, giving J(P(z)) << z^2, and it is the linear sieve run exactly at its sifting limit beta_1 = 2 with no slack outside it; no two-class analogue exists in print at any exponent, the corpus's own x^4.2665 is beta_2 by the same mechanism, and every remaining branch of the field (Matomaki-Radziwill, Gorodetsky, Friedlander-Iwaniec Cor 6.28, Gafni-Tao) carries the almost-all quantifier, which a second-moment statement can never convert into a bound on one empty window. | [recon-0828-rough.md](history/staging/recon-0828-rough.md) |
| 0 | `Q-recon-0828-sieve` Is there anything in the 2008-2026 sieve literature, or in the parity-breaking literature, that lowers beta_2 = 4.26645 or supplies a consumer for a level theta > 1 on the two-class comb? | ANSWERED | No route. Twenty-one angles examined, nineteen dead on arrival, nothing in print beats 4.26645 at kappa = 2 at any level on four calibrated channels; the two survivors are an owning-convention row and one unresolved hypothesis in a five-page 1990 announcement whose stated requirement beta < 3 excludes beta_2 = 4.26645. | [recon-0828-sieve.md](history/staging/recon-0828-sieve.md) |
| 0 | `Q-recon-0829-escapes` Each of the three killers is an obstruction shape that occurs elsewhere in mathematics; where has each shape been beaten in print, by what mechanism, under what hypothesis, and does that hypothesis hold for the tile and zone objects? | ANSWERED | Of nineteen escapes read, fourteen fail a hypothesis check (twelve on a fact already in this corpus), four fail some other way and one (the decoupled vector sieve) stays OPEN as the programme's existing road, so no route opens; Granville-Soundararajan's uncertainty principle is NOT killer 3 in print, is adverse-direction, and is already cited here twice. | [recon-0829-escapes.md](history/staging/recon-0829-escapes.md) |
| 0 | `Q-recon-0829-farfields2` Do any of eight fields still absent from IMPORT-MAP.md and from the three 2026-08-28 recon notes hold a theorem whose hypothesis the tile or the zone satisfies exactly and whose conclusion is a lower bound on a periodic set's count in every window, a maximal-gap bound for a product-structured periodic set, or a positivity statement at a distinguished point? | ANSWERED | No route from any of the eight; the pass banks one PUBLISHED-ANCHOR (Holt and Rudd's transfer matrix has its full spectrum in print, second eigenvalue a2 = prod_{17<=q<=p}(q-3)/(q-2), printed 0.10206751799779 at p = 999999999989, decaying only like 2.82/ln p, and this corpus's prior-art record names the eigenstructure and the binomial eigenvectors but carries the per-prime eigenvalue (p-j-1)/(p-2) at lit-pdf-holt-rudd.md line 259 but no product-over-primes closed form, no numerical value and no rate), one CLOSURE with mechanism (Beurling-Selberg is the proof device behind the large sieve, whose constant N-1+1/delta is an l2-to-l2 statement and whose error 1/delta exceeds the window at the operative theta_total > 2, so the whole extremal-function family reproduces a row already rejected), and three wall addresses; two angles are TPC-strength at the form that would pay and are labelled (ii). | [recon-0829-farfields2.md](history/staging/recon-0829-farfields2.md) |
| 0 | `Q-recon-0830-rec-killrun` Does the literature hold, in its own conventions, a theorem whose hypotheses REC(s, u0) (the sup-versus-rms recovery of the level-D signed remainder over all positions, attack-0829n-rml-proof.md section 3) or the weighted kill-run K*(s) (the longest run of level-s slots the primes in (s, 2s] can kill, attack-0829n-doubling-bridge.md sections 0 and 3) satisfies as stated, or a Maier-type theorem that makes REC false for two-class sifted sets at some u0 below beta_2? | ANSWERED | No theorem applies to either object as stated, on four calibrated channels searched in the owning conventions; every neighbour is graded NEAREST with its unmet hypothesis named, and neither object is on any refuted row. On the Maier question the answer is negative for REC as stated (the Maier family bounds the COUNT, i.e. the full-level remainder, never a level-D truncation) but carries one calibration: at one class and full level the REC-shaped inequality is FALSE asymptotically, by Buchstab's origin ratio against the Montgomery-Vaughan full-period variance ceiling, and the embedded arithmetic puts the level where that falsity first shows at log10 z between 16 and 141 depending on u0 and epsilon, so a finite-z margin of the kind the corpus measures cannot see a failure of this type; at two classes the same full-level statement is HL-conditional at u0 = 2 and unlocated in print at any u0. No exponent moved. | [recon-0830-rec-killrun.md](history/staging/recon-0830-rec-killrun.md) |
| 0 | `Q-recon-0904-sifting-limit-floor` What is actually known, in the owning convention and at the page, about LOWER bounds on sifting limits at dimension kappa > 1, and is the class-blind cap at beta_2 = 4.26645 a barrier or a method artefact? | PARTIAL | Both. The corpus's [ABSENT] is wrong for lower bounds and right for extremal examples: Selberg's Lectures section 17 and Brady's 2017 Corollaries 1 and 3 ARE lower bounds on beta(kappa) at kappa > 1, invisible because Selberg's convention is the reciprocal a_k = 1/beta_kappa so his lower bounds are titled "upper bounds for sifting limits", while no kappa > 1 extremal example exists and Halberstam's own 2003 review says so; the best floor on beta(2) resting on a citation is 1.8394 from Brady's reduction evaluated at kappa = 2, unconditional and below the band, and beta(2) >= 2 follows from monotonicity by a padding argument DERIVED here and probably folklore; the cap at 4.26645 is a METHOD ARTEFACT at rung MEASURED, since the level-D LP is exactly the axiom-only information class and its calibrated floor of 3.3152 sits about 18 per cent below the DHR value and passed, 0 of 15, its first external test against the published beta_3 and beta_4; the band (2, 4.26645] is untouched by anything proven. | [recon-0904-sifting-limit-floor.md](history/staging/recon-0904-sifting-limit-floor.md) |
| 0 | `Q-redteam-0828-closures` Do the five 2026-08-28 closure notes stand, and do they stand for the reasons they give? | ANSWERED | Three stand on corrected sentences (1d, Z5b, 0); one stands in half (10, the 1.074 counter-claim does not); one does not stand for its stated reason (1c, closed on a narrower window than the prior work's significant one, and its CLOSED has overwritten a PARTIAL in the generated index). | [redteam-0828-closures.md](history/staging/redteam-0828-closures.md) |
| 0 | `Q-redteam-0830-floor-growth` Does the DERIVED growth half of attack-0830-rec-cheapest.md sec.4.2 (Omega >> z^{16s/9}/ln^8 z from four-prime Rosser exit chains) survive an adversarial re-derivation on independent code, does it really make REC(s, u0) false for every u0 < 16s/9, and does the blind slope test of blind-0830-omega-floor.md test the LAW or the CONSTRUCTION? | ANSWERED | No break found in six attacks, so the growth half SURVIVES this pass and stays DERIVED (one failed break is not a proof, and the whole thing still rests on the exact half E1-E3 that this pass did not grade); but four claims are corrected - the threshold 16s/9 needs the unstated hypothesis s <= 3 (above it the four-prime LP maximum is 2(2s+2)/3, then 8, both below 16s/9, though the corollary that every legal u0 < beta_2 fails survives at every admissible s because 2 x LP-max > beta_2 for all s > 9beta_2/16 = 2.3999), the 2s - o(1) limit needs 3^k <= ln D / ln 8 so only k = 2 is available at every z below 1.1e9, A_i is >= not ~ the dyadic count, and the certified ratio does NOT rise monotonically (0.0118, 0.0128, 0.0101, 0.0057, 0.0051, 0.0093, 0.0336, 0.0801, 0.1658, 0.3545 on my own recount, which reproduces all ten S4b rows digit for digit); the blind test is ruled a test of the CONSTRUCTION's count and not of the law, since it cannot see E1-E3 or the CRT step; on the ruling Chris asked for, the floor does make the RML route a truth gap asymptotically and conditionally on E1-E4, and changes nothing computable, the literal construction first passing H = z^{u0} at z ~ 5.6e31 on the constant 2.93e-4 measured here; no exponent moved. | [redteam-0830-floor-growth.md](history/staging/redteam-0830-floor-growth.md) |
| 0 | `Q-redteam-0830-floor-sign` Does the EXACT half of attack-0830-rec-cheapest.md sec.4 (E1-E4, the sign facts, the window bound T <= cc(r) + H - 1, the exact Omega, and sec.(d)/(e)'s calibration sentences) survive an adversarial re-derivation on independent code, and does it by itself constrain REC at any u0 without the growth law? | ANSWERED | The mathematics STANDS as PROVEN and is stronger in two places than the note claims, but it constrains REC at NO u0 by itself: E3's identity is pure algebra and holds at every position (0 mismatches in 20.5M positions, both s), E2 holds at every divisor n > 1 under three disjoint routes at every s >= 1 and FAILS at s = 0.8, locating a hypothesis D >= z the note omits, E4 has 0 violations at every x over four complete periods with the wrap, and Omega is reproduced by an independent enumeration at all 26 tabled values and EXTENDED to z = 101 (285, 441, 684, 990, 1155 at z = 79, 83, 89, 97, 101), confirming blind-0830's exact 684 and 1155; three sentences are wrong -- E1's "every pair with gcd \| 2 is realised" (exactly half are; the missing half is all those with 2 dividing one side), the ledger's and sec.0's "251 against z^{u0} = 1.05e6" (1.05e6 is HM, z^{u0} = 7.19e7, so the gap is understated 68.3x), and sec.4.4's reason for lam+(P(z)) = 0 (0.24 exceeds 1/8; the figure that closes the slab is 0.1199 at z = 89, under 1/8 by 4 percent) -- and sup\|rho~\| >= (Omega - M)/2 is loose: sup\|R_1\| = Omega + M exactly. Every exactly known log_z Omega is under 2 while REC needs it above u0 > 2, so the exact half touches REC at no u0 and every adverse consequence in the note still rests entirely on the growth half. No exponent moves. | [redteam-0830-floor-sign.md](history/staging/redteam-0830-floor-sign.md) |
| 0 | `Q-redteam-0830-imports` Do the six lighter notes of 2026-08-30 (varE-identification, smooth-aps, rec-killrun, skeleton-door, at43-bigint, coherence) survive an adversarial pass on independent code and at the source pages, and which of their load-bearing claims are wrong? | ANSWERED | No note is refuted whole and no exponent moves. Every decisive measurement reproduces on code sharing nothing with the producers: the varE mixed remainder and its 0.844 / 0.826 share below 2L and 94.4 / 98.7 percent unbalanced share at x = 13, 17; the Buchstab deviations and all three crossing levels log10 z* = 33.53, 68.80, 33.62; the skeleton door's 9.2 / -0.9 percent, G30_agg 0.1113 / 0.1011 and the 0.0102 cap at @13, @17, by a path that also verifies cap-36 Theorem A; the @43 parity exactness on all 26,157,448 scour classes with 0 above 2^54 and a constructed @47 counterexample; and the five recon-0828 verdict counts summing to 75, which REFUTES rec-killrun's brief-error clause and confirms the orchestrator's rider. Seven claims WEAKEN. The load-bearing one is smooth-aps's "the weight is unmet in print": Harper's J. London Math. Soc. 112 (2025) e70293 proves a Barban-Davenport-Halberstam asymptotic for an ARBITRARY sequence on exactly that dyadic all-classes object, and his own footnote says the missing max over x' can be incorporated, so the NEAREST citation changes even though the step still does not close (the 2025 range is sqrt(2x) < Q <= x and its Theorem 2 route bars sieved sets by name). Also: Henriot Corollary 2 applies, but to the ERRATUM's statement and under two hypotheses the note leaves unstated (eps < alpha/600, not "every eps"; F at prime powers); varE section 4's display (*) carries an unfilled placeholder and is vacuous by a factor L/d; the skeleton door's "would tighten" is wrong in sign at @17, where the closable block is negative and removing it RAISES G30_agg to 0.1020; Halasz-Montgomery is not applicable for the reason given (it is an abstract inner-product inequality); FGKT's heuristic quote is on p. 4, not p. 3; and the "~13x had no source" is a corpus miss, the retired G2-walk figure at CHANGELOG.md:5716. Not TPC-strength; nothing here opens a route. | [redteam-0830-imports.md](history/staging/redteam-0830-imports.md) |
| 0 | `Q-redteam-0830-rml` Do the three HELD notes of 2026-08-29 night and 2026-08-30 on the RML chain survive an adversarial pass — the six-arrow chain and the term-count cap lemma of attack-0829n-rml-proof.md, the same-object ruling and the applied replacement sentences of verify-0830-usup-convention.md, and the reflection identity, custody, pilot bounds and sealed forecast of measure-0830-rho-sup-z41.md? | ANSWERED | The three load-bearing PROVEN claims survive independent re-derivation — the CAP lemma (every step, sine sum at worst ratio 0.585568, the constant 6, 0 per-modulus violations at z = 13, 17), the reflection identity rho~(W-3-y) = -rho~(y) (proved here and its two hypotheses verified at z = 13..37, residual <= 1.7e-10 at every position of z = 13, 17, 19), and the same-object ruling (an independent lattice reproduces the repository's term multiset exactly at z = 13..37 and its {Vabs > 0} set equals LSE's records at all ten levels); five of the seven cited exact sups and three of the five walked sup\|R_H3\| reproduce to <= 5.0e-7, and every figure of the sealed z = 41 forecast reproduces from the seven cited sups alone. Fourteen claims do not survive, none of them reopening a route. The load-bearing one is RML sec.2's ms_m/ask column: it measures the PROVEN mean-square BOUND sqrt(B H), not the <R_H^2>^{1/2} that REC names, the two differing by 36.53x to 200.45x on the tabled rows because <R_H^2> saturates in H while B H does not, so sec.5's ordering (ask below the Gaussian factor at u0 = 3.0 and 3.5) is an artifact and reverses at every row against the true mean square. "gauss -> 0" (sec.5) and "sup/rms <= sqrt(2 lnW) O(1) = z^{o(1)}" (sec.3) are the same error twice, against the note's own sec.0: sqrt(2 ln W) = z^{1/2+o(1)}, measured gauss 0.7905 at z = 19 falling to 0.5645 at z = 1e7, limit 1/2. "the recovery exponent is log_z(2 sup\|rho~\|/rms): about 0.99-1.29" quotes the truth column, which is log_z(2 sup\|rho~\|) alone; the quantity named measures 0.5628 to 0.6712. "REC would be moot rather than false" should read false. "u_cap -> 2s + o(1)" and "n ~ z^{2s}/polylog" are asserted where only "<=" is proven and the data cannot decide: u_cap is 4.2652 at z = 47, crosses beta_2 only at z = 53, reaches 4.4891 at z = 79, and passes u_triv from z = 53. "seven points spanning less than one octave" is 1.509 octaves, still uncorrected in three places including the ledger verdict. verify-0830's applied "polynomially many from z = 223 on" is true at every z >= 13, and its z = 331 crossover silently sets A = 1 (A fitted to LSE's own Ssat moves it to 337). No exponent moves, no route opens or closes, and no ledger verdict changes. | [redteam-0830-rml.md](history/staging/redteam-0830-rml.md) |
| 0 | `Q-redteam-0904-floor-growth-2` Does the growth half of the adverse pointwise floor (Omega >> z^{16s/9}/ln^8 z from four-prime Rosser exit chains) survive a SECOND adversarial pass, and does a floor on the certificate at a CRT-planted window make REC(s,u0) false (a truth gap) or only unprovable by that certificate (a proof gap)? | ANSWERED | SURVIVES, at the same rung and no higher: four new attacks and two unasked ones found no break, so the growth half stays DERIVED and red-teamed twice, which is two failed breaks on a derivation and not a proof; the proof-gap reading is REFUTED because REC is a statement about R_H, the remainder of the very certificate the floor bounds below, and the chain has no step where a certificate value must become a true remainder, so it is a truth gap for REC as the corpus states it; five corrections are owed to the record -- the REFUTED row is UNSCOPED and should read "on the Rosser vector-sieve lattice at equal levels" since only the Rosser instance is derived, the "falsity beyond z ~ 5.6e31" is an s = 2.698721 figure quoted without its s and the fitted crossing at the corpus's own measured family s = 3.0 is z ~ 10^15.3, the analytic p* window (4D^{1/27}, D^{1/9}/4) is neither necessary nor sufficient at reachable levels so the exact onset is 4.42e5 at s = 3.0 rather than the quoted 1.055e6, the four-prime construction has NO exit prime below z once s >= 7 so the first pass's "8 beyond s = 5" holds only on [5,7), and the first pass's escape-(a) density 1/W understates the planted class by the factor W/(n1n2) though the escape still fails by an exponential; the LP maximum 8s/9 is confirmed as an exact vertex and the corollary crossing reproduces 9beta2/16 to 4.4e-16, the pre-registered slope band held at a new s (top step 4.9025 at s = 3.0 against a model 4.8990), and no exponent moved. | [redteam-0904-floor-growth-2.md](history/staging/redteam-0904-floor-growth-2.md) |
| 0 | `Q-redteam-0904-item0` Do the two HELD notes of 2026-09-04 on item 0, the second adversarial pass on the adverse floor's growth half and the L7 one-class-to-two-class transfer, survive an independent adversarial pass, and do the live-layer changes they propose survive verbatim? | ANSWERED | Both notes SURVIVE at their own rungs and neither moves an exponent, but SIX of their proposed live-layer changes need rewording and two of their supporting derivations are wrong; every load-bearing number reproduces on independent code (18 of 18 A1A2 cells digit for digit, the LP maximum 8s/9 at 0 deviations of 16 with residual 4.441e-16, the crossing 2.399878284834 against 9beta2/16 at 1.097e-13, the fitted C = 1.1206e-4 and the s = 3.0 crossing 10^15.30, the onsets 4.390e5 / 1.111e6 / 1.860e6, ln(n1n2) = 7.4993e7, and the L7 CRT counts EQUAL at x = 7, 11, 13), so the truth-gap reading of REC is CONFIRMED and the growth half stays DERIVED and red-teamed twice, not proven; what does not survive is the scoping, the exit-window and the price wording: the proposed clause "at equal levels D1 = D2 = z^s" is NARROWER than the derivation supports, since over 1643 admissible upper-and-lower level splits the floor beats the decoupled window at every cell by at least 0.644444, so no level split escapes and the sibling rider "asymmetric levels give 8s1/9 + 8s2/9 with s1 + s2 pinned" is REFUTED as written (it holds only while both s_i <= 3); the record's z ~ 5.6e31 is u0-specific as well as s-specific (10^31.68 at u0 = 4.2165 against 10^35.36 at u0 = beta2, same s), so replacing it with a beta2-convention 10^15.30 mixes two conventions; the onset correction is right numerically and wrong in wording, since at the record's own s = 2.698721 the exact onset is 1.875e6, LATER than the quoted analytic 1.055e6, not earlier; the escape-(a) correction is right in substance but its "(A1A2)^2 / (2 n1n2)" is a LOWER bound on the split's contribution, and the two-sided version through lambda+(n) <= 2^omega(n) reads 10^{-3.004323e+7} against B ~ 10^{10.1}, still no contradiction; and on the L7 side the union-bound argument and the CRT count are CONFIRMED while the coupled vector-sieve price 2(1 + sqrt e) = 5.297442541400 is the FORCED-equal-level constant, the corpus's live figure being K_BF = 5.158064680330, reproduced here to twelve digits at (a, b) = (2.229949, 2.928115), and the sieve-on-holes is the vector sieve only after the Ford-Halberstam substitution step that sift-limit-attack.md 7b(1b) already owns; the "no third mechanism excluded" line is honest but incomplete, since weighted sieves with Chen switching are already priced and closed at sift-limit-attack.md 4.2; scope of death gains one row, L7's mechanism 2, which the growth note's own section 10 calls untouched while its sibling calls it dead; no exponent moved. | [redteam-0904-item0.md](history/staging/redteam-0904-item0.md) |
| 0 | `Q-redteam-0904-sifting-limit` Do recon-0904-sifting-limit-floor.md's five claims survive adversarial re-derivation at the page, and in particular is the 4.26645 cap a method artefact at rung MEASURED? | ANSWERED | Four of five claims survive with corrections and the headline does not. Claim d is REFUTED as stated on four grounds, each sufficient: the level-D LP fixes one omega-profile out of a class Ford defines by a ONE-SIDED inequality, and inside the classical (Omega_2(kappa,L)) budget a legal profile at x = 13 gives a calibrated reading of 5.0113, above beta_2 = 4.26645, which fires the target note's own pre-registered refutation of its floor; the calibration is a 1.72 multiplicative correction fitted at one point and it misses the second proven point beta(1/2) = 1 by 66 to 82 per cent, two and a half times the 28.7 per cent effect the headline rests on; the pooled 3.3152 averages four statistics of which only s* is the definitional analogue of beta, and that route reads 3.4678 here and 3.9487 at x = 43 in the corpus's own data, still climbing at +0.4297 per ln x with the fitted line reaching 4.26645 at x = 104; and 3.3152 is 22.2961 per cent below 4.26645 rather than the 18 per cent the note prints. Claim a is CONFIRMED with a second source off the OCR channel (Ford 2023 p. 37, "Some authors, e.g. Selberg, refer to 1/beta(kappa) as the sieve limit"), one page correction owed (Halberstam is p. 117, not p. 116). Claim b is CONFIRMED and strengthened: Brady's class is stated on his p. 10 and IS the axiom-only interval class Face 4 needs, his v_R table is reproduced here, and the identity v_{2d+2} = v_{2d+1} his proof asserts is confirmed at d = 0, 1, 2, so 1.819592 rests on proved facts alone. Claim c is CONFIRMED but demoted: beta(2) >= beta(1) = 2 is two lines from Ford's own one-sided (Omega) plus his own beta(1) >= 2, so the padding construction is correct and unnecessary. Of the eight proposed live-layer changes, two survive verbatim, five need rewording and one is refuted; the new SEARCH-CONVENTIONS row adds exactly three clearing phrases and changes nothing for any existing absence claim. | [redteam-0904-sifting-limit.md](history/staging/redteam-0904-sifting-limit.md) |
| 0 | `Q-rho-maximal-law` What is the rho maximal law, what is its weakest sufficient form against the crossing, and where does it sit against print? | PARTIAL | The pricing lemma turns any RML(alpha) with alpha < beta_2 = 4.26645 into G2(z#) << z^alpha ln^2 z, every step proven except the law itself; the sufficiency curve lambda_max falls from 2.31949 at z = 13 to 1.78446 at z = 47, the weakest measured point, and whether it ever reaches zero is model-dependent and undecided, so nothing here is an unconditional exponent. | [rho-exact-z31-01.md](history/staging/rho-exact-z31-01.md), [rho-maximal-law.md](history/staging/rho-maximal-law.md) |
| 0 | `Q-rho-sup-z41-0830` What is the exact sup over all positions of the centred sawtooth remainder at z = 41 (period 7.42e12), and of R_H at H = z^3 and z^4, and what does the eighth exact point do to the truth's slope and to the u0 = 3 form of REC(s, u0)? | PARTIAL | Not run in full; the exact z = 41 point prices at 4.8 to 5.4 h on this machine from measured per-position costs (naive 69.8, table 23.5, table-plus-windows 36.6 ns per worker; fleet 4.52 ns of wall at z = 41), above the 3.5 h rule, so what exists is a new engine (a PROVEN reflection that halves the walk, a P(29) periodic table worth 2.9x, per-block exact re-seeding) reproducing every cited exact sup at z = 13..37 digit for digit, sup\|R_H\| at H = z^3 walked for the first time at z = 19..37 (F3 = 26.4 to 35.9, the factor 2 was 1.5 to 2.2x loose), a sealed pre-registration (forecast sup 60.07, band [47.25, 76.37], kill needs sup\|R_H3\| >= 1807.417), one pilot twelfth giving lower bounds sup\|rho~\|(41) >= 70.651250 and sup\|R_H3\| >= 64.416936, and an eleven-segment plan for the box; no bound-and-prune exists on three routes; nothing asymptotic can move whatever the point turns out to be. | [measure-0830-rho-sup-z41.md](history/staging/measure-0830-rho-sup-z41.md) |
| 0 | `Q-rho2-bound` Is there an analytic upper bound on <rho^2>(z) from its proven closed form, and does it matter for RML? | ANSWERED | Already proven 2026-08-21 (attack-rhoms-01); the constant is now named, 170.88 z^{2s} ln^8 z; Chebyshev off any second moment diverges from RML (the true C_L = ms = 1 floor clears at z = 41 and 43 and misses by 2.155x at z = 47), so it is an ingredient, not a route. | [attack-rhoms-01.md](history/staging/attack-rhoms-01.md), [rho2-analytic-bound.md](history/staging/rho2-analytic-bound.md) |
| 0 | `Q-rml-proof-0829n` Starting from Lemma V's PROVEN mean-square bound, what is the exact chain of implications to a two-class exponent below beta_2 = 4.26645, which single arrow is open, and does it close? | PARTIAL | The chain from the proven mean square to an exponent below beta_2 has exactly one open arrow, the mean-square-to-sup recovery REC(s,u0): sup_x \|R_H(x)\| <= z^{u0/2 - eps} rms(R_H) at H = z^{u0} for one fixed u0 in (2, beta_2); every attempt here dies at a named place (term-by-term accounting is capped at 2s + o(1), the trivial-level exponent; position-union pays e^{theta(z)/q}; window smoothing and the P(y) lever move polylog only; the smooth-profile form is closed on hypothesis and priced above beta_2), the arrow is measured TRUE with certified margin z^1.72 to z^1.92 at u0 = 4 over z = 19..37 and the truth's slope 2.766 +/- 0.212 sits 5.8 se under u0 = 4 on seven points under one octave, so the failure is a proof gap at every computable z and undecided asymptotically; no exponent moved. | [attack-0829n-rml-proof.md](history/staging/attack-0829n-rml-proof.md) |
| 0 | `Q-tail-deficit-model` Does the exact compound-geometric thinning of the previous level's own gap histogram, with the qualifying-gap constraint g = 0, +/-2 (mod q) carried through the ladder, predict the tile's tail-deficit factor G2/(mbar ln D) at zero parameters, and does that make object-models-read-0829's D5 residue-level classification constructive rather than inferred? | ANSWERED | NO. The zero-parameter CRT-constrained thinning predicts a tail HEAVIER than the tile's at every level, delta_M2 = 0.6461, 0.6746, 0.7021 against a measured 0.4577, 0.4463, 0.4791, so the pre-registered "classification was wrong" arm fires and D5 returns to OPEN with C3's constructive route REFUTED; the constraint is informative but small, carrying 4.0 to 10.0 percent of ln(null/truth) at the far tail, or 7.7 to 14.4 percent read against a rate-matched control, against the grain's ORDER at 39.4 to 54.6 percent at the deepest abscissa each level resolves; at shallow abscissae the ordering reverses (B 8.7 against C 4.8 at x = 23, u = 4), which the exact operator on a shuffled true grain confirms without any model (maximum 276, 354, 426 against the true 204, 258, 348), and the order effect is now localised (sections 7 and 9): a first-order Markov word from the true adjacent-pair statistics carries 32.3, 34.2 and 60.8 percent of ln(shuffled/truth) at the deepest abscissa of the three folds, and a SECOND-order word from the true adjacent-triple statistics carries 97.3, 97.9 and 102.6 percent there, r = 0.972, 1.061 and 1.000 on draw-mean maxima over 40, 20 and 10 draws, so the folded tile's tail is MEASURED to be a function of the previous grain's three-consecutive-gap statistics and of essentially nothing longer-range; that surrogate is seeded on the true previous grain at one fold, is not iterated, predicts no delta and does not revive C3, and the 348.0 sd 0.0 at 29->31 rests on ten draws. | [measure-tail-deficit-0829.md](history/staging/measure-tail-deficit-0829.md) |
| 0 | `Q-theta-ladder` Does the all-positions exponent theta turn over below 2, converge to exactly 2, or settle above 2? | CLOSED | The answer is above 2 with an amendment, and the route is retired regardless: theta does not turn over (it dips and comes back, need/z^2 = 0.3550 to 0.6119 at z = 13..31 and rising from 31), convergence to exactly 2 is not supported (e = 1 rejected at 95% in all four fits), point estimates run 2.37 to 2.99 without settling, and OUTCOMES.md records the certificate route as RETIRED because the sharp maximal law it needs is itself TPC-implying. | [theta-ladder.md](theta-ladder.md) |
| 0 | `Q-usup-convention-0830` Are lemmaV-sup-extension.md's u_sup and u_sat and attack-0829n-rml-proof.md sec.4.1's CAP(z) statements about the same object (level D = z^s at s = 3.0, same moduli, weights and normalisation), so that the sec.4.1 correction in passing applies, or does a level-convention mismatch void it? | ANSWERED | SAME object, VERIFIED at the code: both notes build the lattice through buildTerms(z, z^3), the modulus sets and Vabs(e) agree to 6.9e-18 at z = 13..23 and the count convention matches at all ten levels, the cited Ssat and u_sat reproduce on the RML lattice to every printed digit at z = 13..19 and the full-level alternative does not (19.544 against 19.602 at z = 13, 45.827 against 50.314 at z = 17); so the PROVEN cap Ssat <= CAP <= z^{2s+o(1)} applies and refutes lemmaV-sup-extension.md's asymptotic prose at lines 485-486 and 508-516 (2^pi(z) moduli, a C^pi(z) theorem as the reachable end), while sec.4.1's attribution sentence overreaches by calling that note's "reading" a shape it lists as one of two indistinguishable fits and flags as its likeliest error; neither ledger verdict line changes. | [verify-0830-usup-convention.md](history/staging/verify-0830-usup-convention.md) |
| 1d | `Q-applied-0828-closures` Were the closures red team's corrections applied to the five HELD notes? | ANSWERED | Applied. 47 prose corrections across the five notes; c2prime-refit-22 drops from CLOSED to PARTIAL and three ledger verdicts are rewritten; four producer READINGS blocks and eleven live-document lines carry the same defects and are listed here uncorrected, behind the fence. | [applied-0828-closures.md](history/staging/applied-0828-closures.md) |
| 1d | `Q-delta-reader-0830` Can any instrument read the sign of the log-power correction delta in G2 ~ c n^beta (ln n)^delta at reach 79, passing the one-class control first? | ANSWERED | No. Six readers were pre-registered against stepped synthetic laws and the one-class control; the four power-chain readers (the diagonal meter among them) are killed by the P(n) stepping alone, the joint fit is calibrated but reads the control's finite-reach delta NEGATIVE (-0.38 +- 0.14 at 64 terms) where its conjectured asymptotic delta is +2, and the one reader that passes does so by importing the exponent, its sign being the sign of (1.777 - beta_hat). delta's sign for G2 is unreadable at reach 79 by any instrument tried, and the control shows a finite-reach reading would not carry the asymptotic sign anyway; item 1d's all-bases form stays unattackable. | [measure-0830-delta-reader.md](history/staging/measure-0830-delta-reader.md) |
| 1d | `Q-fekete-1d-defect47` Does the bounded-defect Fekete route survive a probe at 47#? | PARTIAL | The defect at 47# is ordinary and the 47# enumeration cannot move item 1d's TPC threshold whatever value it returns; the bounded-defect Fekete lemma is stated exactly and proved with every hypothesis except the candidate itself discharged, so the route reduces to one named inequality and is neither closed nor open beyond that. | [fekete-1d.md](history/staging/fekete-1d.md) |
| 1d | `Q-g2-falls-decision-rule` Does G2(x#)/x^2 fall, and what pre-registered decision rule would settle it? | PARTIAL | The instrument is calibrated and sharp, resolving the one-class control at 11.6 sigma on the same nine points where it returns 0.9 sigma on G2, and the honest band on the slope is +/-0.117 at nine terms, so the rule is registered; but the power analysis puts separation at x = 53 only if the falling law is x ln^2 x and at x = 151 if it is x ln^3 x, so phase 1's extra terms settle nothing and no reachable exact ladder does either. | [phase1-T3prep-decision-rule.md](history/staging/phase1-T3prep-decision-rule.md) |
| 1d | `Q-hsub-reductions` Can (H-sub) be proven or refuted, and what does the fold machinery reach? | PARTIAL | Neither, but the statement is smaller: three reductions of the hypothesis are proven, the lemma consuming only power pairs so that it weakens to (H-sub-pow) with the conclusion unchanged, the fold machinery's inability to reach any of them is made exact, and the hunt over all 111 reachable pairs found no drifting family and no counterexample. | [attack-hsub-01.md](history/staging/attack-hsub-01.md) |
| 1d | `Q-hsubpow-K` Can (H-sub-pow) be proven with an explicit K in the legal zone? | CLOSED | NO by three mechanisms: the CRT lift (K* >= pi(y') - pi(y) diverges), anchored caps (diverge at every base), Iwaniec at two classes (it IS beta2-note); TODO 1d's legal zone is mis-stated, the trusted zone is [1.3946, 11.3568). | [hsubpow-explicit-K.md](history/staging/hsubpow-explicit-K.md) |
| 1d | `Q-hsubpow-K-0829n` Can (H-sub-pow) be proven with an explicit K inside the trusted legal zone [1.3946, 11.3568) by a mechanism the 2026-08-28 pass did not close? | OPEN | No K is proven at any base; the single open inequality is the uniform-in-k ratio cap G(b^(k+1))/G(b^k) <= e^K G(b), which is a proof gap at a fixed base and a possible truth gap across bases, since for any law G ~ c n^beta (ln n)^delta the all-bases hypothesis holds with finite K if and only if delta >= 0. | [attack-0829n-hsubpow-K.md](history/staging/attack-0829n-hsubpow-K.md) |
| 1d | `Q-import-interp` Does the Bayati-Gamarnik-Tetali interpolation method reach the G2 Fekete object? | ANSWERED | No: BGT closes on hypothesis H1, since the constraint count never splits (pi(st) - pi(s) - pi(t) is zero at no pair with st >= 25, minimum 2, maximum 12, VERIFIED on 104 pairs), and the one coordinate that does split has limit +infinity; the row lands as WALL-ADDRESS plus the identity that the submultiplicativity defect is the Overshoot slack. | [import-interp.md](history/staging/import-interp.md) |
| 1d | `Q-redteam-0828-closures` Do the five 2026-08-28 closure notes stand, and do they stand for the reasons they give? | ANSWERED | Three stand on corrected sentences (1d, Z5b, 0); one stands in half (10, the 1.074 counter-claim does not); one does not stand for its stated reason (1c, closed on a narrower window than the prior work's significant one, and its CLOSED has overwritten a PARTIAL in the generated index). | [redteam-0828-closures.md](history/staging/redteam-0828-closures.md) |
| 1d | `Q-redteam-0830-fekete` Do the load-bearing claims of attack-0829n-hsubpow-K.md (the sign lemma, the K -> beta_bound map, the zone, the TODO.md base-16 correction) and measure-0830-delta-reader.md (the six pre-registered readers, their kill gates, the joint fit's calibration, the RB circularity argument) survive independent re-derivation, and are the two live-doc corrections they caused the right sentences? | ANSWERED | Every number in both notes reproduces on independently written code (all 14 cells of the beta_bound / K_min table, all 48 cells of the reader-calibration table, all 24 figures of the real-control table, the margins, the sups, the 5.607 correction, the 10-of-81 count), and the sign lemma is re-proven as stated for continuous exact laws. Two claims are WEAKENED and one live-doc sentence needs a qualifier: the sign lemma's constant 1.0597 loses 43% of its value if the base floor moves from 2 to 3 and its whole shape fails for the stepped law that a primorial ladder must present, where beta re-enters the sup and a delta = 0 law already needs K = 1.37 at beta = 2, inside the trap; and TODO.md 1d's "the sign of delta is unreadable for G2 at reach 79 by any instrument tried" is wrong on the letter, since reader RB passed all four pre-registered criteria and read delta_hat = +0.80 +- 0.09, the note voiding it post-hoc on a circularity the pre-registration flagged but did not make a kill criterion; the honest sentence adds "non-circular". No claim in either note is refuted. | [redteam-0830-fekete.md](history/staging/redteam-0830-fekete.md) |
| 1d | `Q-y2-recompute` Does the sixteen-level Y2 ladder reproduce on the corrected instrument, and does Y2/x^2 fall? | ANSWERED | The ladder reproduces exactly, sixteen of sixteen from sixteen independent processes, digit for digit against the published 2026-08-18 ladder, and Y2/x^2 falls at 15 of the 15 consecutive steps; this does NOT show that G2(x#)/x^2 falls, since the shortfall Y2/(G2-1) is unmeasured above x = 79. | [y2-recompute.md](history/staging/y2-recompute.md) |
| 0b | `Q-gate-multiplies` Does "the gate multiplies" close the entire u-frame recursion branch, or only the merge chain? | ANSWERED | Only the merge chain and one relative of it: the no-fixed-point argument does not reach TODO 0b at all, though 0b is wrong as stated for an unrelated reason and the error is a factor of ln u; what survives is the copy theorem for maxsum (VERIFIED 40 of 40), which needs a residue-deleted maxsum bound that does not pass through a kill count. | [gate-multiplies.md](gate-multiplies.md) |
| 0b | `Q-import-thinning` Do point-process thinning and interval coalescence give H'' a null model? | ANSWERED | Yes and exactly: the fold recursion is an exactly solvable thinning whose gap pgf transforms by a Mobius map fixing 0 and 1, so under independent thinning the gap word of T_x is exactly geometric with mean mbar/6 at every rung with no error term, which turns both of the record's fitted parameters into derived ones. | [import-thinning.md](history/staging/import-thinning.md) |
| 0c | `Q-0c-holesweep` At a fold, how does maxsum degrade copy by copy as the two deleted residues sweep through their possible positions? | ANSWERED | The full curve is on disk for nine folds (5->7 through 31->37, every copy) and it is a PALINDROME: the Mirror-Sweep Lemma is proven here and verified exhaustively, giving the fingerprint any kill-count-free bound must reproduce, but no such bound was produced by this pass. | [attack-0c-holesweep.md](history/staging/attack-0c-holesweep.md) |
| 0c | `Q-0c0e-level-selection` Can a residue-deleted maxsum bound that only has to hold at levels of the argument's choosing carry the weak Zone Postulate? | CLOSED | CLOSED, and the mechanism has a name: the level-selection licence is worth 0.3187 nats once and is falling, no selection rule beats its own null by anything worth having across T_11..T_29, and the BV/EH sweep supplies no moduli-selecting statement to spend. | [attack-0c0e-level-selection.md](history/staging/attack-0c0e-level-selection.md) |
| 0c | `Q-foldL-maxsum-direct` Can maxsum_m(T_x), plain and residue-deleted, be bounded above by an argument that never counts kills? | CLOSED | The brief's premise contradicts the corpus's own Bridge Floor (maxsum_k >= maxsum_1 = G2(T_x) for every k), so the bridge cannot convert far enough however good the bound is; all four routes close (R1 partial then closed, R2 tautological and quantitative, R3 busts the budget), and the order-m object is in print, so item 0c's absence sentence has to change. | [attack-foldL-05-maxsum-direct.md](history/staging/attack-foldL-05-maxsum-direct.md) |
| 0c | `Q-import-chaining` Can Dudley's entropy bound or Talagrand's generic chaining beat the union bound over positions on the maxsum law? | CLOSED | No, and the reason is geometric rather than probabilistic: the entropy integral of the true increment metric is already 1.054-1.099 times rms*sqrt(2 lnW) at its lower branch and 1.484-1.545 at its upper, flat across z = 13..23, so chaining's ceiling with a perfect universal constant sits below the union bound's floor; the honest constant-carrying chain measures 2.878 to 3.027. | [import-chaining.md](history/staging/import-chaining.md) |
| X | `Q-verify-cofactor-convolution` Does the cofactor-convolution identity at the anchor hold, and does it test the joint law? | ANSWERED | RESTATED with corrections: the arithmetic is right, an independent re-derivation reproducing every figure to the digit at all five levels and confirming the asserted closed-form step, but the framing does not survive, since X is pinned by the identity X = M - Nbar + n_0 so the whole comparison collapses to one cell and the joint is measurably not a product elsewhere; the model error is 0.52 per cent, not 0.050. | [verify-cofactor-convolution.md](history/staging/verify-cofactor-convolution.md) |
| X | `Q-xchan-at29-prereg` Does the joint-deficit closed form survive a blind test at @29? | OPEN | Pre-registration only, committed alone before any producer existed: the statistic, the predictions adopted verbatim from the record, two acceptance bands, the validation gate the instrument must clear before any @29 number is reported, and what each verdict does to TODO item X. | [xchan-at29-prereg.md](history/staging/xchan-at29-prereg.md) |
| X | `Q-xchan-at37-offset` Does any registered offset-correction candidate for the ~3.8 law survive at @37? | ANSWERED | Sealed and committed alone before any @37 census of any kind existed, fixing the candidates, the sigma model and its projection band, the scoring rule and what each verdict does to item X's offset clause; scored in xchan-at37-score.md, where every registered candidate is killed and the number survives an independent recount. | [xchan-at37-offset-prereg.md](history/staging/xchan-at37-offset-prereg.md) |
| X | `Q-xchan-at37-score` What does the @37 census say about the sealed X-channel offset pre-registration? | ANSWERED | The census measured 1 - J = 0.020823, below every registered prediction, so scored exactly as registered every one of the seven candidates dies at \|z\| = 104 to 122 and the survivor set is EMPTY, an outcome the sealed prereg has no consequence clause for; the number itself survives an independent recount on a different marking scheme, and the offset question is replaced by a larger one. | [xchan-at37-score.md](history/staging/xchan-at37-score.md) |
| X | `Q-xchannel-at23` What is the fifth point of the X-channel statistic, at @23, and does the monotone rise hold? | PARTIAL | The fifth point is +0.2658 at @23, the rise holds at five levels and is larger than the four-point trend predicted, and the deficit has migrated into m >= 3, whose share of the X-gap runs 10.5, 23.5 and 81.1 per cent at @17, @19 and @23; the constant itself is not derived here. | [xchannel-at23.md](history/staging/xchannel-at23.md) |
| X | `Q-xchannel-closedform` Does the zero-parameter closed form for the joint deficit survive its two blind tests at @29 and @31? | PARTIAL | 1 - J = 4S2 is the only one of the three pre-registered laws left standing and it is not exact: a clean hit at @29, z = -0.90, and 4.93 sigma low at @31 where sigma_J falls to 0.000024, with the two rivals dying at 6.35 and 20.81 sigma; both blind levels agree on a stable relative offset of about half a percent, -0.41% and -0.48%, whose absolute residuals match to 2%. | [xchan-at29.md](history/staging/xchan-at29.md) |
| X | `Q-xchannel-offset` What produces the ~3.8 law's -0.45% offset, and which candidate correction survives? | PARTIAL | The best available description is a finite-level correction of S3's size and sign - 1 - J = 4S2 - S3 scores z = +0.04 at @29 and -0.41 at @31 where the standing law scores -0.43 and -2.32 - but it is POST HOC; two candidate corrections and one shape are refuted on existing data, the sigma behind the @31 detection is calibrated on seven known-truth controls, and the deciding blind test at @37 is pre-registered and committed alone. | [item-x-offset.md](history/staging/item-x-offset.md) |
| X | `Q-xchannel-triples` Does the joint deficit deepen or decay as the mixed super-W triple census is extended past @17? | ANSWERED | It decays: J = 0.9025, 0.9599, 0.9659 at @17, @19, @23, so the deficit runs 9.7%, 4.0%, 3.4%, both new points land inside the pre-registered DECAYING FASTER THAN FORCED band, and the DEEPENING instinct is refuted by 3.50 sigma between @17 and @19 and a further 1.68 sigma to @23. | [xchannel-triples.md](history/staging/xchannel-triples.md) |
| A | `Q-anchored-ladder` Does the unified anchored ladder generalize past @11 and @13, and what does cheap K buy at each level? | ANSWERED | It generalizes verbatim to @17 and @19, and the K = 0 unified floor is DEAD there (vacuous at -1262 and -55865); what survives and grows is the family lead at the classic certification depth K*, margin +2, +5, +26, +110 across @11 to @19. | [attack-anchored-02.md](history/staging/attack-anchored-02.md) |
| A | `Q-anchored-ladder-17-0830` At @17 and above, at which depth K does the composed (unified) anchored floor first turn positive and at which K does it reach the truth, and does the depth-cost curve K_first_positive(level), K_truth(level) move with level? | ANSWERED | At @17/@19 the answer was already on record (Q-anchored-ladder: positive at K = 2/10, truth at ascending K = 109/410, minimal pool 88/350) and is re-derived here as the custody gate; the new level @23 ran under a sealed 14-of-14 forecast: positive first at K = 27 = K* (PROVEN from the record before the run), truth at ascending K = 1732 of 1739, minimal pool 1543 = 0.887 of the scour (PROVEN lower bound meets VERIFIED upper bound); across five levels positivity costs exactly K* while the truth fraction rises 0.40, 0.62, 0.73, 0.81, 0.89, a MEASURED finite table with no law in x and no exponent touched. | [attack-0830-anchored-ladder-17.md](history/staging/attack-0830-anchored-ladder-17.md) |
| A | `Q-anchored-unify` Can the three anchored mechanics be unified at @11, and what floor family does the unified cap certify? | ANSWERED | MEASURED and PROVEN-here but HELD: extending the staircase's cofactor injection to m = 1 folds the self-strike allowance into the count, the unified-cap lemma gives fresh <= capU_K <= cap_K at every depth and prime at @11 and @13, and the floor family runs 36 to 45; the x = 37 secondary is a clean negative. | [attack-anchored-01.md](history/staging/attack-anchored-01.md) |
| A | `Q-history-dial` Does revealing the scour primes' classes concentrate the floor on a bounded set of strike locations, and what is the history dial worth? | ANSWERED | Disconfirming: the class axis is linear at 2.90 survivors per prime read, so no bounded set of strike locations carries the floor, and the touch-count ceiling is proven and tight; deliverable (1) of the brief already existed as canonical state (the forcing ladder 16 -> 45 at @11), so nothing new was bought there. | [attack-history-dial.md](history/staging/attack-history-dial.md) |
| A | `Q-redteam-0830-engine` Do attack-0830-buchstab-deep.md, attack-0830-comb-tail.md and attack-0830-anchored-ladder-17.md survive an adversarial re-derivation on code that shares nothing with their producers, and does REFUTED row 97 stand as worded? | ANSWERED | Every headline number in the three notes reproduces exactly on independent code (26 of 26 comparisons, including F2/f2 = 3.6682 at sigma = 4.7088 by a near-analytic route, the 0-of-1512930 pair count, the tail defect at five levels, the full 419328-term Legendre split, and the whole @23 anchored ladder including K* = 27, floorU = 5364, truth 597475 and the minimal pool 1543 proven exact); one load-bearing DERIVATION is REFUTED — "\|B - 1\| >= c forces sigma(q) < u_c - 1" fails at @23 on 21134 (q, K) pairs for the engine's model B at c = 0.1 and on 33875 high-count pairs for the measured B at c = 0.01, because the step bounds every u in a weighted average by the largest one and treats the denominator as e^-gamma, so the "level-free" clause of buchstab-deep section 4 and REFUTED row 97's "\|B - 1\| >= 0.01 forces sigma < 1.798" must be re-graded from DERIVED to MEASURED-at-@23 (where the conclusion survives: the worst sigma is 2.159, still far below beta2 = 4.26645); row 97's "the best sigma any level has" is separately WEAKENED, since @29's head sigma is 5.5785 with width 1.5325 and @97's is 17.1422 with width 1.0000; comb-tail derives its main-term factor from prod (1 - 1/q_i) and measures it against prod (1 - 1/(q_i - 1)), which is what natal-cap-28 line 283 computes against its own line 20 and against certificate-engine.md section 1, a 0.9% difference at @23 that moves nothing certified; comb-tail also misquotes its own cited source as F1 in [1.5, 4] where that source says [1.5, 3] and says there is no bound at all at s < 1; four smaller slips are listed and none opens or closes a route. | [redteam-0830-engine.md](history/staging/redteam-0830-engine.md) |
| 1 | `Q-at43-bigint-0830` Can the K-30 natal march be carried past its 2^53 ceiling to @43 exactly, and is the @43 point worth its cost? | PARTIAL | The engine side is done and VERIFIED (five paths promoted to BigInt, @7..@37 and a 0.248% slice of @41 reproduced digit for digit); the @43 point is NOT run, because the measured extrapolation is 579 h of eight cores on this machine (a 43x tile times a 2.23x per-cell cost, against the brief's ~13x), which is a weeks-class box job whose only payoff is a sixth point on a curve with no consumer; the forecast 0.8393 raw / 0.8399 persisted stands unscored. | [engine-0830-at43-bigint.md](history/staging/engine-0830-at43-bigint.md) |
| 1 | `Q-redteam-0830-imports` Do the six lighter notes of 2026-08-30 (varE-identification, smooth-aps, rec-killrun, skeleton-door, at43-bigint, coherence) survive an adversarial pass on independent code and at the source pages, and which of their load-bearing claims are wrong? | ANSWERED | No note is refuted whole and no exponent moves. Every decisive measurement reproduces on code sharing nothing with the producers: the varE mixed remainder and its 0.844 / 0.826 share below 2L and 94.4 / 98.7 percent unbalanced share at x = 13, 17; the Buchstab deviations and all three crossing levels log10 z* = 33.53, 68.80, 33.62; the skeleton door's 9.2 / -0.9 percent, G30_agg 0.1113 / 0.1011 and the 0.0102 cap at @13, @17, by a path that also verifies cap-36 Theorem A; the @43 parity exactness on all 26,157,448 scour classes with 0 above 2^54 and a constructed @47 counterexample; and the five recon-0828 verdict counts summing to 75, which REFUTES rec-killrun's brief-error clause and confirms the orchestrator's rider. Seven claims WEAKEN. The load-bearing one is smooth-aps's "the weight is unmet in print": Harper's J. London Math. Soc. 112 (2025) e70293 proves a Barban-Davenport-Halberstam asymptotic for an ARBITRARY sequence on exactly that dyadic all-classes object, and his own footnote says the missing max over x' can be incorporated, so the NEAREST citation changes even though the step still does not close (the 2025 range is sqrt(2x) < Q <= x and its Theorem 2 route bars sieved sets by name). Also: Henriot Corollary 2 applies, but to the ERRATUM's statement and under two hypotheses the note leaves unstated (eps < alpha/600, not "every eps"; F at prime powers); varE section 4's display (*) carries an unfilled placeholder and is vacuous by a factor L/d; the skeleton door's "would tighten" is wrong in sign at @17, where the closable block is negative and removing it RAISES G30_agg to 0.1020; Halasz-Montgomery is not applicable for the reason given (it is an abstract inner-product inequality); FGKT's heuristic quote is on p. 4, not p. 3; and the "~13x had no source" is a corpus miss, the retired G2-walk figure at CHANGELOG.md:5716. Not TPC-strength; nothing here opens a route. | [redteam-0830-imports.md](history/staging/redteam-0830-imports.md) |
| Z7 | `Q-zonegap-03-score` Do the ten predictions sealed in zonegap-03-prereg.md score against the stage-3 sweep at X = 1e12? | ANSWERED | All ten sealed rows score HIT and none miss, after a second pass added a band-edge argument to zonegap-01.js and re-ran the decade so the two rows that named an unprinted band could be scored; the four Group T hits are a custody promotion that follows from CUSTODY 1 and 3 passing, one sub-clause of T5 (the full-decade sd) stays unprinted, and the sweep still needs a DERIVED engine because zonegap-01.js's inlined 41-record ladder makes it exit at 1e12. | [zonegap-03-score.md](history/staging/zonegap-03-score.md) |
| 2 | `Q-var41` What does the stable law predict for Var(41), and what can the tenth Var/E point pin? | OPEN | Pre-registration only, sealed and committed alone before any Var(41) engine exists: it freezes the prediction, a band taken from the law's own residuals at z <= 37, the derived z(41) prediction, and the honest statement that one more point cannot separate a limit from a drift. | [var41-prereg.md](history/staging/var41-prereg.md) |
| 8 | `Q-applied-0828-engine` Were the engine red team's corrections applied to the five HELD notes? | ANSWERED | Applied, 37 edits across the five notes: two numbers corrected (first s >= 10.82 at x = 263 not 239, first non-empty kappa=1 level @37 not @53), two ledger verdict lines and one note title rewritten, one proof step given BV's max-over-y form, the one-class freshness factor restated on P^-(m) >= q so it holds at every scour prime, and two mislabelled columns renamed; six corrections that land on live documents are collected here unapplied, and no producer was touched. | [applied-0828-engine.md](history/staging/applied-0828-engine.md) |
| 8 | `Q-applied-0828-live` Which engine and head red-team corrections reached the live layer? | ANSWERED | Nineteen edits across four documents: the glossary's cap_K dimension count with its mandatory sifted-versus-assumed clause plus three new entries (twin opener, head, tail); the survey's one-class density factor, S1's restored pi(q-1) terms and r in N_x hypothesis, the dropped Chen absorption, Theorem C with its emptiness, dimension 1 for q_i < q, the comb-conditioning qualifier and the inverted shallow-band bullet; the certificate engine's equidistribution status cell, the q = T^{o(1)} second hypothesis and the Comb Discrepancy scope cell; and the census's R as the continuum functional with its three comparators; paper/staircase-note.md, TODO.md and QUESTIONS.md are owed and untouched. | [applied-0828-live.md](history/staging/applied-0828-live.md) |
| 8 | `Q-buchstab-deep-0830` Can the certificate engine's deep-ladder Buchstab transfer be proven at dimension 2 at the depths the run levels reach by a route that does not go through the fundamental lemma at s >= 22.06 or the constant-free DH Theorem 9.1 (TODO 8a)? | CLOSED | NO by any instrument this corpus can cite, and the non-closing step is structural, not a constant: the transfer is an asymptotic for a ratio of two dimension-2 sifting functions at one sifting depth z = q, so a sieve bracket [f2, F2] survives undivided in the ratio (width 3.67 at the best sigma any level has, 4.71 at the @23 head); a correction \|B - 1\| >= 1% can only occur at sigma(q) < 1.8 where f2 = 0 and F2 >= 7.85, while a lower bound exists only at sigma > 4.266 where \|B - 1\| < 1e-5; the Buchstab identity iterated once is already negative at K = 1 for q = 37 at @23 and is the sieve itself when iterated fully; Jurkat-Richert fails Omega(1) as stated; in the certificate's legal direction F2 beats the trivial cap_K <= cap2 at 0 of 1512930 (q, K) pairs at @23, so the sharp-sieve floor is -1733138 at every K; the transfer stays HEURISTIC, what would move it is a kappa = 2 asymptotic in the open band 2 < sigma < 4.266, and part (b) is scoped and graded, not attacked. | [attack-0830-buchstab-deep.md](history/staging/attack-0830-buchstab-deep.md) |
| 8 | `Q-buchstab-transfer` Is the certificate engine's Buchstab transfer provable in the shallow regime y = T^{o(1)}? | ANSWERED | PROVEN conditional on the fundamental lemma and EMPTY at every run level (needs s >= 22.06; available 4.7 @23, 17.1 @97); the engine's B is a dimension-1 object, the survey's pair-Buchstab is dimension 2, the certificate needs a third. | [thm-buchstab-transfer-shallow.md](history/staging/thm-buchstab-transfer-shallow.md) |
| 8 | `Q-comb-discrepancy` Can the Comb Discrepancy Lemma's constant 2*3^k be tightened (TODO 8c)? | PARTIAL | The lemma IS the trivial per-block bound; the attained optimum is max G - min G, a computed number per level (slack 29x @23, 54x @29, growing); term-by-term pricing lifts the certified head share to about 28-29 percent, not the 50 hoped for. | [comb-discrepancy-tight.md](history/staging/comb-discrepancy-tight.md) |
| 8 | `Q-comb-tail-0830` Can TODO item 8's remaining part (b), prime-comb equidistribution in the tail regime, be proven at the depths the certificate needs, or at least measured and priced at the enumerable levels (8b)? | PARTIAL | Not proven and no exponent moves: the tail defect is measured exactly for the first time (signed -0.01% of the tail main term at @23, -0.00% at @29, unsigned 0.60% and 0.25%, smaller than the head's 1.00% in aggregate but 8 to 37% per prime at its worst), the Comb Discrepancy Lemma's method fails in the tail on its MAIN TERM (off by a derived factor e^gamma(1/u - q^(1-u)), measured aggregate 1.14x at @23) before its error term (10^27 x main), the prime-comb Legendre form has 2^(k+2) terms of which the short ones obey the lemma's <1 bound and the long ones are prime-in-AP discrepancies whose term-by-term sum is 11.2% of main at @23 against a signed -0.01%; the all-x form at K = 0 is Theorem C (PROVEN, limit only) and at the certificate's depth K* the non-closing step is a kappa = 1 asymptotic at sifting parameter s < 2, a proof gap on data that show B_tail = 0.998-1.000 at K* through @29; the full-depth half is 8(a), CLOSED. | [attack-0830-comb-tail.md](history/staging/attack-0830-comb-tail.md) |
| 8 | `Q-redteam-0828-engine` Do the five 2026-08-28 certificate-engine notes survive an adversarial re-derivation, and does the one-class freshness factor correction hold before it reaches a live document? | ANSWERED | The one-class factor holds and is stronger than either note states; four numbers are refuted (first s>=10.82 is x=263 not 239, first non-empty kappa=1 level is @37 not @53, rho*g_max is off by one gap, the @17 certified share and per-term constant carry the wrong convention) and one proof step needs the max-over-y form of BV; the cluster's shared verdict stands. | [redteam-0828-engine.md](history/staging/redteam-0828-engine.md) |
| 8 | `Q-redteam-0830-engine` Do attack-0830-buchstab-deep.md, attack-0830-comb-tail.md and attack-0830-anchored-ladder-17.md survive an adversarial re-derivation on code that shares nothing with their producers, and does REFUTED row 97 stand as worded? | ANSWERED | Every headline number in the three notes reproduces exactly on independent code (26 of 26 comparisons, including F2/f2 = 3.6682 at sigma = 4.7088 by a near-analytic route, the 0-of-1512930 pair count, the tail defect at five levels, the full 419328-term Legendre split, and the whole @23 anchored ladder including K* = 27, floorU = 5364, truth 597475 and the minimal pool 1543 proven exact); one load-bearing DERIVATION is REFUTED — "\|B - 1\| >= c forces sigma(q) < u_c - 1" fails at @23 on 21134 (q, K) pairs for the engine's model B at c = 0.1 and on 33875 high-count pairs for the measured B at c = 0.01, because the step bounds every u in a weighted average by the largest one and treats the denominator as e^-gamma, so the "level-free" clause of buchstab-deep section 4 and REFUTED row 97's "\|B - 1\| >= 0.01 forces sigma < 1.798" must be re-graded from DERIVED to MEASURED-at-@23 (where the conclusion survives: the worst sigma is 2.159, still far below beta2 = 4.26645); row 97's "the best sigma any level has" is separately WEAKENED, since @29's head sigma is 5.5785 with width 1.5325 and @97's is 17.1422 with width 1.0000; comb-tail derives its main-term factor from prod (1 - 1/q_i) and measures it against prod (1 - 1/(q_i - 1)), which is what natal-cap-28 line 283 computes against its own line 20 and against certificate-engine.md section 1, a 0.9% difference at @23 that moves nothing certified; comb-tail also misquotes its own cited source as F1 in [1.5, 4] where that source says [1.5, 3] and says there is no bound at all at s < 1; four smaller slips are listed and none opens or closes a route. | [redteam-0830-engine.md](history/staging/redteam-0830-engine.md) |
| 8 | `Q-sharp-sieve-range` Do the sharp sieve functions (Jurkat-Richert, DHR) make the two empty certificate-engine theorems non-empty at run levels? | CLOSED | NO at finite level: DH Thm 9.1 carries no written constant and the crude fundamental lemma is strictly better; as limit statements kappa=1 is first non-empty @37 (a 19.8-wide bracket; @53 is the first narrow one, 1.656) and kappa=2 @23. | [thm-sharp-sieve-range.md](history/staging/thm-sharp-sieve-range.md) |
| 8 | `Q-u2-engine-depth` Is the certificate engine's operative depth heading to u = 2, and does that make TODO item 8's payout form TPC-strength? | ANSWERED | It is not: the measured operative depth runs u = 4.191 at @17 down to 3.557 at @97 and is still falling, so the brief's conditional does not fire and item 8 is shown neither TPC-strength nor safe; a WALL-ADDRESS in the weakest sense, every figure SCRATCHPAD-GRADE. | [u2-engine-depth.md](history/staging/u2-engine-depth.md) |
| Z0 | `Q-applied-0828-census` Were the census red team's corrections applied to the three HELD notes? | ANSWERED | Every WEAKENED and REFUTED verdict in redteam-0828-census.md is applied to its target note in the present tense; two producer defects and four live-doc corrections stay open and are listed here. | [applied-0828-census.md](history/staging/applied-0828-census.md) |
| Z0 | `Q-applied-0828-quadpoint` Were the quadpoint red team's corrections applied to the four HELD notes? | ANSWERED | Applied: the nine REFUTED and WEAKENED verdicts that target the four notes are written into them in present tense, with ledger blocks added; the tenth targets the sealed prereg, outside the fence, and is recorded in attack-quadpoint-02.md instead; three corrections owed by TODO.md Z2 and one by Z0 are listed here and are NOT applied. | [applied-0828-quadpoint.md](history/staging/applied-0828-quadpoint.md) |
| Z0 | `Q-redteam-0828-census` Do destroyer-census-01.md, stretch-01.md and records-placement-01.md survive an independent re-derivation of every load-bearing claim, and may they leave HELD? | ANSWERED | All three survive on arithmetic, every decisive number reproducing exactly on an independent engine; one sealed reading (records READ-3) is REFUTED as vacuous and four sentences need correcting before integration. | [redteam-0828-census.md](history/staging/redteam-0828-census.md) |
| Z0 | `Q-redteam-0828-quadpoint` Do the four HELD quadpoint notes of 2026-08-22 survive an adversarial pass: the capture identity's proof line by line, the depth law and its asymptote, the sealed prereg scoring, and the prior-art citations at page level? | ANSWERED | The identity is PROVEN once its window convention is written down and holds at every K of 50 anchors under an independent implementation; four load-bearing sentences are wrong (section 4's gloss on Sum capU, v1 section 2's limit, the prior-art note's 2%, and the note's unconditional y* sentences), and none of the four defects opens or closes a route. | [redteam-0828-quadpoint.md](history/staging/redteam-0828-quadpoint.md) |
| Z0 | `Q-review-request-0907` Which claims of the 2026-09-07 session should an independent math agent check, in what order, against which records, and what must the review return? | ANSWERED | Reviewed 2026-09-08 by an outside reader (history/reviews-0907/10): ranked claims 1 (conditional on the unread 1974 page), 2, 4, 5, 6 verified within stated scope; claim 3 verified with its quoted tolerances corrected (max deviation 1.8e-4, not 1e-4 or 1e-5); the Corollary 1 slip sharpened (fails for every representative other than 1, and mis-signs even then); ASSUMED items 4 and 6 discharged, 2 partially, 1, 3, 5 not. Twin-prime infinitude and every sufficient signed margin remain OPEN. Ranked below: the §6.2 demotion in the two-class manuscript (a change to a proof's dependency), the D_y identity reading (a change to what a census can show), the Erdős #687 attribution, and the two measurement artifacts. Twin-prime infinitude and every sufficient signed margin remain OPEN. | [review-request-0907.md](review-request-0907.md) |
| A9 (retired) | `Q-a9-histogram-operator` What is the exact evolution of the gap-size histogram under folding, as a transfer operator on count(d), and what is the tail P(gap >= 2p)? | ANSWERED | The operator is derived and then verified by exact computation at every fold from T5 to T31 and the tail law is computed exactly, but the machinery is a rediscovery of Holt and Rudd arXiv:1408.6002 section 5 and may not be presented as new; only the G2 spacing beyond their \|s\| < 2p restriction is ours. | [a3-09-histogram-operator.md](a3-09-histogram-operator.md) |
| G (retired) | `Q-block-L-first-dead` Is the block-1 counting bound on L the first-dead 62 or the last-alive 111, and does downward closure hold in the block coordinate? | ANSWERED | Downward closure HOLDS in the block coordinate: L <= 62 is sound and recomputed from scratch rather than inherited, L <= 111 is true, implied by 62 and weaker by 1.79x, and the adjudication's supposedly sharper instrument is attack 3's instrument. | [adjudicate-L-bound.md](history/staging/adjudicate-L-bound.md) |
| 1c (retired) | `Q-c2prime-drift` Why does c2' drift on the 22-term ladder? | PARTIAL | Class-count-blind (attack-c2drift-01 §1); on item 1c's own band x >= 41 the ten-point rate is unresolvable: c2' 0.3745 +/- 0.1411 against c1's 0.3344 +/- 0.2358 on the same primes, a difference of 0.0401 = 0.12 of the control's ten-point window sd. Whether the drift is real is NOT closed here: attack-c2drift-01 measured it at p = 0.0053 on x >= 17 and left (i)' and (ii) alive. exponent-control §2/§4/§6 refit at 22 terms. | [attack-c2drift-01.md](history/staging/attack-c2drift-01.md), [c2prime-refit-22.md](history/staging/c2prime-refit-22.md) |
| 11 (retired) | `Q-capK-bv` Is the prime-regime cap_K over the full wheel an unconditional asymptotic via the fundamental lemma over Bombieri-Vinogradov? | ANSWERED | PROVEN at short-note grade for q_K = W^{o(1)}, and EMPTY in every computable range (needs s >= 10.82, first cleared at x = 263; the lemma's floor s >= 10 is first reached at x = 239); the deep ladder is untouched. | [thm-capK-bv.md](history/staging/thm-capK-bv.md) |
| 11b (retired) | `Q-consolidation-wave` Can the five cost-class scripts be bound to their own output, and can U-FRAME's two lost tables be rebuilt? | ANSWERED | All four runnable cost-class embeds are bound and the hand-pasted-tail counter falls 19 to 15 with the gate at TOTAL 0; three needed --force at a cost of 24 tokens out of 211 with no value changed anywhere, and natal-cap-33-overnight.js is a three-run composite that should never have been on the cost list. | [consolidation-wave.md](history/staging/consolidation-wave.md) |
| 10 (retired) | `Q-excess-chain-c` Does the excess chain's constant c pin to 1.074 via a compressed-tail max correction? | CLOSED | NO: for any FIXED correlation length the derived family tends to 1 and both named corrections lower the maximum, so 1.074 is not derivable from a compressed-tail max correction; c measures 1.05 +/- 0.07 (sd) over x = 17..31, MEASURED, which does not separate 1.05 from 1.074. | [excess-chain-c.md](history/staging/excess-chain-c.md) |
| 1b (retired) | `Q-greedy-oracle` Is the corrected greedy a G2 oracle? | ANSWERED | ORACLE ESTABLISHED, 13 of 13 exactly-known terms hit with minimum ratio 1.0000, so the greedy RULE is an exact solver where the answer is checkable at x <= 41; the rider matters more, the search budget needed grows 3.31x per additional prime and two objects whose truth reaches further show the same estimator's fidelity DECAYING, so nothing is established for the greedy AS RUN on the ladder. | [greedy-oracle-validation.md](history/staging/greedy-oracle-validation.md), [phase1-T1-greedy-oracle.md](history/staging/phase1-T1-greedy-oracle.md) |
| 4 (retired) | `Q-import-fracparts` Does Saffari-Vaughan Theorem 10 cover the branches carrying the Skeleton door's mass? | ANSWERED | Prediction HIT: the covered branches carry at most 8 percent of the mass; anchor and a sharper wall-address banked; the THEOREM column is struck, not merely overpriced, because Theorem 10's range condition is x^{6/11+eps} < y, which fails at fixed M; no route; no cap-36 line is upgraded. | [import-fracparts.md](history/staging/import-fracparts.md) |
| 0e (retired) | `Q-ioslack-survey` Does any instrument in the corpus carry a sharp-level signature that would let the infinitely-often slack be spent? | CLOSED | None does: 23 instruments surveyed and 19 eligible, smallest per-instrument p_FWE = 0.1082 and 0.8865 after Šidák, so dial 4's fourth channel closes and the dial is finished; the second finding is that maxsum_{L+1} is sharp exactly when L = 1. | [ioslack-survey.md](history/staging/ioslack-survey.md) |
| Z5b (retired) | `Q-lambda-ledger` Does parity information survive in the lambda-weighted fold ledger? | CLOSED | REJECT, against a pre-registered threshold fixed before the producer existed: the lambda multiplier exists and is parity-free, so the ledger is blind at its design point rather than at its margins; two columns are pinned by proof, and nothing here is novel mathematics. | [attack-lambda-ledger.md](history/staging/attack-lambda-ledger.md) |
| Z5b (retired) | `Q-ledger-forced` Which properties of the fold ledger's columns are FORCED rather than expected? | ANSWERED | Fourteen forced constraints, all identities or wrong-direction bounds; by_new is forced only in the prime gap (its O(1) is MEASURED); nothing forces net from below. | [fold-ledger-forced.md](history/staging/fold-ledger-forced.md) |
| 11 (retired) | `Q-mod30-tail` Are the BV survey's S1 (mod-30 tail) and S2 (fixed truncation and depth) provable as stated? | ANSWERED | Both PROVEN at short-note grade (no second reader) once S2's freshness factor is corrected to one class per prime, which needs only P^-(m) >= q > q_i and so holds at every scour prime, not only in the prime regime; tail constant 2 ln 2 -> (ln 2)/2; nothing in the head. | [thm-mod30-tail.md](history/staging/thm-mod30-tail.md) |
| 3 (retired) | `Q-monotonicity-sweep` Does anything in the corpus assume certificate validity is monotone in L? | ANSWERED | One unsound artifact and one invalid inference: attack-beta2-04-loss-budget.js section 6 bisects on a predicate measured not upward-closed and is wrong at 3 of 5 levels, true first-crossings 30/72/132/174/210 against the reported 36/72/144/174/354, and redteam-DP1-certificate.js draws a global minimality conclusion from a two-point local check; corrected, worst-casing certifies within 1.00 to 2.00 of true G2 and the exponent penalty runs 0 to 0.27 and falls with x. | [monotonicity-sweep.md](history/staging/monotonicity-sweep.md) |
| Z6 (retired) | `Q-records-placement` Do the seven unswept twin-gap records 76-82, above 2^53, land uniformly inside their stretches, or is there square-anchor coupling in record-start placement? | ANSWERED | Sealed alone before the producer existed: the uniform band, the fixed definitions, the registered readings, the calibration abort gate and the riders are all fixed here and no placement fraction, q or stretch boundary was evaluated; scored in records-placement-01.md. | [records-placement-01.md](history/staging/records-placement-01.md), [records-placement-02.md](history/staging/records-placement-02.md), [records-placement-prereg.md](history/staging/records-placement-prereg.md) |
| 5 (retired) | `Q-shadow-amplitude` Where does the kill shadow's drift amplitude come from, and does the record's counting floor explain it? | MIXED (shadow-amplitude-prereg.md: OPEN; shadow-amplitude.md: PARTIAL) | The finite-y correction is an identity with no free parameter and both measurement routes agree 10 of 10, but the record's own counting floor is four to six times too small and its candidate explanation is the wrong half, so the label stays PARTIALLY EXPLAINED. | [shadow-amplitude-prereg.md](history/staging/shadow-amplitude-prereg.md), [shadow-amplitude.md](history/staging/shadow-amplitude.md) |
| 5 (retired) | `Q-shadow-prereg` Is the kill shadow's 0.85 the band-average of the Unification-Law survival curve over the post-crystallization window? | ANSWERED | Scored in shadow-buchstab.md: SHAPE-ONLY under the original y >= 997 rule; D3 passes in the reported ten clusters but D1 fails near y = 1000 at 1.49 times the 0.011 tolerance. Later finite-y normalisation and counting-floor corrections do not promote this verdict. The pair-Buchstab identification remains conjectural; the pre-registration body is preserved. | [shadow-prereg.md](history/staging/shadow-prereg.md) |
| 0d (retired) | `Q-single-alignment` Does the head's single-alignment fold recursion for M(x, x^3) give a proven-shaped handle on the per-fold multiplier that the max-over-alignments recursion lacked? | CLOSED | The answer splits: the multiplier IS different in shape, measured - exactly 1 at 225 of 240 folds from x = 53, total spend 1.09 nats against a tile-shaped ladder's 7.12, measured M(1613) = 2220 against a tile-shaped 3.7e5 - but the route to a growth law through the recursion closes anyway, because the growth is initiated by the window's expansion into fresh ground, a boundary term that is the localized gap problem re-posed and that no fold reaches. | [localized-single-alignment.md](localized-single-alignment.md) |
| 4 (retired) | `Q-skeleton-decide-0830` Should TODO item 4, "Skeleton Equidistribution: restate or demote", be restated around the modulus-W mass or demoted off the board, and what exactly is banked either way? | ANSWERED | DEMOTE. Over every scour prime the branches on which the door is a fixed-modulus question carry 9.2, -0.9, 0.2 and 0.5 percent of the skeleton at @13, @17, @19, @23 (the -10.8 and 5.5 percent on record were 9 and 2 percent subsamples), so the door as named removes at most 0.0102 from a G30_agg whose open part is 0.094 to 0.126; on the open side the phase never wraps and no equidistribution statement remains, only the inequality; nothing on the live board consumes G30_agg < 1/2; no first move exists that is not already ANSWERED. Banked regardless: the Skeleton Collapse Theorem (PROVEN, all x, all q) and G30_agg < 1/2 CERTIFIED at six levels @11..@29. | [decide-0830-skeleton-door.md](history/staging/decide-0830-skeleton-door.md) |
| 4 (retired) | `Q-skeleton-door` Is the Skeleton Equidistribution Conjecture the blocker on the anchored calm? | ANSWERED | It is not the blocker as far as the door can be seen: Theorem A (Trapezoid Cancellation) is proven for all x, q and branches, @29 is certified as an exact integer inequality at G30_agg = 0.1176 with margin 0.3824 over 7,863 scour primes, and the decay-law shortcut is REFUTED, the six levels being flat within their own spread with every fit made strictly worse by adding @29. | [natal-cap-36-skeleton-door.md](natal-cap-36-skeleton-door.md) |
| Z3 (retired) | `Q-stretch-structure` What is the stretch S_q = [q^2, q'^2) as an object, where does the Stretch Postulate sit against the Zone Postulate, and does the square anchor's QR structure buy any density advantage? | ANSWERED | The implication chain and the QR kill law re-derive independently arrow by arrow; the anchor's structure is real, deterministic and redistribution-only (exactly two killed offset classes at every prime anchor checked), so there is structure and no advantage, and SP sits strictly above the strong Zone Postulate. | [stretch-01.md](history/staging/stretch-01.md) |
| 0e (retired) | `Q-verify-monotone-depth` Does the Monotone Depth obstruction, which retires dial 4, survive an adversarial re-derivation? | ANSWERED | NARROWED: every measurement in the record reproduces, several to the last digit, but the mechanism as named is false as a general law and the corpus already holds a counterexample to it; what survives is an accounting of three channels priced in tenths of a nat against a need of 6.700, 8.191 and 9.637 nats, so dial 4 becomes priced slack with one channel open and unpriced. | [verify-monotone-depth.md](history/staging/verify-monotone-depth.md) |
| 1e (retired) | `Q-wrongdirection-audit` Are any of the ten live targets secretly TPC-strength, before the sessions are spent on them? | ANSWERED | The audit closes no target: two of the ten come out TPC-strength and three more carry a TPC-strength face under a quantifier they are likely to drift into, which is a labelling result and not a reason to drop them; item 1e is settled only because the answer was already on disk, and one route-blocking number in it is hand arithmetic and unstamped. | [attack-wrongdirection-audit.md](history/staging/attack-wrongdirection-audit.md) |
| Z3 (retired) | `Q-z3-immune` Do the square anchor's immune offset classes (stretch-01 §4) carry a survivor surplus beyond the redistribution-only guardrail, do they attract the floor's first survivor, and does restricting the transplanted caps to them lower K*? | CLOSED | No, on all three. The preregistered surplus test is VOID on its own matched control (a 0.6% ratio-of-means bias present with and without the quadratic point); the preregistered placement test HOLDS at Z = +0.49; the design-free class test reads the guardrail's r/(r-2) over 3.4 million twin openers with a largest per-prime deviation of 0.11% and per-prime Z in -0.48..+1.66; and the restricted certificate, while lowering K* at 61% of anchors, has no certificate at all at 93 of 1219 and is beaten head to head by the QR-BLIND restriction that certifies 1219 of 1219. The refinement is closed. | [attack-z3-immune-01.md](history/staging/attack-z3-immune-01.md) |
| Z (retired) | `Q-zonegap-reduction` What must be proven for Z2, what already is, and what does the proven head machinery give the zone? | PARTIAL | The Zone Restriction Lemma is proven and verified at five levels - the in-zone twin slots of T_p ARE the in-zone twin primes, so Z2(p) IS the whole-tile gap object restricted to the head window - the three-slack chain is graded honestly, the transfer inventory is listed item by item, and the deep end is proven an onset desert over 24 levels; section 5 lists what was not reached. | [zonegap-02-reduction.md](history/staging/zonegap-02-reduction.md) |

## 2. Every question, by id

| id | status | question | verdict | TODO | records |
|---|---|---|---|---|---|
| `Q-0c-holesweep` | ANSWERED | At a fold, how does maxsum degrade copy by copy as the two deleted residues sweep through their possible positions? | The full curve is on disk for nine folds (5->7 through 31->37, every copy) and it is a PALINDROME: the Mirror-Sweep Lemma is proven here and verified exhaustively, giving the fingerprint any kill-count-free bound must reproduce, but no such bound was produced by this pass. | 0c | [attack-0c-holesweep.md](history/staging/attack-0c-holesweep.md) |
| `Q-0c0e-level-selection` | CLOSED | Can a residue-deleted maxsum bound that only has to hold at levels of the argument's choosing carry the weak Zone Postulate? | CLOSED, and the mechanism has a name: the level-selection licence is worth 0.3187 nats once and is falling, no selection rule beats its own null by anything worth having across T_11..T_29, and the BV/EH sweep supplies no moduli-selecting statement to spend. | 0c, 0e (retired) | [attack-0c0e-level-selection.md](history/staging/attack-0c0e-level-selection.md) |
| `Q-DP1-mechanism` | ANSWERED | Does anything consume two-point data about a sifted set? | One consumer exists and is priced: the sharp degree-2 Boole-Frechet bound on empty windows is unconditional and concludes at every window position, but it over-certifies G2 with a log-log slope of +5.20 against x over x = 5..19, so the price of stopping at two-point data grows as a power of x rather than as a constant. | none | [attack-DP1-mechanism.md](history/staging/attack-DP1-mechanism.md) |
| `Q-L-own-law` | ANSWERED | Does L, the adjacent-kill run length, have a law of its own level by level, and which abscissa is it linear in? | L has no law of its own: (L+1)*mbar(T_v) is approximately G2(y#) at every tile and top prime where both sides are exact, spread 1.0000 to 1.0838 over four tiles at y >= 23 with mean 1.0198, so the residue is quantisation, the abscissa question returns a calibrated negative, and the distance to 529 is priced rather than closed. | none | [attack-L-law.md](history/staging/attack-L-law.md) |
| `Q-L-subadditivity` | ANSWERED | Is L sub-additive when two prime sets merge, as the intuition that L should be smaller for the combined set suggests? | Read literally the intuition is wrong by a one-line proof rather than an edge case: L is super-additive, exhaustively censused to nine primes; read as a statement about reusing primes it is right, and that reading is worth more than the refutation. | none | [attack-L-subadditivity.md](history/staging/attack-L-subadditivity.md) |
| `Q-T2a-prediction` | PARTIAL | What are G2(43#) and G2(47#), predicted blind from the thirteen exact terms? | Registered blind: G2(43#) central 630, window 561 to 747, and G2(47#) central 720, window 653 to 868, with the method's calibration PASSING on the eight-term prefix; the 43# term has since been enumerated at 618, inside the window and below the central value, and 47# remains unmeasured, with the report's own largest risk being that c2' may be about to turn down. | none | [phase1-T2a-prediction.md](history/staging/phase1-T2a-prediction.md) |
| `Q-W1a-applied` | ANSWERED | Were the unapplied findings for partition A, the paper suite and citation-heavy files, applied? | Thirty-three findings, 24 applied, 3 refused at a primary source (two of which would have written a falsehood into the corpus) and 6 handed back; the most consequential item was not on the list, since covering-dive's stated reason for dismissing Kalmynin-Konyagin was false by the corpus's own proof and the corrected reason had to be found rather than copied. | none | [phase1-W1a-applied.md](history/staging/phase1-W1a-applied.md) |
| `Q-W3-literature` | ANSWERED | What do the four literature targets give: the Omega(kappa, L) quantifier, the Kalmynin-Konyagin transfer, Erdos-Ruzsa 1980, and the two-class upper bound? | The quantifier is over all pairs, confirmed verbatim in two independent sources, and every page and section citation in beta2-note checks out; the higher-consequence find is that covering-dive's stated reason for dismissing Kalmynin-Konyagin is false, since the proof only sees the size of Omega_p, and the two-class upper bound survives a second independent attempt as ABSENT. | none | [phase1-W3-literature.md](history/staging/phase1-W3-literature.md) |
| `Q-X-upper-0829n` | PARTIAL | Can the rough-pair census X(K) on the stretch window be bounded above, unconditionally and with an explicit error term, by a dimension-2 upper-bound sieve, and how loose is the bound against exact X(K)? | Yes, as a theorem with nothing open (Selberg's Λ² inequality with a remainder bounded by the interval structure alone, VERIFIED at all 10908 anchor-depth pairs), but it is loose by 7.82 to 10.13 against exact X(K) at the band depths, decomposed as a sieve loss 1.78 to 2.53 times a structural loss 4.01 to 4.39 that no upper-bound sieve can remove, the window holds the level below z² (s_max 1.81 to 1.96) so the bound stops improving past p_K = 31 to 61, its main term is the sifting function's and not the census's, and the drift is a crossing quantity outside the legal half and is not evaluated. | Z2 | [attack-0829n-X-upper.md](history/staging/attack-0829n-X-upper.md) |
| `Q-a144311-vocabulary` | ANSWERED | In the vocabulary the literature actually uses, is there a published upper bound for G2, and is beta2 still the best known kappa = 2 sifting limit? | The terms of art are the paired Jacobsthal function and Jacobsthal-type functions for polynomials, and in that vocabulary no published upper bound exists at any exponent, beta2 is unimproved since 2008, nothing is found on A144311's asymptotic growth, and an Erdős-Rankin lower bound is free; both load-bearing corpus claims survive. | none | [audit-a144311-vocabulary.md](history/staging/audit-a144311-vocabulary.md) |
| `Q-a3-05-bound-L` | PARTIAL | Can L be bounded unconditionally from run consistency, and where does that stop? | Theorem B gives the first unconditional bound, L <= 1 + m*, sitting 0 to 3 above the truth at all eight measured folds, but it is of order G2(old)/p, which is linear in x on the fold diagonal; section 8 locates the wall at one large-deviation hypothesis H″ the residue side cannot reach, and Theorem C inherits it for kappa(m). | none | [a3-05-bound-L.md](a3-05-bound-L.md) |
| `Q-a9-histogram-operator` | ANSWERED | What is the exact evolution of the gap-size histogram under folding, as a transfer operator on count(d), and what is the tail P(gap >= 2p)? | The operator is derived and then verified by exact computation at every fold from T5 to T31 and the tail law is computed exactly, but the machinery is a rediscovery of Holt and Rudd arXiv:1408.6002 section 5 and may not be presented as new; only the G2 spacing beyond their \|s\| < 2p restriction is ours. | A9 (retired) | [a3-09-histogram-operator.md](a3-09-histogram-operator.md) |
| `Q-ab-coupling` | MIXED (attack-ab-coupling.md: PARTIAL; verify-ab-coupling.md: ANSWERED) | How much of the counting criterion's known slack does the rigidity of the two kill channels A = 0 mod p and B = -2 mod p close? | The pilot survives, every held number reproducing on an independent code path, and the one correction is in its favour: the depth-3 ceiling is 38 slots, not 39; the LP answers NO, its exact depth-2 optimum over the full polytope being 54 slots, identical to the pilot's, so it prices the idea and does not clear 51. | none | [attack-ab-coupling.md](history/staging/attack-ab-coupling.md), [verify-ab-coupling.md](history/staging/verify-ab-coupling.md) |
| `Q-adversary-wave2` | ANSWERED | Do the four same-evening headlines (kill shadow, scanstat, sofic, Shearer) survive a refute-first adversarial pass? | Nothing BROKEN: sofic SURVIVES and the other three SURVIVE WITH CORRECTIONS, the corrections being one verdict label a grade too high by the record's own prereg rule, three false custody sentences and an oversold prediction, a misdescribed extremal witness, and an atomicity hypothesis that is load-bearing and not shown. | none | [adversary-wave2.md](history/staging/adversary-wave2.md) |
| `Q-advmin-1113` | CLOSED | Can joint caps quantified over classes recover the staircase-to-truth gap at @11 and @13? | CLOSED at @11: the adversarial minimum for the whole family is 16, below the class-blind ceiling and 18 under the staircase floor of 34, which also refutes the task's own framing that it would sit between floor and truth; at @13 the same family is priced at advmin <= 152. | none | [attack-advmin-1113.md](history/staging/attack-advmin-1113.md) |
| `Q-agent-start` | ANSWERED | What must an incoming agent read and preserve before continuing the reviewed arithmetic campaign? | Onboarding and document ownership only. The second dispatch is completed and independently reviewed on 2026-09-09. RESEARCH-EXECUTION.md owns current dispositions and candidate next obligations; RESEARCH-HANDOFF.md owns the updated exact contract. No assignment is started by that review. Twin-prime infinitude and required signed estimates remain OPEN. | C | [AGENT-START.md](AGENT-START.md) |
| `Q-anchored-calm` | PARTIAL | What is proven about the anchored calm, and what is not? | The calm names a phenomenon and never a claim: the Mirror-Sibling, Fusion, Mirror-Phase Doubling and Minus-Half results are PROVEN at all x and all scour q, the phenomenon itself is MEASURED (the anchored rotation at rank 2 of 510,510 at @17), and two things stay unproven, of which the Skeleton Equidistribution Conjecture is one. | none | [anchored-calm.md](anchored-calm.md) |
| `Q-anchored-ladder` | ANSWERED | Does the unified anchored ladder generalize past @11 and @13, and what does cheap K buy at each level? | It generalizes verbatim to @17 and @19, and the K = 0 unified floor is DEAD there (vacuous at -1262 and -55865); what survives and grows is the family lead at the classic certification depth K*, margin +2, +5, +26, +110 across @11 to @19. | A | [attack-anchored-02.md](history/staging/attack-anchored-02.md) |
| `Q-anchored-ladder-17-0830` | ANSWERED | At @17 and above, at which depth K does the composed (unified) anchored floor first turn positive and at which K does it reach the truth, and does the depth-cost curve K_first_positive(level), K_truth(level) move with level? | At @17/@19 the answer was already on record (Q-anchored-ladder: positive at K = 2/10, truth at ascending K = 109/410, minimal pool 88/350) and is re-derived here as the custody gate; the new level @23 ran under a sealed 14-of-14 forecast: positive first at K = 27 = K* (PROVEN from the record before the run), truth at ascending K = 1732 of 1739, minimal pool 1543 = 0.887 of the scour (PROVEN lower bound meets VERIFIED upper bound); across five levels positivity costs exactly K* while the truth fraction rises 0.40, 0.62, 0.73, 0.81, 0.89, a MEASURED finite table with no law in x and no exponent touched. | A | [attack-0830-anchored-ladder-17.md](history/staging/attack-0830-anchored-ladder-17.md) |
| `Q-anchored-unify` | ANSWERED | Can the three anchored mechanics be unified at @11, and what floor family does the unified cap certify? | MEASURED and PROVEN-here but HELD: extending the staircase's cofactor injection to m = 1 folds the self-strike allowance into the count, the unified-cap lemma gives fresh <= capU_K <= cap_K at every depth and prime at @11 and @13, and the floor family runs 36 to 45; the x = 37 secondary is a clean negative. | A | [attack-anchored-01.md](history/staging/attack-anchored-01.md) |
| `Q-anchored-vs-global-gap` | CLOSED | Is the anchored gap A(v) = F(v) - v easier to bound than the global gap G2(v#)? | The separation is real and correctly measured but worth exactly one unit of exponent against a deficit of 2.2665, and the anchored quantity's only proven bound is beta_2 = 4.26645, the IDENTICAL theorem rather than a consequence, because the DHR sieve is position-uniform; so the anchored object sits further from its bound, and Proposition D is a closure at today's exponent only. | none | [attack-block-09-anchored.md](history/staging/attack-block-09-anchored.md) |
| `Q-anchored-windows` | SUPERSEDED | How much does anchoring at the origin enrich a window against a random window, and for how long? | SPENT, live treatment is paper/anchored-note.md: Theorems A-C proven (A and B unconditional, C's constants HL-conditional), anchored enrichment bounded by e^{2gamma} = 3.172 and mortal, the head-window dip constant e^{2gamma}/4 = 0.79305 with 0.89 a finite-size blend; the kill shadow is no longer a separate object and section 3's peak sequence remains unreproduced. | none | [anchored-windows.md](anchored-windows.md) |
| `Q-applied-0828-backfill-1` | ANSWERED | Which legacy notes in chunk 1 received ledger blocks? | All 86 notes in the chunk received a block and none was skipped; 85 distinct question ids were minted, no id was reused from QUESTIONS.md section 2, and two notes were chained onto one shared id. | none | [applied-0828-backfill-1.md](history/staging/applied-0828-backfill-1.md) |
| `Q-applied-0828-backfill-2` | ANSWERED | Which legacy notes in chunk 2 received ledger blocks? | 85 of the 86 notes in chunk 2 carry a block; only GLOSSARY.md was left unindexed, as a vocabulary registry that poses no question, and one id (Q-records-placement) was reused from QUESTIONS.md section 2 with its question text copied exactly. | none | [applied-0828-backfill-2.md](history/staging/applied-0828-backfill-2.md) |
| `Q-applied-0828-backfill-3` | ANSWERED | Which legacy notes in chunk 3 received ledger blocks? | All 86 notes in the chunk carry a block; none was skipped, one id (Q-quadpoint-transplant) is reused from QUESTIONS.md section 2 with its question text copied exactly, one id (Q-f-census) is shared by the two notes of the f-from-census chain, and seven blocks name a TODO item whose Ledger line does not yet list them. | none | [applied-0828-backfill-3.md](history/staging/applied-0828-backfill-3.md) |
| `Q-applied-0828-backfill-4` | ANSWERED | Which legacy notes in chunk 4 received ledger blocks? | All 85 notes of chunk 4 carry a ledger block, none reuses an id already in QUESTIONS.md section 2, and none was left unclassified. | none | [applied-0828-backfill-4.md](history/staging/applied-0828-backfill-4.md) |
| `Q-applied-0828-census` | ANSWERED | Were the census red team's corrections applied to the three HELD notes? | Every WEAKENED and REFUTED verdict in redteam-0828-census.md is applied to its target note in the present tense; two producer defects and four live-doc corrections stay open and are listed here. | Z0, Z4, Z6 (retired) | [applied-0828-census.md](history/staging/applied-0828-census.md) |
| `Q-applied-0828-closures` | ANSWERED | Were the closures red team's corrections applied to the five HELD notes? | Applied. 47 prose corrections across the five notes; c2prime-refit-22 drops from CLOSED to PARTIAL and three ledger verdicts are rewritten; four producer READINGS blocks and eleven live-document lines carry the same defects and are listed here uncorrected, behind the fence. | 10 (retired), 1c (retired), 1d, Z5b (retired), 0 | [applied-0828-closures.md](history/staging/applied-0828-closures.md) |
| `Q-applied-0828-engine` | ANSWERED | Were the engine red team's corrections applied to the five HELD notes? | Applied, 37 edits across the five notes: two numbers corrected (first s >= 10.82 at x = 263 not 239, first non-empty kappa=1 level @37 not @53), two ledger verdict lines and one note title rewritten, one proof step given BV's max-over-y form, the one-class freshness factor restated on P^-(m) >= q so it holds at every scour prime, and two mislabelled columns renamed; six corrections that land on live documents are collected here unapplied, and no producer was touched. | 11 (retired), 8 | [applied-0828-engine.md](history/staging/applied-0828-engine.md) |
| `Q-applied-0828-glossary` | ANSWERED | Was the hyperuniformity conflation corrected? | In the vocabulary yes: GLOSSARY's single entry is split into Sub-Poisson window counts (Var/E), which keeps every measured value, and Hyperuniformity, which now carries Torquato's definition, the class I/II/III taxonomy, the tile's vacuous class I by periodicity and the sub-Poisson-not-hyperuniform reading at L = y^u; in the corpus no, one staging note is corrected here and ten further loose uses in nine .md files plus eighteen in seven scripts sit outside the fence with their replacement sentences listed below. | none | [applied-0828-glossary.md](history/staging/applied-0828-glossary.md) |
| `Q-applied-0828-head` | ANSWERED | Were the head red team's corrections applied to the three HELD notes? | Applied. Every WEAKENED and REFUTED row of redteam-0828-head.md lands in the note it targets as 42 prose edits, and all three ledger verdict lines now carry the surviving chain; four corrections fall outside the fence and are owed elsewhere, the load-bearing one being destroyer-census-01 §6(b)'s R and its h/R = 1.09 -> 1.03. | Z4 | [applied-0828-head.md](history/staging/applied-0828-head.md) |
| `Q-applied-0828-litimports` | ANSWERED | Were the lit/imports red team's corrections applied to the six HELD notes? | Applied, 64 substantive edits across the six notes: the Saffari-Vaughan range exponent is 6/11 in both import notes, the fixed-M THEOREM in import-fracparts is struck and the cap-36 MEASURED to PROVEN upgrade withdrawn, row 15 loses its theorem column and row 16 is regraded stale, and the six weakened sentences in the four literature notes now read as the audit requires; four claims are declined with reasons, and nine live documents plus two fenced staging notes are recorded here as owing corrections that this pass did not apply. | Z5, 4 (retired) | [applied-0828-litimports.md](history/staging/applied-0828-litimports.md) |
| `Q-applied-0828-live` | ANSWERED | Which engine and head red-team corrections reached the live layer? | Nineteen edits across four documents: the glossary's cap_K dimension count with its mandatory sifted-versus-assumed clause plus three new entries (twin opener, head, tail); the survey's one-class density factor, S1's restored pi(q-1) terms and r in N_x hypothesis, the dropped Chen absorption, Theorem C with its emptiness, dimension 1 for q_i < q, the comb-conditioning qualifier and the inverted shallow-band bullet; the certificate engine's equidistribution status cell, the q = T^{o(1)} second hypothesis and the Comb Discrepancy scope cell; and the census's R as the continuum functional with its three comparators; paper/staircase-note.md, TODO.md and QUESTIONS.md are owed and untouched. | 11 (retired), 8, Z4 | [applied-0828-live.md](history/staging/applied-0828-live.md) |
| `Q-applied-0828-quadpoint` | ANSWERED | Were the quadpoint red team's corrections applied to the four HELD notes? | Applied: the nine REFUTED and WEAKENED verdicts that target the four notes are written into them in present tense, with ledger blocks added; the tenth targets the sealed prereg, outside the fence, and is recorded in attack-quadpoint-02.md instead; three corrections owed by TODO.md Z2 and one by Z0 are listed here and are NOT applied. | Z0, Z2 | [applied-0828-quadpoint.md](history/staging/applied-0828-quadpoint.md) |
| `Q-applied-0828-queue0827` | ANSWERED | Were the 2026-08-27 drafted corrections applied? | Eighteen edit entries applied across six files, the Wu band-label inference and the saturation claim being the load-bearing ones; six proposals declined, two on ownership, one because the brief forbids promoting its note, one as already carried in paraphrase, one on an unverified inferred theta-law, and one because two scratchpad notes disagree on the number. | none | [applied-0828-queue0827.md](history/staging/applied-0828-queue0827.md) |
| `Q-applied-0828-registries` | ANSWERED | Which lit/imports corrections reached the registries? | 13 edits across six files, plus one appended changelog section: IMPORT-MAP gains rows 15 (no THEOREM, the column struck), 16 (STALE) and 17 (CLOSURE, two-sided) with its three counts recounted to seventeen rows; SEARCH-CONVENTIONS gains the Kourbatov-b, generalized-Dickman and VC-of-multiples rows with each channel's calibration state; import-map-construction's determinantal cell, natal-cap-36's separate-census sentence, one REFUTED row and one PRIOR-ART block are corrected; GLOSSARY, TODO, QUESTIONS, the five loose hyperuniformity documents and two staging notes are left for their holders and listed here. | Z5, 4 (retired) | [applied-0828-registries.md](history/staging/applied-0828-registries.md) |
| `Q-applied-0828-registries2` | ANSWERED | Which queued registry corrections were applied? | 15 edits across four files: SEARCH-CONVENTIONS gains four §1 rows (the census as a pretentious correlation with the Chowla warning, Boolean analysis on the CRT product, covering a cyclic group by translates, the fractional parts of N/n) and five §3 rows, plus one pipe fix that was hiding a clearing phrase from the gate; import-rough-anatomy's λ₁ → λ₂ comparand is corrected in four places, 12–23× becoming 2.11 to 2.86×; lit-dickman-variance §6.3's "row 15" is disambiguated to the drafted row it means; IMPORT-MAP's circularity and payoff tallies are recounted and now sum to seventeen; REFUTED.md needed no edit and got none. | none | [applied-0828-registries2.md](history/staging/applied-0828-registries2.md) |
| `Q-applied-0828-todo-prune` | ANSWERED | Which TODO items left the file under its charter after 2026-08-28? | Five left (11, 10, 1c, 1e, Z5b), nine were restated on what remains (Z2, Z4, Z5, Z6, Z7, Z0, A, 0, 1d, 4, 8), the rest stand; every retained Ledger line is verbatim, no claim's rung moved, and eleven notes now need `(retired)` on their todo lines before the gate is green. | none | [applied-0828-todo-prune.md](history/staging/applied-0828-todo-prune.md) |
| `Q-applied-0828-varE` | ANSWERED | Were the Var/E red team's corrections applied to the four HELD notes? | Every WEAKENED and REFUTED verdict in redteam-0828-varE.md is applied to its target note in the present tense; four ledger verdicts are rewritten, the theta=1 row is raised to PROVEN, and seven live-doc sentences plus one producer reading stay open and are drafted here. | 9 | [applied-0828-varE.md](history/staging/applied-0828-varE.md) |
| `Q-applied-0829-ledger` | ANSWERED | Were today's notes linked into the question ledger's TODO guard, the Z2 draft's last two non-fit lines fixed, and the covering-prune root corrected? | All three landed and none of them moves a result: nine of thirty notes read now name the TODO item their move executes and four TODO items carry the new ids, so `node research/qc.js` reports the ledger check clean at 0 findings; the Z2 draft's legal items 3 and 4 carry the audit's instrument rider and the quantifier-police clause the red team asked for; and the covering-prune producer now computes the root of a*ln(a/e) = 1 instead of quoting it, giving a = 3.5911214767 and a divergence constant of 7.1822 lnln x against the 7.19 the file carried, a 0.08 per cent change with nothing downstream consuming it. | none | [applied-0829-ledger.md](history/staging/applied-0829-ledger.md) |
| `Q-applied-0829-measure-a` | ANSWERED | Were red team A's corrections applied to the notes it reviewed? | Of the nine APPLY items in redteam-0829-measure-a.md §3a-3c, seven were applied here as exact string edits, two (E1 and E5) were verified as already applied by the producing agent with a producer fix and a forced re-embed, one clause of E1's proposed wording is left unapplied and is recorded as owed, and the four live-document items of §3d plus the QUESTIONS.md regeneration are left for the orchestrator; node research/qc.js returns TOTAL 0 across all thirteen checks after the edits. | none | [applied-0829-measure-a.md](history/staging/applied-0829-measure-a.md) |
| `Q-applied-0829-measure-b` | ANSWERED | Were red team B's corrections applied to the notes it reviewed? | 17 of 17 APPLY items whose target is a staging note are applied in place, 2 ledger verdict lines rewritten as the red team specified (measure-record-null2-0829 and zone-tail-02-0829), 3 HOLD/DECLINE items deliberately not applied, 5 live-document items left verbatim for the orchestrator, and 3 producer items recorded as OWED without touching any .js; the fast gate returns 0 findings after the pass, the single mid-pass finding having belonged to another agent's file, research/measure-g2z2-0829.js:432, and never to any edit made here. | none | [applied-0829-measure-b.md](history/staging/applied-0829-measure-b.md) |
| `Q-applied-0829-measure-c` | ANSWERED | Were red team C's corrections applied to the notes it reviewed? | 22 of the 25 items in section 3 target the four HELD staging notes and all 22 are applied (21 as the exact old-text to new-text strings the red team wrote, 1 as a minimal carry because filling its column for all nineteen rows would be a fresh grading judgement rather than a citation), plus 1 directed edit to lit-scourfield-2008.md section 0 that red team section 1g names and section 3 gives no string for; 3 items are flagged HOLD and are left verbatim for the orchestrator (varE-theta2-proof.md, lit-smooth-divisors.md, SEARCH-CONVENTIONS.md); 1 producer item is OWED and untouched, since the producer's readings 13 and 14 still carry the M-P1 failure that E8 and E9 reverse in the note and correcting them needs a re-embed; node research/qc.js returned TOTAL 1 on the run straight after the edits, the one finding being research/measure-g2z2-0829.js:432 in another agent's file, and TOTAL 0 on the run after this note was written, with refs, quotes and ledger clean on both. | none | [applied-0829-measure-c.md](history/staging/applied-0829-measure-c.md) |
| `Q-applied-0829-refuted` | ANSWERED | Were the four refuted-claims audits' APPLY row rewrites applied to REFUTED.md? | 25 of the 27 APPLY items are in the file, 1 more merged into a sibling's text at the shared boundary row, 1 deferred to the in-progress red team, 7 HOLD items untouched and listed here for Chris, 4 items owed outside REFUTED.md; the table still holds exactly 67 data rows and qc.js reports refs 0 and crosslinks 0. | none | [applied-0829-refuted.md](history/staging/applied-0829-refuted.md) |
| `Q-applied-0829-registries` | ANSWERED | Were the registry debts of 2026-08-29 (IMPORT-MAP rows, the PRIOR-ART spectrum line, the escape labels, the REFUTED HOLD proposals) landed? | All four debts are discharged as far as a non-adjudicating pass may take them: IMPORT-MAP carries rows 20 and 21 at CLOSURE-plus-anchor and anchor-plus-wall-address with nothing opened, PRIOR-ART's Holt-Rudd attribution now names the printed spectrum and the SCRATCHPAD-GRADE 2.82/ln p mixing rate with priority stated as Holt and Rudd's, recon-0829-escapes.md section 6 carries all sixteen owed (i)/(ii)/(iii) labels of which nine are fresh judgements and three come out (ii), and three of the seven REFUTED HOLD proposals were applied as wording and calibration while four are left verbatim for Chris because they touch a producer, a canonical file, a cross-file number or the index's format; the table stands at 67 rows and qc.js is 0 on refs, crosslinks, calibration and search-convention. | none | [applied-0829-registries.md](history/staging/applied-0829-registries.md) |
| `Q-applied-C` | ANSWERED | Which wave-2 consistency findings were applied to the paper suite? | Applied across the seven paper/ files with post-edit line numbers, plus a CHRIS-DECIDES list, handoffs to other partitions and one unresolved item: two scopes for the Cov_adj anticorrelation exception count, both now printed, one of which should be checked and the other dropped. | none | [applied-C.md](history/staging/applied-C.md) |
| `Q-applied-G` | ANSWERED | Which wave-3 partition G findings were applied, and what did the pass find on its own? | Applied to the eleven owned files: the OEIS off-by-one confirmed and provable four ways, a factor of two found in the seam draft's Hardy-Littlewood heuristic, the L gap corrected in three files from a flat 0.58 ln p to the home's 0.58 to 0.95 ln p range, seven orphans swept, and one supplied answer refused as wrong before it reached a header banner. | none | [applied-G.md](history/staging/applied-G.md) |
| `Q-applied-Q` | ANSWERED | Do the two OEIS drafts survive an instrument that recomputes them rather than reads them? | Two defects found in the G2 draft (the Maier-Pomerance conjecture cited in the wrong direction, and a no-upper-bound-published claim the repository itself contradicts) plus a third error class routed from partition P; every DATA term was recomputed and audit-numbers went from 37/39 to 76/78 checks. | none | [applied-Q.md](history/staging/applied-Q.md) |
| `Q-applied-wave2-A` | ANSWERED | Which wave-2 partition A corrections were applied, and to which files? | Five jobs applied across G2-STATE.md, LOCALIZED-GAP.md, maier-matrix.md and origin-excess.md, with partition A's own qc columns at 0 on every check afterwards; handoffs to other partitions and one decision needing Chris are listed rather than guessed. | none | [applied-A.md](history/staging/applied-A.md) |
| `Q-applied-wave2-B` | ANSWERED | Which wave-2 partition B corrections were applied to U-FRAME.md, ATTACKS3.md and gate-multiplies.md? | Applied with the U-FRAME section map preserved (128 inbound pointers, 47 on 5a, nothing renumbered), the strategic contradiction resolved, statistics corrected, one dead quotation removed and two further corrections to the record found on the way; section 12 lists what stayed unresolved. | none | [applied-B.md](history/staging/applied-B.md) |
| `Q-applied-wave2-D` | ANSWERED | Were wave-2 partition D's findings applied to the eight entry-path documents? | Applied across all eight files with qc total 22 to 21 and one refs finding of its own (a framework bug), two transfers pairs word-diffed; the em-dash scope question and one GLOSSARY entry are flagged as judgement calls rather than omissions, and other partitions were live in the same tree so the deltas are not all this partition's. | none | [applied-D.md](history/staging/applied-D.md) |
| `Q-applied-wave2-E` | ANSWERED | Which wave-2 partition E corrections were applied, and to which files? | Seven jobs applied across covering-dive, two-class-lower-bounds, PRIOR-ART, sift-limit-attack, theta-ladder, maxgap-law and dhr-verification, with refs and quotes at 0 in this partition before and after; one novelty verdict in a publication-track file is weakened by de Polignac 1849 and flagged for Chris. | none | [applied-E.md](history/staging/applied-E.md) |
| `Q-applied-wave2-F` | ANSWERED | Which wave-2 partition F corrections were applied to the natal-cap family and its compound claims? | Applied across nine natal-cap files with two new homes created (anchored-calm.md and certificate-engine.md); the Fused-Window Calm Lemma was decomposed and its name retired, the X-limitation theorem's scope is confirmed a scope error, and the refutation is recorded as bigger than it had been reported. | none | [applied-F.md](history/staging/applied-F.md) |
| `Q-applied-wave3-H` | ANSWERED | Were wave-3 partition H's U-FRAME sections 10-12 split into child documents? | Split and applied: U-FRAME falls 1,032 to 772 lines with three children created, but the corpus as a whole is 87 lines larger and that must not be reported as a shrink; refs and crosslinks stay at zero and no transfers finding exists between any stub and its child. | none | [applied-H.md](history/staging/applied-H.md) |
| `Q-applied-wave3-I` | ANSWERED | Was the flagship paper split as wave 3 partition I directed, and what did the split expose? | Split into paper/moire-primes.md and the new paper/wall-note.md, with every deliberate change to moved text word-diffed; three open defects sit inside the split, two of them already landed and one not, and the judgement calls are listed so they can be overruled. | none | [applied-I.md](history/staging/applied-I.md) |
| `Q-applied-wave4-P` | ANSWERED | Which calibration defects sit on a3-05-bound-L.md, localized-04-maxsum.md and level-ledger-tight.md, and were they fixed? | Fourteen defects found and fixed on the one axis wave 3 never ran, none of them reachable by any check in qc.js: two numbers contradicting the file's own pasted script output, one slot count against thirteen other sites and an exact closed form, one superseded sifting limit and three dropped scopes; the gate stayed at zero on all six checks. | none | [applied-P.md](history/staging/applied-P.md) |
| `Q-at43-bigint-0830` | PARTIAL | Can the K-30 natal march be carried past its 2^53 ceiling to @43 exactly, and is the @43 point worth its cost? | The engine side is done and VERIFIED (five paths promoted to BigInt, @7..@37 and a 0.248% slice of @41 reproduced digit for digit); the @43 point is NOT run, because the measured extrapolation is 579 h of eight cores on this machine (a 43x tile times a 2.23x per-cell cost, against the brief's ~13x), which is a weeks-class box job whose only payoff is a sixth point on a curve with no consumer; the forecast 0.8393 raw / 0.8399 persisted stands unscored. | 1 | [engine-0830-at43-bigint.md](history/staging/engine-0830-at43-bigint.md) |
| `Q-attacks-wall-ten` | ANSWERED | Which ten attacks on the frontier-zone wall were executed, and what did each return? | All ten are marked DONE with their learnings recorded; none breached the wall, parity stands, and the durable yields are attack 8's unconditional small-gap theorem for p >= 17 and the anchored-origin phase picture. | none | [ATTACKS.md](ATTACKS.md) |
| `Q-attacks2` | ANSWERED | What did the ten copy-geography attacks of the second wave find? | All ten complete: one theorem-grade result (the Exact Invariance Lemma, fossil depth frozen at birth, proved independently twice) and one MEASURED, Hardy-Littlewood-conditional law (the Unification Law, to about 1 percent); no unexplained novelty survives and the wall stands. | none | [ATTACKS2.md](ATTACKS2.md) |
| `Q-attacks3-uframe` | ANSWERED | What did the ten-attack u-frame wave (A1-A10) settle about the fold structure and the Zone Postulate? | The R/I split held: every residue attack returned an exact object and no interval attack moved; the additive chain G2(new) <= G2(old) + L*mbar it was framed around is itself REFUTED (U-FRAME 5a step 4), A5's Theorem B is structurally capped, and A10's exactness route is a dead end (rate 0.927 over 329 cells, excess 6..120 not shrinking). | none | [ATTACKS3.md](ATTACKS3.md) |
| `Q-audit-campaign` | ANSWERED | Does the campaign archive layer - the natal-cap notes, ATTACKS, covering-dive and their neighbours - hold internal inconsistencies? | Six files and eight of the natal-cap notes are clean and need no change; the remainder carry per-file findings recorded in place, and this is a diagnosis pass rather than an edit. | none | [audit-campaign.md](history/staging/audit-campaign.md) |
| `Q-audit-cross-doc` | ANSWERED | Where does the corpus carry two values for the same object in two different documents? | Twenty-six findings ranked A, B and C, eighteen of them the Kourbatov shape where the resolution was already on disk in a document the stale one cites by name, including a retracted theta column quoted as live in nine places and a prior-art collision on the dimension-2 Rankin accounting; the gate read 0 findings before and after. | none | [audit-cross-document-constants.md](history/staging/audit-cross-document-constants.md) |
| `Q-audit-front-door` | ANSWERED | Does someone arriving after the 2026-08-19/20 wave get the true current picture from README, G2-STATE section 0 and CHRONICLE in ten minutes? | All three are STALE: README's Status is dated 2026-08-17 with a broken map row and four missing files, G2-STATE section 0 stops at the second attack wave, and CHRONICLE ends at Day 5; drafts are ready for two of the three and README's rewrite is left in Chris's register. | none | [audit-front-door.md](history/staging/audit-front-door.md) |
| `Q-audit-new1` | ANSWERED | Do G2-STATE.md, LOCALIZED-GAP.md, localized-04-maxsum.md, exponent-control.md and gate-multiplies.md agree with themselves and with their sources? | Findings per file, the leading one a NARROWED Origin Excess claim: the lemma carries an unstated third hypothesis, positivity of D_y(y'^2) - 2(pi(x) - pi(y) + 1), which forces ln x*/ln y near 1.44 at every level computed and caps the advantage at about 2.2 rather than order (ln x / ln y)^2. | none | [audit-new1.md](history/staging/audit-new1.md) |
| `Q-audit-new2` | ANSWERED | Are the seven research documents of the new2 partition internally consistent and correctly scoped? | Per-file findings across the seven, mostly dropped scopes and attribution defects, plus four documents that were missing the standard current-understanding footer, which was added. | none | [audit-new2.md](history/staging/audit-new2.md) |
| `Q-audit-numbers` | ANSWERED | Does the corpus's arithmetic survive recomputation from scratch by an independent method? | The ladder is right: all twelve G2 terms reproduce under a method sharing no code with the one that produced them, 37 of 39 assertions pass in 152 s, and the four errors found are small and none is load-bearing. | none | [audit-numbers.md](history/staging/audit-numbers.md) |
| `Q-audit-papers` | ANSWERED | Are the paper suite and the root README consistent with their research homes? | Per-file corrections applied across the six paper/ files and README, with a Not fixed section naming what was deliberately left, including the exposition question the Holt attribution raises and one stylistic sentence of Chris's that was left alone. | none | [audit-papers.md](history/staging/audit-papers.md) |
| `Q-audit-reading-path` | ANSWERED | Can a cold reader reach every live result in two hops? | The two-hop test passes for eight of the ten headline results of 2026-08-19/20 and no staging record is orphaned; what fails is narrower, the front door being three days behind and contradicting REFUTED.md on u_sup, G2-STATE's section 10 table still the 2026-08-17 list, and kappa-not-L carrying nothing from the L wave. | none | [audit-reading-path.md](history/staging/audit-reading-path.md) |
| `Q-audit-spine` | ANSWERED | Do the spine documents - ZONE-POSTULATE, THE-DIALS, THE-LENS, GLOSSARY, OBSERVATIONS - state their objects correctly? | Findings per file, the leading one a frame error in ZONE-POSTULATE section 5: G2's own exponent measures 1.57 central, bracket 1.3 to 1.9, against a calibrated one-class control, while theta is above 2 and rising, so the two readings that sat on boundary exponent 2 resolve in opposite directions. | none | [audit-spine.md](history/staging/audit-spine.md) |
| `Q-audit-staleness` | ANSWERED | How much of the live layer is stale against changelog passes 26 to 48? | Eleven of the nineteen files in scope are clean and eight carry at least one stale sentence (U-FRAME three, G2-STATE two and others), with a separate list of upgrades the live layer has not absorbed; report only, nothing outside the report was edited. | none | [audit-staleness.md](history/staging/audit-staleness.md) |
| `Q-audit-uframe` | ANSWERED | Do the u-frame documents' claims survive an audit against their own sources? | Several are REFUTED: the multiplier requirement ln c <~ 2 ln^2 u / u is off by a factor ln u and is replaced by the per-fold rate ln c(p) <= 2 ln p / p, the Inertness Lemma's rate is narrowed to 4/u, and SUM L*mbar ~ 2 x ln^3 x is false because U-FRAME step 4 is false. | none | [audit-uframe.md](history/staging/audit-uframe.md) |
| `Q-b2mean` | ANSWERED | Can the mean value of B2 = Sum e^2 Vabs(e)^2 be bounded below its trivial qmax*B ceiling? | Yes, by one logarithm: B2 = O(qmax*ln^7 z) against the trivial O(qmax*ln^8 z), with the mass located on primorial-core smooth e nowhere near qmax, the primitive-mode weight J2(e)/12 proved and priced as a flat 1.48x cut of MS3, and the finite forms computed exactly at z = 13..47. | none | [attack-b2mean-01.md](history/staging/attack-b2mean-01.md) |
| `Q-barrier-kappa2` | CLOSED | Does Granville's exceptional-character construction, which makes the Jurkat-Richert f and F attained by interval sieving problems at kappa = 1, transfer to kappa = 2 and supply the missing barrier on wall-note Face 4, so that no class-blind argument can beat beta_2 = 4.26645 on intervals? | No. Verdict (b): the transfer runs, fixes the axiom obstruction that sift-limit-attack.md section 2 blamed for the mixed-sign sketch's death, and then hits a hard ceiling at u = 2, because the character's only gift is the one-point identity lambda = chi on z-rough integers and a sign pattern with a +1 coordinate is empty exactly when z^2 >= x; above u = 2 the surviving question is the shifted intersection of two positive-density lambda-classes, which is Chowla-strength, so the section 2 verdict stands with a corrected reason; the band (2, 4.26645] is untouched, and the hypothesis itself implies the target by Heath-Brown 1983. | 0 | [attack-barrier-kappa2.md](history/staging/attack-barrier-kappa2.md) |
| `Q-bc-parity-floor` | CLOSED | Is the 2 that the census's B/C ratio limits to the same object as the parity floor's 2? | REFUTED at the first step, before any kappa-scan: the certificate dies where B/C crosses 1, not 2 (B = 503 against C = 497 at the death zone), the constant reads the sifting dimension while the threshold does not, and the parity floor's 2 cannot be this one. | none | [attack-bc-parity-floor.md](history/staging/attack-bc-parity-floor.md) |
| `Q-beta2-AB-bounded` | ANSWERED | Is B(z,s) bounded, and does bounding it move the 4.2665 exponent? | B(z,s) <= 9 A(z)^2 (E(z) - 1) = O((log z)^8) is proven, unconditional, explicit and uniform in s, but the gap it closed was never load-bearing, the estimate has a published neighbour at s >= 9, Opera de Cribro Lemma 6.18, which does not cover this corpus's s in [2.0, 3.4], and the route to B = O(1) is measured dead as a uniform statement. | none | [attack-AB-bounded.md](history/staging/attack-AB-bounded.md) |
| `Q-beta2-exact-strata` | CLOSED | Does re-inserting exact Buchstab strata (DP3) lower the dimension-2 positivity threshold below beta2 = 4.26645? | A sharp negative with a price tag: exact strata are legitimate and worth 1.72 to 1.84 of exponent, taking the positivity threshold to 2.0260 at finite levels, but they produce no theorem because the exact stratum value is the upper sieve function of a dilated tile one level down, so the regress terminates at every finite z and at no uniform z. | none | [attack-beta2-03-exact-strata.md](history/staging/attack-beta2-03-exact-strata.md) |
| `Q-beta2-loss-budget` | ANSWERED | Where in the chain from truth to beta2 = 4.26645 is the loss, and which discard point is worth attacking? | Aim at theta: it carries the largest derivative (-4.2665 per unit) and the only consumer in the literature, beta is worth at most 1.07 and has no consumer, DP2 and the o(1) are worth exactly zero, and the two live knobs together stop at 1.597, so the last factor of 1.6 down to truth is in neither of them. | none | [attack-beta2-04-loss-budget.md](history/staging/attack-beta2-04-loss-budget.md) |
| `Q-beta2-theta-total` | CLOSED | What is the largest theta_total defensible position-uniformly, and does it clear the break-even the beta2 upper-bound attack needs? | The largest defensible theta_total is 1 and it does not clear break-even: it misses by 0.2417 under the brief's symmetric arithmetic and by 0.2090 under the corrected asymmetric one, no part of the gap closes, and the weakest link in the negative is an ABSENT rather than a PROVEN. | none | [attack-beta2-02-theta-total-minimal.md](history/staging/attack-beta2-02-theta-total-minimal.md) |
| `Q-beyond-chebyshev` | PARTIAL | Can the ensemble bound on P(S = 0) be pushed beyond Chebyshev, and how far? | Two beyond-Chebyshev bounds now stand, at @11 where capacity gives P(S = 0) = 0 exactly and at @13 where P(S = 0) <= 1.898e-6, a factor 513 below Chebyshev's 9.74e-4, with 683 assertions machine-checked; @17 is blocked on a 4.9e16-term sum and needs a 4-point wrap identity that does not exist. | none | [natal-cap-21-beyond-chebyshev.md](natal-cap-21-beyond-chebyshev.md) |
| `Q-bf-split` | ANSWERED | Is Brüdern-Fouvry's level split optimal for their own theorem, or is there unclaimed exponent in it? | It was 99.3 per cent a trap: their condition (iii) binds at the published split and the proposed re-split violates it by x^{0.040403}, leaving 0.0000120536 in theta of the claimed 0.0295482779, real but invisible at the four decimals they print. | none | [attack-bf-split.md](history/staging/attack-bf-split.md) |
| `Q-bilinear-fold-first-attack` | ANSWERED | Does assigning each Mobius factor to its first fold, or applying a direct second-moment bound, establish the missing one-sided estimate? | The first-fold identity yields no saving; a direct second moment has a negligible diagonal and an open two-prime off-diagonal. Fixed-fold covariance is an exact residue-imbalance square and the beta weights balance at each fixed modulus. Growing-depth joint control remains OPEN; B>=-C2*x+o(x) is not improved. | C | [bilinear-fold-attack.md](bilinear-fold-attack.md) |
| `Q-bilinear-transplant` | CLOSED | Does this programme's frame have anywhere to put bilinear or Type-II arithmetic information, the only thing that defeats parity in practice? | The tile side cannot host it, since no corpus object is a signed sum over two ranging element ranges; the zone side can express one, and the estimate that one needs is the one already recorded absent. Section 9 lists the four findings that would reopen the row. | none | [attack-bilinear-transplant.md](history/staging/attack-bilinear-transplant.md) |
| `Q-block-L-first-dead` | ANSWERED | Is the block-1 counting bound on L the first-dead 62 or the last-alive 111, and does downward closure hold in the block coordinate? | Downward closure HOLDS in the block coordinate: L <= 62 is sound and recomputed from scratch rather than inherited, L <= 111 is true, implied by 62 and weaker by 1.79x, and the adjudication's supposedly sharper instrument is attack 3's instrument. | G (retired) | [adjudicate-L-bound.md](history/staging/adjudicate-L-bound.md) |
| `Q-block-alternation` | CLOSED | Is there a block-level alternation law? | No: a block-level inequality exists and is a real theorem, but it is not an alternation law - over a block the alternation law is strictly weaker than plain slot counting by the exact factor mbar(T_v)/6, at least 10/6 and growing like ln^2 v, and the resulting Block Partition Inequality closes only at v = 5 and v = 7 and is vacuous from v = 11 because 2*Sum_{v<p<=v^2} 1/p rises to 2 ln 2 = 1.3863. | none | [attack-block-03-alternation.md](history/staging/attack-block-03-alternation.md) |
| `Q-block-combined-L` | CLOSED | Does combined L grow slower than the window, the criterion for the v -> v^2 block ladder to sustain itself? | No: on the eleven-term exact ladder (this attack computed G2(41#) = 546) the ratio is flat at slope +0.05 +/- 0.11 on b >= 11 against a 12.3 per cent band, while the same estimator resolves the one-class control's falling ratio at 11.6 sigma; and the criterion is not independent, since at the natal it IS G2(x#)/x^2, the Zone Postulate itself. | none | [attack-block-01-ladder.md](history/staging/attack-block-01-ladder.md) |
| `Q-block-exponent` | CLOSED | Does the block sub-problem have a better exponent than the proven 4.2665? | The required exponent for the ladder to close is 2, not 4 (the brief's step-3 arithmetic carried a factor error), and 2 is the TPC-equivalent line, so the useful part of the open band (2, 4.2665] is empty; the block's own prime range pins kappa = 2 and starting from T_v does not change the dimension. | none | [attack-block-05-exponent.md](history/staging/attack-block-05-exponent.md) |
| `Q-block-greedy` | ANSWERED | Does the block-restricted adversarial greedy reach the truth at v = 5, and does block restriction cost anything? | Deterministic greedy reaches 17 against truth 19, randomised restarts reach 19 and an exhaustive DP confirms it, so greedy as a rule is optimal at v = 5 and the shortfall is a search failure; block restriction costs nothing on ten points with the same estimator on both sides, and the published Y2 ladder's bisection on a non-monotone predicate is a real defect. | none | [attack-block-04-greedy.md](history/staging/attack-block-04-greedy.md) |
| `Q-block-kappa` | CLOSED | What does the block version of kappa(m) buy over the per-fold form? | Nothing: kappa_block(1) = 19 equals combined L at block 1 by construction, the minimal shift j*(m) equals kappa_block(m) at every m from 1 to 12 so there is zero slack in the block object, and the block form of Theorem C is empty, its vacuity coefficient 1.552 against a requirement of 1 at block 1 and growing like ln^2 v. | none | [attack-block-07-kappa.md](history/staging/attack-block-07-kappa.md) |
| `Q-block-killers` | ANSWERED | For a maximal run of deleted T_v slots under the block v -> v^2, which primes do the deleting and how concentrated is the work? | Not concentrated: across 40 runs in five datasets every block prime kills at least one slot of every run and the exact minimum set cover is 82 to 100 per cent of the block, so no bound ranging over the block gets a reduction; the one favourable number is 915 of 1146 slots, 79.8 per cent, with exactly one killer. | none | [attack-block-02-killers.md](history/staging/attack-block-02-killers.md) |
| `Q-block-literature` | ANSWERED | Does the literature already own the range-restricted covering object behind the block v -> v^2? | FOUND, and it has a name: the range-restricted covering problem is Erdős Problem #688 and is OPEN, the bounded-capacity conjecture #1200 is a third trap of the same class as the brief's two, and the Kalmynin-Konyagin journal version that covering-dive.md says does not exist does; the remaining negatives are ABSENT-AFTER-COMPETENT-SEARCH on calibrated channels. | none | [attack-block-06-literature.md](history/staging/attack-block-06-literature.md) |
| `Q-block-reformulation` | CLOSED | Does the v to v^2 block reformulation, treating the block as a set, give a smaller combined L and an exponentially growing window? | Sound reformulation, no open path: no primality input is needed anywhere, nothing is deleted inside the window at all so combined L there is identically zero, and the object has to live in the tile; this note's own correction (the counting bound is 111, not 62) was itself reversed the same day by adjudicate-L-bound.md. | none | [attack-block-00-ADJUDICATION.md](history/staging/attack-block-00-ADJUDICATION.md) |
| `Q-block-secondmoment` | CLOSED | Can a second moment over a block bound the empty windows, and is it allowed to work? | NO, on a tile-independent impossibility: Chebyshev needs dist(E, Z) < E/sqrt(W) and the measured shortfall at H = 204 is a factor 8.41e6, so a second moment gives a density bound that is legal at every H and TPC-relevant nowhere; the TPC line sits at eps = 1/W and at H about w^2, and quantifying over w buys nothing. | none | [attack-block-08-secondmoment.md](history/staging/attack-block-08-secondmoment.md) |
| `Q-block-target` | CLOSED | What exponent does the squaring ladder v -> v^2 actually need, and do the steps get easier up the ladder? | The required exponent is exactly 2 with a constant below 1, which by the p^2 rule is TPC-equivalent, and the requirement is exponent-invariant at every step, so as a route to a theorem weaker than TPC the ladder is dead. | none | [attack-block-10-target.md](history/staging/attack-block-10-target.md) |
| `Q-bonferroni-degree` | CLOSED | What degree does the Boole-Frechet certificate need, and does raising the degree reach an asymptotic bound? | Dead for asymptotics on a loop that closes on itself: raising the degree divides the over-certification exponent by the number of pairs without removing it (measured slopes 0.5441, 0.5425, 0.2816, 0.2937, 0.1695 at k = 2..6 against the predicted 1/(2 floor(k/2))), and Theorem A gives k >= (theta(x) - O(1))/(log G2 + O(1)), so the better the G2 bound assumed the higher the degree needed. | none | [attack-bonferroni-degree.md](history/staging/attack-bonferroni-degree.md) |
| `Q-buchstab-deep-0830` | CLOSED | Can the certificate engine's deep-ladder Buchstab transfer be proven at dimension 2 at the depths the run levels reach by a route that does not go through the fundamental lemma at s >= 22.06 or the constant-free DH Theorem 9.1 (TODO 8a)? | NO by any instrument this corpus can cite, and the non-closing step is structural, not a constant: the transfer is an asymptotic for a ratio of two dimension-2 sifting functions at one sifting depth z = q, so a sieve bracket [f2, F2] survives undivided in the ratio (width 3.67 at the best sigma any level has, 4.71 at the @23 head); a correction \|B - 1\| >= 1% can only occur at sigma(q) < 1.8 where f2 = 0 and F2 >= 7.85, while a lower bound exists only at sigma > 4.266 where \|B - 1\| < 1e-5; the Buchstab identity iterated once is already negative at K = 1 for q = 37 at @23 and is the sieve itself when iterated fully; Jurkat-Richert fails Omega(1) as stated; in the certificate's legal direction F2 beats the trivial cap_K <= cap2 at 0 of 1512930 (q, K) pairs at @23, so the sharp-sieve floor is -1733138 at every K; the transfer stays HEURISTIC, what would move it is a kappa = 2 asymptotic in the open band 2 < sigma < 4.266, and part (b) is scoped and graded, not attacked. | 8 | [attack-0830-buchstab-deep.md](history/staging/attack-0830-buchstab-deep.md) |
| `Q-buchstab-transfer` | ANSWERED | Is the certificate engine's Buchstab transfer provable in the shallow regime y = T^{o(1)}? | PROVEN conditional on the fundamental lemma and EMPTY at every run level (needs s >= 22.06; available 4.7 @23, 17.1 @97); the engine's B is a dimension-1 object, the survey's pair-Buchstab is dimension 2, the certificate needs a third. | 8 | [thm-buchstab-transfer-shallow.md](history/staging/thm-buchstab-transfer-shallow.md) |
| `Q-bv-import-survey` | ANSWERED | Which unproven legs of the tile programme become theorems if Bombieri-Vinogradov, Elliott-Halberstam or GRH is imported? | Two legs become provable now, the fixed-modulus tail refinements S1/S2 by Siegel-Walfisz and the full-wheel prime-comb equidistribution in the tail regime by BV; the Buchstab transfer at bounded u and Assumption A for d = 2 are parity-blocked at every one of the four inputs. | none | [bv-import-survey.md](bv-import-survey.md) |
| `Q-c2prime-drift` | PARTIAL | Why does c2' drift on the 22-term ladder? | Class-count-blind (attack-c2drift-01 §1); on item 1c's own band x >= 41 the ten-point rate is unresolvable: c2' 0.3745 +/- 0.1411 against c1's 0.3344 +/- 0.2358 on the same primes, a difference of 0.0401 = 0.12 of the control's ten-point window sd. Whether the drift is real is NOT closed here: attack-c2drift-01 measured it at p = 0.0053 on x >= 17 and left (i)' and (ii) alive. exponent-control §2/§4/§6 refit at 22 terms. | 1c (retired) | [attack-c2drift-01.md](history/staging/attack-c2drift-01.md), [c2prime-refit-22.md](history/staging/c2prime-refit-22.md) |
| `Q-cal4-routing` | ANSWERED | Does the standing certificate plan point at the right obstruction, and what is CAL4 worth at @17? | The plan is aimed at the wrong obstruction, but not for partition W's reason: the @13 1e-9 gate is met today only by an assembly containing the brute-force C(990,4) march whose @17 counterpart is 513 days on ten cores and is not codeable here, the @17 requirement is a ladder whose first useful rung is relT4 <= 5.05e-5, a factor of 7.9 rather than six orders, and CAL4 has no correct constant value. | none | [phase1-W2-cal4-routing.md](history/staging/phase1-W2-cal4-routing.md) |
| `Q-calm-lemma-identities` | PARTIAL | What in the fused window and the anchored calm is proven, exactly? | Three identities and the exact spectral forms are proven and verified as exact integers or floats; the uniform-in-q anticorrelation is REFUTED rather than open, with six counterexample primes across six levels, and the Anchored Typicality Measurement is the anchored-escape wall one level down with no proof mechanism in sight. | none | [natal-cap-19-calm-lemma.md](natal-cap-19-calm-lemma.md) |
| `Q-calm-vs-kill` | PARTIAL | What does the anchored calm buy against annihilation? | Two theorems, the @11 closure and the X-Limitation Theorem at @11, @13, @17 and @19, and two refutations, calm implying concentration and minimizer loudness; the overlap-floor candidate that would prove non-annihilation dies on the anchor's own drift, with the anchored rotation t = 0 its worst case at @17, leaving the X-floor open. | none | [natal-cap-31-calm-vs-kill.md](natal-cap-31-calm-vs-kill.md) |
| `Q-capK-bv` | ANSWERED | Is the prime-regime cap_K over the full wheel an unconditional asymptotic via the fundamental lemma over Bombieri-Vinogradov? | PROVEN at short-note grade for q_K = W^{o(1)}, and EMPTY in every computable range (needs s >= 10.82, first cleared at x = 263; the lemma's floor s >= 10 is first reached at x = 239); the deep ladder is untouched. | 11 (retired) | [thm-capK-bv.md](history/staging/thm-capK-bv.md) |
| `Q-capture-identity` | ANSWERED | Does the transplanted cap family collapse onto a classical object, and what does the collapse say about the depth law and the wall? | PROVEN, elementary: floor_K = T − X(K) on the half-open window with both members in [Q², Q′²), a convention that is load-bearing; the wall is renamed, not weakened; Σ capU counts each member against its own threshold, not against a uniform p_K, the two differing 11% to 37% at K*. | Z2 | [quadpoint-identity-01.md](history/staging/quadpoint-identity-01.md) |
| `Q-centered-discrepancy-estimate` | PARTIAL | Can the top of D_y be removed using ordinary prime distribution after an exact divisor flip, and what estimate remains? | Equations (3)-(4), the exact split and flip, survive review and finite controls. A repair of the top-range bound T^top=O_(A,eps)(x/log^A x) is DERIVED in section 3a (2026-09-08) with the endpoint atom retained, odd square divisors, the corrected reciprocal-totient local factors with (m',g)=1, explicit truncation powers, a Cauchy multiplicity device, and a uniform Mobius mean proved from the q=1 Siegel-Walfisz statements; its inputs are the terminal-point BV of Tao Notes 3 Theorem 17 with the prefix form derived by rounding. The handler (lane V) read the derivation on 2026-09-08, reconstructed (BV*), (3a.9), (3a.14) and (3a.16), checked the limiting constant of (3a.9) numerically at eight (b,g) pairs and found no defect; it is accepted at its stated scope, with ineffective constants. The payoff is D_y=D^(e_1)+O_(A,eps)(x/log^A x) only, so the handoff consumer is equivalent to D^(e_1)>=-4x/25+o(x). The fixed-endpoint signed discrepancy, D_y>=-4x/25+o(x) and twin-prime infinitude remain OPEN. | C | [centered-discrepancy-estimate.md](centered-discrepancy-estimate.md) |
| `Q-centered-discrepancy-measurement` | ANSWERED | At reachable x, is the OPEN sufficient input D_y>=-4x/25 numerically violated, is the absolute form (13) numerically plausible, and does D_y carry structure beyond a random-sign model? | MEASURED to x=2^38. Neither pre-registered falsifier fires. D_y/x stays within 0.0043 of zero for the measured j>=26. Over 30<=j<=38, D_y/x differs from -(T1/x-C2) by at most 2e-4, with maximum 1.84401e-4 at j=30; the classical term dominates this finite comparison. The data do not establish an asymptotic fluctuation scale, an impossibility of informative future measurements, or the sufficient signed estimate. No proof status changes. | C | [centered-discrepancy-measurement.md](centered-discrepancy-measurement.md) |
| `Q-certificate-engine` | PARTIAL | What did natal-cap-28 assemble, and at what calibration does the certificate engine stand? | There is no fully analytic certificate law and nothing here is closed: what reads as one object is nine at five calibrations with one of the nine refuted, the Certified-Head Theorem is PROVEN on 1/3/6 certified primes at @17/@19/@23, and every engine output carries the status of its weakest input, the HEURISTIC Buchstab Transfer Hypothesis. | none | [certificate-engine.md](certificate-engine.md) |
| `Q-chain-review-0906` | ANSWERED | Do the written derivations from S(x) down to E_dagger hold as stated, with every imported theorem used inside its hypotheses and every discarded term at the claimed O_H(x/log^H x) rate, and where does the chain remain unreviewed? | Three independent adversarial passes found no defect in the six classical contributions from S(x) to E_>, none in the grouped moment (1)-(20) including the E_* to E_dagger step, and none in the residual-coverage link E_> to E_*, whose block-shape derivation was reconstructed and verified exactly. Every imported theorem was confirmed in its primary source except the Mobius Bombieri-Vinogradov citation, which points at an exercise sheet and needs a published replacement. Stale o(x) rates in three note bodies were replaced. A checked argument is not a refereed theorem; the OPEN signed margin is untouched. | C | [chain-review-0906.md](chain-review-0906.md) |
| `Q-changelog-add-B` | ANSWERED | Which superseded text from wave-2 partition B belongs in the changelog? | The per-document entries for U-FRAME, ATTACKS3 and gate-multiplies, staged for the shepherd to merge in one pass; nothing was written to CHANGELOG.md here. | none | [changelog-add-B.md](history/staging/changelog-add-B.md) |
| `Q-changelog-add-C` | ANSWERED | What history left wave-2 partition C's paper-suite files, and what has to be staged for the CHANGELOG? | Staged: Door 2's two load-bearing numbers are RETRACTED because the column they came from was disclaimed by its own script's correction banner, the corrected artifact reverses the conclusion, the OEIS term count is corrected to twelve, the matching lower bound is retired, and Zone Equivalence is demoted from spine theorem to framing device. | none | [changelog-add-C.md](history/staging/changelog-add-C.md) |
| `Q-changelog-add-F` | ANSWERED | Which superseded text from wave-2 partition F, the natal-cap family, belongs in the changelog? | Entries for eleven natal-cap documents and two new files, led by the retirement of the Fused-Window Calm Lemma and the certificate law with it, plus the prose-note index that closes qc-arch E4; staged only, not merged. | none | [changelog-add-F.md](history/staging/changelog-add-F.md) |
| `Q-changelog-add-G` | ANSWERED | What history left wave-3 partition G's files, and what has to be staged for the CHANGELOG? | Staged verbatim with file and line: the twin-candidate census index is corrected from A059861(n-1) to A059861(n) with four independent confirmations, two script banner titles are retired as contradicted by their own companion prose, and two scripts that had no banner title gained one. | none | [changelog-add-G.md](history/staging/changelog-add-G.md) |
| `Q-changelog-add-P` | ANSWERED | Which superseded text from wave-4 partition P's three files belongs in the changelog, and what does calibration against the home document find? | Fourteen defects came out of the check wave 3 recorded it had not run, and none of them is reachable by any existing gate check; the removed or rewritten text is reproduced verbatim per file for the shepherd. | none | [changelog-add-P.md](history/staging/changelog-add-P.md) |
| `Q-changelog-add-Q` | ANSWERED | What history left wave-4 partition Q's files, and what has to be staged for the CHANGELOG? | Staged: the Maier-Pomerance clause in the OEIS draft is RETIRED because it drew a >= from a << (they state an upper bound), and audit-numbers.js gained an oeis part of 39 checks carrying three retired values, including the exponent 1.57 quoted for G2 when 1.57 is A288815's. | none | [changelog-add-Q.md](history/staging/changelog-add-Q.md) |
| `Q-changelog-wave2-A` | ANSWERED | What changelog entries does wave-2 partition A owe research/history/CHANGELOG.md? | Staged per-document entries for G2-STATE.md, LOCALIZED-GAP.md, maier-matrix.md and origin-excess.md, each naming the claim as it stood, what replaced it and the artifact that forced the change; a staging file for the parent to merge, not an edit to the changelog. | none | [changelog-add-A.md](history/staging/changelog-add-A.md) |
| `Q-changelog-wave2-D` | ANSWERED | Which changelog entries does wave 2 partition D stage for CHANGELOG.md? | Staged entries in the changelog's house form for research/README.md (repurposed from a summary into the router), README.md, GLOSSARY.md, TODO.md, THE-DIALS.md, ZONE-POSTULATE.md, THE-LENS.md and FOLD-PROFILE.md, for the parent to merge. | none | [changelog-add-D.md](history/staging/changelog-add-D.md) |
| `Q-changelog-wave2-E` | ANSWERED | What changelog entries does wave-2 partition E owe research/history/CHANGELOG.md? | Staged entries covering covering-dive.md, two-class-lower-bounds.md, PRIOR-ART.md, sift-limit-attack.md, theta-ladder.md, maxgap-law.md and dhr-verification.md, led by the FKMPT constant moved across two files together. | none | [changelog-add-E.md](history/staging/changelog-add-E.md) |
| `Q-changelog-wave3-H` | ANSWERED | Which changelog entries does wave 3 partition H stage for CHANGELOG.md? | Entries for U-FRAME.md's split, in which sections 10, 11 and 12 keep their numbers and heading text and lose their bodies, plus the three new child documents kappa-not-L.md, operator-and-pair-count.md and f-decays.md. | none | [changelog-add-H.md](history/staging/changelog-add-H.md) |
| `Q-changelog-wave3-I` | ANSWERED | What changelog entries does wave-3 partition I, the flagship split, owe research/history/CHANGELOG.md? | Staged entries for the split of the flagship's wall chapter into the new paper/wall-note.md and the pointer repairs that split forces, in house form, newest first and grouped by the document changed. | none | [changelog-add-I.md](history/staging/changelog-add-I.md) |
| `Q-chen-fold-benchmark` | ANSWERED | Can the fold framework reproduce a classical Chen lower bound on long intervals with every imported hypothesis and error budget stated? | The classical implication is derived below using three explicitly imported theorem statements, with the combinatorial minorant proved and its integral margin certified by exact rational arithmetic. This is a benchmark, not a new prime theorem, and it does not prove twins or a short-zone result. | C | [chen-fold-benchmark.md](chen-fold-benchmark.md) |
| `Q-chen-opportunity` | ANSWERED | Does the signed Chen target identify an approachable proof mechanism, and what should the next research obligation be? | The target is sufficient but subtracts an avoidable odd-composite penalty; even cancellation of its obvious signed components does not close the existing separate bounds. Select a prime-detecting weight against explicitly justified arithmetic input ranges before pursuing a new estimate. The opportunity is a research judgment, not a proved mechanism. | C | [chen-opportunity-audit.md](chen-opportunity-audit.md) |
| `Q-chen-signed-target` | PARTIAL | What exact additional arithmetic estimate would turn the completed Chen benchmark into a proof of infinitely many twin primes? | An elementary prime minorant gives a conditional twin theorem with all weights, ranges, quantifiers and errors specified. The opportunity audit identifies an avoidable negative-weight penalty and a separate-estimate budget that fails even under component cancellation; this sufficient target remains OPEN and is not the sole next proof obligation. | C | [chen-signed-target.md](chen-signed-target.md) |
| `Q-coefficient-structure` | ANSWERED | Does the arithmetic structure of the aggregated coefficients reduce the endpoint estimate beyond the previous rectangle, and can smaller coefficient norms alone supply the remaining power saving? | Exact classification gives a nonsquarefree L2 norm of size at most sqrt(D)*W^(1/4) times logarithms, while the squarefree top-band energy is at least a constant times D*W*log(W). At d~x^0.277, e~x^0.467 every endpoint sector except the squarefree-squarefree prime sum has a power saving. This reduces that rectangle to one explicit endpoint correlation; prime-dispersion.md supplies the remaining estimate and controls the full rectangle. Finite algebra, CRT sectors and archived prefixes are checked separately. | C | [coefficient-structure.md](coefficient-structure.md) |
| `Q-cofactor-progression-transfer` | PARTIAL | Can the corrected full-cofactor kernel be estimated on a growing cofactor range by representing its actual arithmetic on CRT progressions, and does the resulting bound reach the twin consumer? | Derived from named imports: for some positive absolute kappa and d, all prime-r cofactor pairs s,t <= floor((log x)^kappa), including non-squarefree inputs and mixed transition/smoothed profiles, admit a dyadic scale-average O(log^(2-d) X) bound after division by x. The extension uses bounded multiplicative Euler modifications on the progression s\|n, t\|n-2 and keeps its density 1/lcm(s,t), so summing cofactors costs only O((log log X)^2). This goes beyond s=t=1 but remains short of o(x). The large-cofactor joint remainder, outside residual and twin margin remain OPEN; the attempted extension to power-sized cofactors fails on source modulus range and accumulated logarithmic cost. | C | [cofactor-progression-transfer.md](cofactor-progression-transfer.md) |
| `Q-coherence-0828` | ANSWERED | Are the 2026-08-28 notes consistent with each other? | 20 contradictions, 8 convergences, 46 live-doc corrections collected (34 mechanical, 12 need a second reader). | none | [coherence-0828.md](history/staging/coherence-0828.md) |
| `Q-coherence-0829` | ANSWERED | After the 2026-08-29 edits, does every live document state each changed fact the same way, and do the papers still agree with the notes? | 24 changed facts checked at 63 live-layer sites: 16 live disagreements (11 APPLY, 5 HOLD) plus one count error inside a HELD note; the worst is the localized band 2.9 to 4.2 attributed to "two engines" when only one of the two reads it, the other reading 2.14 to 4.39; qc.js 1 finding, in a file another agent holds; audit-numbers 251/251. | none | [coherence-0829.md](history/staging/coherence-0829.md) |
| `Q-coherence-0830` | ANSWERED | Do the live layer (TODO, README, G2-STATE, REFUTED, anchored-calm, GLOSSARY, CHANGELOG, QUESTIONS) and the eighteen notes landed 2026-08-29 evening and 2026-08-30 morning agree sentence by sentence? | They mostly agree; 27 distinct disagreements found, 15 graded APPLY (both sides quoted, no judgement needed) and 12 ASK, none touching a note's mathematics: the live layer lags the landed notes in six places (a PROPOSAL listed under PROVEN in G2-STATE section 0, 67 for 71 closed routes, the skeleton door still open in README and two anchored-calm sentences, Z5's body contradicting the record-mechanism note, item 9's one-versus-two open steps, a stale Z2 first move), carries four numeric slips (8-of-10 for 10-of-10, 27 for 25 clauses, u* in the seventh digit, nine for ten levels), one rung inflation (a text-layer reading called read at the page), and one landed note (recon-0830-rec-killrun) is itself wrong about the record on the seventy-five count; qc.js --full at 09:23 fails only on two ledger ids from notes that landed during the run. | none | [coherence-0830.md](history/staging/coherence-0830.md) |
| `Q-comb-discrepancy` | PARTIAL | Can the Comb Discrepancy Lemma's constant 2*3^k be tightened (TODO 8c)? | The lemma IS the trivial per-block bound; the attained optimum is max G - min G, a computed number per level (slack 29x @23, 54x @29, growing); term-by-term pricing lifts the certified head share to about 28-29 percent, not the 50 hoped for. | 8 | [comb-discrepancy-tight.md](history/staging/comb-discrepancy-tight.md) |
| `Q-comb-tail-0830` | PARTIAL | Can TODO item 8's remaining part (b), prime-comb equidistribution in the tail regime, be proven at the depths the certificate needs, or at least measured and priced at the enumerable levels (8b)? | Not proven and no exponent moves: the tail defect is measured exactly for the first time (signed -0.01% of the tail main term at @23, -0.00% at @29, unsigned 0.60% and 0.25%, smaller than the head's 1.00% in aggregate but 8 to 37% per prime at its worst), the Comb Discrepancy Lemma's method fails in the tail on its MAIN TERM (off by a derived factor e^gamma(1/u - q^(1-u)), measured aggregate 1.14x at @23) before its error term (10^27 x main), the prime-comb Legendre form has 2^(k+2) terms of which the short ones obey the lemma's <1 bound and the long ones are prime-in-AP discrepancies whose term-by-term sum is 11.2% of main at @23 against a signed -0.01%; the all-x form at K = 0 is Theorem C (PROVEN, limit only) and at the certificate's depth K* the non-closing step is a kappa = 1 asymptotic at sifting parameter s < 2, a proof gap on data that show B_tail = 0.998-1.000 at K* through @29; the full-depth half is 8(a), CLOSED. | 8 | [attack-0830-comb-tail.md](history/staging/attack-0830-comb-tail.md) |
| `Q-consolidation-wave` | ANSWERED | Can the five cost-class scripts be bound to their own output, and can U-FRAME's two lost tables be rebuilt? | All four runnable cost-class embeds are bound and the hand-pasted-tail counter falls 19 to 15 with the gate at TOTAL 0; three needed --force at a cost of 24 tokens out of 211 with no value changed anywhere, and natal-cap-33-overnight.js is a three-run composite that should never have been on the cost list. | 11b (retired) | [consolidation-wave.md](history/staging/consolidation-wave.md) |
| `Q-constants-audit-2` | ANSWERED | For every load-bearing number that appears in two or more live documents, does it agree everywhere, and does it trace to exactly one custody-bound producer? | 25 findings over 69 of 70 files, 8 rank A, 12 rank B, 5 rank C: 46 named-constant groups carry two or more distinct values across two or more files, and 439 numerals of five or more significant digits in the live layer have no producer printing them at any precision; nothing was fixed and five judgement calls stayed queued. | none | [constants-audit-2.md](history/staging/constants-audit-2.md) |
| `Q-consumer-comparison` | ANSWERED | How does the sufficient margin C_2 x + E_dagger(x) >= c_0 x/(log x)^K compare logically with the published sufficient routes to twin primes, and what does the literature already own of the corner object? | The sufficient margin remains OPEN. The published conditional routes imply it where their hypotheses and stated lower bounds apply; reverse implications are not established. The dictionary is E_dagger(x)/x = C_2(2 delta_x - delta_{x/2} - 1) + o(1), with K>0 below that normalisation's resolution. Independent review corrects the comparison: cumulative and dyadic consumers on unbounded scales are equivalent at the same fixed K with possibly different positive constants. At K=0 an eventual cumulative lower bound also implies the unbounded-scale dyadic consumer. The nonnegative-weight corner identification applies only to the prime-cofactor subfamily; the full residual retains additional branches. Every surveyed route remains conditional. | C | [consumer-comparison.md](consumer-comparison.md) |
| `Q-corner-branch-diagnostic` | ANSWERED | Can future experiments enumerate the full coefficients C(n) and C'(n-2) branch by branch, without silently dropping proper prime powers, cofactors s>1, non-squarefree inputs or either gcd branch? | The driver exists and its two independent constructions of each side agree exactly on 8192 retained sides and 1802 fixture sides; five deletion and reconstruction controls are ACTIVE in both runs. Its split by gcd(n,n-2) measures integer parity, not the per-term CRT gcd partition. The fixed-eta corner is empty on the retained prefix, and Elo exceeds E0 across the entire J_x, so the matrix is a proxy window. This is finite algebra and tool preparation, with no asymptotic estimate or twin margin. | C | [corner-branch-diagnostic.md](corner-branch-diagnostic.md) |
| `Q-corner-coefficient-energy` | ANSWERED | Can the full corner coefficients be studied before splitting their cofactor branches, and what do exact energy and classical smoothed sieve weights supply? | The sharp coefficient energy is an explicit signed quadratic form in short cofactors plus O_epsilon(x^(1/2)K^2*x^epsilon), a power below x at the fixed corner. Logarithmically averaging the divisor cutoff gives Barban–Vehov weights and an O_eta(x log x) squared norm on each side and absolute shifted-product bound. The follow-up sharp-corner-transition.md gives sharp O_eta(x log^2 x) norms and proves a non-negligible norm transition for sufficiently small fixed eta. Signed transition saving and the global complement remain OPEN; no exact residual cut or twin margin changes. | C | [corner-coefficient-energy.md](corner-coefficient-energy.md) |
| `Q-corner-correlation` | PARTIAL | On the corner S_0 where both cofactors sit just above their own cutoffs, what exactly is the remaining endpoint sum, what does the sufficient consumer need there, and does any reviewed correlation theorem supply it? | The full corner is exactly sum_n C(n)C'(n-2). Proper-prime-power terms above the cutoffs are negligible at fixed eta by §1.1; the remaining prime-r terms with s>1 or s'>1 and non-squarefree inputs remain OPEN. The s=s'=1 piece has a nonnegative Mobius-product weight with exact moving cuts. The multiplicative lift and round-review sampling give small continuous and dyadic scale-average log savings for that subfamily, with no o(x), full-corner control or twin margin. The complement is still open. | C | [corner-correlation.md](corner-correlation.md) |
| `Q-corner-log-average` | PARTIAL | What do logarithmically averaged correlation theorems and their quantitative successors actually supply for the prime-cofactor corner weight, with exact support, rates and scale quantifiers? | The pure band is invariant under dilation by primes outside it; the exact cofactor window is not, but its support extends to x^(1-2eta) and need not leave the window under a fixed dilation. Uniform-prefix logarithmic bounds imply block bounds by Abel summation; a relative exponent above 3 is one sufficient route to o(x), not a universal necessary threshold. Pilatte's 1/(96e) calculation applies only to his displayed parameter choice. A bounded multiplicative Fourier lift now gives a small continuous scale-average log saving for the prime-cofactor subfamily via Tao-Teravainen v2; see prime-band-transfer.md. No o(x), dyadic pointwise estimate, full-corner estimate or positive twin margin follows. | C | [corner-log-average.md](corner-log-average.md) |
| `Q-corner-measurement` | PARTIAL | At finite dyadic x, how large is the corner two-point correlation K(x)=sum_{x/2<n<=x} mu(n)mu(n-2)L(n)L'(n-2) of corner-correlation (5) relative to C_2 x, to its own absolute mass, and to a matched random-sign control, and does \|K\|/mass fall with x? | MEASURED, on the range and cutoffs recorded in the bound OUTPUT block of corner-measurement.js. The dominant finding is disconfirming for the measurement itself, not for the corner: at every reachable x the actual right cutoff Z=floor(x^(1/20)) admits at most one prime in its band and is empty at several j, so the actual-parameter rows are a one-prime object rather than the asymptotic corner, and the enlarged-cutoff rows are a model of the corner's shape and not the corner. On the rows that exist, \|K\|/mass falls with x at a rate that is not faster than the matched random-sign control's own decay, so the runs give no evidence of arithmetic cancellation beyond square-root-of-count. K stays many orders below C_2 x at every j measured and never falls below -C_2 x. No asymptotic rate, saving or cancellation is established, and nothing here changes the OPEN status of the corner or of the sufficient twin margin. | C | [corner-measurement.md](corner-measurement.md) |
| `Q-covadj-sign` | PARTIAL | Is Cov_adj < 0 for every scour prime q at every level? | Uniform-in-q anticorrelation is REFUTED, with six counterexample primes known; the aggregate is negative at all four levels in exact integer arithmetic over 599 scour primes, and the Low-Band Lemma is true but is not the mechanism, so the all-x aggregate theorem stays OPEN. | none | [natal-cap-23-covadj-proof.md](natal-cap-23-covadj-proof.md) |
| `Q-covering-dive` | ANSWERED | What do the one-class versus two-class Jacobsthal, covering-system and interval-sieving literatures hold for our object? | No two-class upper bound exists in print: Iwaniec's g(q) << (log q)^2 is one class per prime, and four independent passes (including the 82-work citation graph of Iwaniec 1978 and a zbMATH title sweep of 324 records) came back ABSENT; the synthesis names where the proof breaks when the second class enters. | none | [covering-dive.md](covering-dive.md) |
| `Q-covering-pruning` | CLOSED | Run backwards, does the pruning test inside OEIS A144311's branch-and-bound program give an upper bound on G2? | The pruning test is admissible (PROVEN, confirmed three ways), so A144311's terms above x = 43 are proven maximal, but run backwards it gives nothing from x = 13 onward because its whole content is sum_{5<=p<=x} 2/p < 1 and Mertens crosses 1 between 11 and 13; the cheapest admissible repair is Brun's pure sieve, whose exponent diverges like 7.182 lnln x. | none | [attack-beta2-05-covering-pruning-bound.md](history/staging/attack-beta2-05-covering-pruning-bound.md) |
| `Q-cross-campaign-synthesis` | ANSWERED | What can be recovered by comparing the fold, anchored, arithmetic and literature campaigns, including the proposed papers, against the actual twin-prime consumer? | The full-coefficient viewpoint leads to an exact sharp energy quadratic form, a Graham/Barban–Vehov O_eta(x log x) bound for smoothed full coefficients, and a small-prime cutoff-difference identity. The follow-up sharp-corner-transition.md prices the full sharp norm and rules out negligible L2 transfer for sufficiently small fixed eta. The local proposals supply quantifier and dependency lessons; a reversed anchored inequality, overbroad Suen closure and stale proposal header are repaired. Signed transition correlations and the global margin remain OPEN. The subsequent global-cutoff-averaging.md gives the current complete global formulation and signed research priority; its one-point cancellation is not a shift-2 estimate. | C | [cross-campaign-synthesis.md](cross-campaign-synthesis.md) |
| `Q-custody-embed-migration` | ANSWERED | How many script tails are bound by a formal embed, and what does the slow tier that had never been run turn up? | The unbound count went from an honest 107 to 47, with 55 tails bound in this pass and every one verified against the pre-embed block recovered from 97e2cfa to have lost nothing; four files were forced and their old blocks are quoted verbatim, and the findings the adjudicator owns are listed separately. | none | [custody-embed-migration.md](history/staging/custody-embed-migration.md) |
| `Q-custody-external` | ANSWERED | Which scripts carry an OUTPUT block that no single run of themselves produces, and is that evidence still reachable? | Sixteen scripts, 14 reproducible in one night, 2 longer than a night, 0 unreproducible, with six long runs re-earned figure for figure; the larger finding is the instrument, since tailfmt's outputText returns an empty body for 50 of the 113 scripts carrying a tail, so nearly half the pasted evidence is unread by the gate and the --force guard is inert on the same 50. | none | [custody-external-evidence.md](history/staging/custody-external-evidence.md) |
| `Q-custody-overnight` | ANSWERED | Can the five expensive artefacts every earlier custody wave skipped be bound to their outputs? | Two of the five were already bound and need only a --check; the other three cannot be bound at all, and the obstruction is shared and is a property of qc/tailfmt.js rather than of the files. | none | [custody-overnight.md](history/staging/custody-overnight.md) |
| `Q-custody-wave3` | ANSWERED | Can the remaining hand-pasted script tails be bound to the code that produced them? | Nine of the twelve are now bound by qc/embed.js and the counter falls from 12 to 3; the three that remain are the three priced over budget and each carries a recorded reason, with qc.js at TOTAL 0 for this wave's scope throughout. | none | [custody-wave3.md](history/staging/custody-wave3.md) |
| `Q-d2-d4-bijection` | ANSWERED | Is Labos Elemer's 2001 remark on OEIS A059861, that d = 2 and d = 4 differences are equinumerous in the hole gap word, a theorem? | Proven, with a three-line proof and an explicit bijection (doubling on the odd part), both counts equal prod_{3<=p<=p_n}(p-2) = A059861(n), verified at P = 30, 210, 2310, 30030; the grain (twin gap word) analog is REFUTED, the apparent equalities at T_7 and T_11 breaking at T_13. | none | [d2-d4-bijection.md](d2-d4-bijection.md) |
| `Q-data-reuse-audit` | ANSWERED | Do existing runs or their embedded inputs retain what the current determinant-2 sum needs, and can useful data be recovered without repeating the old campaigns? | The fold CSV supplies a verified base-prime list and archived interval boundaries; three old rows are reproduced and their bounded prefixes reconstructed with full factorizations retained. Other inspected outputs are aggregate statistics or twin-gap records. These finite inputs support coefficient and grouping tests, not an asymptotic twin bound. | C | [data-reuse-audit.md](data-reuse-audit.md) |
| `Q-defect-class-hunt` | ANSWERED | Do the five bug classes this corpus has already been burned by, plus numeric precision, appear anywhere in its 247 scripts? | Confirmed defects in every class swept, with 2^53 overflow at five confirmed in seven files (an assert that cannot fail, an LCG of period 10,466) and wall-clock gating at eight, and not one of the five confirmed overflow defects is in a deep-level script, which refutes this file's own first-pass conclusion; no gate check lints for any of these. | none | [defect-class-hunt.md](history/staging/defect-class-hunt.md) |
| `Q-defect-repairs` | ANSWERED | Were the fourteen script defects repaired, and what moved in each output? | Repaired with the state named per item rather than hidden: the broken LCG was in FIVE files not three, item 8 is left FIXED-AWAITING-REEMBED with an honest code-sha256 mismatch, one of six format fixes was applied and five skipped with reasons, and the gate ends at one finding belonging to a concurrent session. | none | [defect-repairs.md](history/staging/defect-repairs.md) |
| `Q-delta-reader-0830` | ANSWERED | Can any instrument read the sign of the log-power correction delta in G2 ~ c n^beta (ln n)^delta at reach 79, passing the one-class control first? | No. Six readers were pre-registered against stepped synthetic laws and the one-class control; the four power-chain readers (the diagonal meter among them) are killed by the P(n) stepping alone, the joint fit is calibrated but reads the control's finite-reach delta NEGATIVE (-0.38 +- 0.14 at 64 terms) where its conjectured asymptotic delta is +2, and the one reader that passes does so by importing the exponent, its sign being the sign of (1.777 - beta_hat). delta's sign for G2 is unreadable at reach 79 by any instrument tried, and the control shows a finite-reach reading would not carry the asymptotic sign anyway; item 1d's all-bases form stays unattackable. | 1d | [measure-0830-delta-reader.md](history/staging/measure-0830-delta-reader.md) |
| `Q-delta37` | ANSWERED | What sources the depth term exp(-delta*theta/mbar) of the M_p law, and does x = 37 fall out under the Hardy-Littlewood lens? | None of the three candidate families sources delta, each failing its parameter-free prediction (a source needs tilt slope -0.277 per unit z; the measured flattening is +0.0247); the residual sub-field IS the second singular-series layer (interior 6-tuple comb, zero parameters, correlation 0.907, sd 0.18 to 0.083), and 37 stays a G2-side anomaly no comb explains. | none | [attack-delta37-01.md](history/staging/attack-delta37-01.md) |
| `Q-derive-0904-L7-transfer` | PARTIAL | Is the legal open-set target L7, G2(x#) << g(x#) (ln x)^A for a fixed A (which would give exponent 2 + o(1) from Iwaniec's one-class bound, below beta2 and above the TPC line), reachable by a TRANSFER from the one-class Jacobsthal bound, and if not, what does each transfer mechanism reduce to? | No transfer mechanism in the corpus reaches L7, DERIVED: the union-bound transfer is vacuous already in the period average from x = 11 (the exact CRT budget sum of 1/(p - 1) over 3 <= p <= x passes 1 at x = 11), and the sieve-on-holes transfer is the Bruedern-Fouvry vector sieve, whose coupled unconditional form lands at 2(1 + sqrt e) = 5.2974 above beta2 and whose decoupled form needs the sup-over-positions remainder law that item 0 ruled a truth gap; L7 stays a legal OPEN statement with no mechanism, and the conjectural A = 1 is truth-side evidence only. | 0 | [derive-0904-L7-transfer.md](history/staging/derive-0904-L7-transfer.md) |
| `Q-derive-0904-r0-extension` | ANSWERED | Which pieces of the R0 decomposition (the tile form, the zone form, head, tail, Z2, and the composites R0/R1/R2/stretch) carry the parity obstruction's forbidden extension, and is any single piece both legal on the TPC-strength axis and exempt from it? | No piece of R0 is both legal and exempt with content: the criterion reduces to a coordinate count (Proposition A) under which every statement forcing a twin pair into a range where roughness implies primality is covered, and the exempt residue is exactly the statements that assert no such forcing (R0's identity, lower bounds, boundary artefacts) plus the tile form, whose exemption is a property of the statement and provably does not close under deduction (Proposition B), so it survives only for routes with no sieve weight anywhere. | Z2 | [derive-0904-r0-extension.md](history/staging/derive-0904-r0-extension.md) |
| `Q-destroyer-census` | ANSWERED | Who destroys each channel pair, what does the zone kill budget certify, and where does the counting certificate die? | The census reproduces digit-exactly on an independent engine; the destroyer rule is positional, not temporal, the certificate holds at 15 zones and dies at p = 67 where B/C first crosses 1, and no first-mover excess survives the derived null. | Z4 | [destroyer-census-01.md](history/staging/destroyer-census-01.md) |
| `Q-determinant-corollary` | ANSWERED | Does Bettin-Chandee Corollary 1, applied to d*k-e*t=2 after moving the non-smooth part of beta_V and beta_Z onto the coefficient side, control any part of the endpoint remainder that the current estimates do not? | The transfer is legal and exact: the smoothness hypothesis the literature scout recorded as the blocker is removable, at the cost eta=x^kappa and a boundary error O(x^(1-kappa)log^C x). Priced, it adds nothing. Requiring all four pieces and all bands gives 22max(a,b)+17min(a,b)<20, whose supremum of delta+nu is 2869/3900 < 19/25, so the region is strictly inside the already controlled delta+nu<19/25; the added area is exactly 0. A split by the size of the moved prime power also adds nothing, because every per-band budget is nondecreasing in the band exponents and the top band reproduces the full box. The log-log piece alone is controlled on 12.97 percent of the domain outside the current region, which is one of four pieces and changes nothing for R. W_dagger does not shrink, E_dagger is unchanged, and the sufficient twin margin remains OPEN. | C | [determinant-corollary.md](determinant-corollary.md) |
| `Q-dhr-verification` | ANSWERED | Does the beta2 note's use of the Diamond-Halberstam-Richert dimension-2 sieve survive verification against the primary sources? | The note's Theorem survives: every mismatch found is a remainder-weight convention absorbed by the z^{eps/2} slack, beta2 = 4.26645028414864191641 on Booker-Browning's rigorous table, and the fundamental-lemma fallback exponent corrects to about 19+eps rather than 18+eps. | none | [dhr-verification.md](dhr-verification.md) |
| `Q-dim2-standalone` | ANSWERED | Is the dimension-2 instantiation of the DHR sieve a real step, or an exercise? | An exercise: Diamond-Halberstam's Example 1.2 sets up the same sieve problem and Theorem 9.1 is stated for every half-integer kappa >= 1 with the density condition as its only hypothesis, so what beta2-note adds is two parameter choices and one dimension-free observation that is zeb's at kappa = 1; the honest response is to state the k-class family, whose k = 1 row is a known theorem. | none | [attack-dim2-standalone.md](history/staging/attack-dim2-standalone.md) |
| `Q-discrepancy-two-class` | ANSWERED | What is the two-class analogue of Holt's signed discrepancy DeltaPhi, and do the three candidate growth laws on the table agree? | One object in three norms rather than three agreeing measurements: the proven Level Ledger bound 2*3^(pi(x)-1) and natal-cap-29's spectral level law share the integer 3 provably, since R_k(p) tends to k+1, so the apparent agreement is an identity; the custody gate reproducing Holt's Table 2 passed. | none | [discrepancy-two-class.md](discrepancy-two-class.md) |
| `Q-dispersion-range` | ANSWERED | How far do the dispersion and coefficient-sector estimates extend across divisor sizes, and does a better orientation or gcd budget enlarge their overlap? | Averaging the nonzero gcd losses over the original divisor gives a different dispersion bound with cross-prime exponent (5/4)a+(1/2)b+3/50, where a=delta+6/25 and b=nu+1/20. Explicit diagonal, prime-cut and sparse-sector inequalities control a region of full rectangles, including d~x^0.282, e~x^0.522 at product scale x^0.804. Its cross-prime and left-sparse budgets are 0.9985 and 0.9988. The supremum of product exponents in this sufficient region is 5397/6700; it is not a uniform product cutoff. Balanced supports separately allow 12/25<s<94/175. The global remainder and twin margin remain OPEN. | C | [dispersion-range.md](dispersion-range.md) |
| `Q-doubling-C2` | PARTIAL | Does the doubling inequality hold on the base-2 chain, and can a bridging certificate prove it? | Not proven and not refuted: the exact C2 table has sup 5.2727 at s = 16, eleven proven finite-level bounds C2 <= K*+1 tight to a factor <= 2.91, two closures refuted outright, and the alarm is that K* drifts up (slope 0.6881 +/- 0.1328) while C2 does not (0.2018 +/- 0.1412). | D | [attack-doubling-01.md](history/staging/attack-doubling-01.md) |
| `Q-doubling-bridge-0829n` | PARTIAL | Can a bridging certificate carry Ghat(2s) <= 8 Ghat(s) from level s to level 2s uniformly in s, all s, on the base-2 chain? | Not by any proven mechanism: the K*-product bridge is CLOSED at every C2 by the cited run floor K* >= pi(2s)-pi(s) (K* = 17 at s = 16 by exact walk, VERIFIED, so the certificate reads 18 against 8 on the chain itself; it exits the whole legal band at s = 128, PROVEN); the sharper maxsum bridge Ghat(2s) <= maxsum_{K*+1}(T_s) is PROVEN and holds under 8 at all fourteen enumerable steps (VERIFIED), but its all-s form needs an upper bound on K* against the entering primes' two-class covering that nothing proven supplies; the doubling inequality itself is untouched. | D | [attack-0829n-doubling-bridge.md](history/staging/attack-0829n-doubling-bridge.md) |
| `Q-doubling-killrun-0830` | PARTIAL | Can the exact per-fold L bounds of the pi(2s) - pi(s) folds inside one doubling step compose to an upper bound on the weighted kill-run below the allowance 8 Ghat(s)/gbar(s), for all s, without passing through K*? | No, and the composition is closed as a route, not merely unproven: the folds compose as a PRODUCT, K*+1 <= prod_j (1+L_j) (PROVEN here, exact at fourteen steps, 540 against 18 at s = 16), the composed certificate never sits below yesterday's maxsum certificate (PROVEN by monotonicity), it exceeds the allowance at 8 of 14 enumerable steps starting at s = 9 (VERIFIED), and since every fold kills a slot the composed index is at least 2^N, whose floor 2^N gbar(s) alone exceeds 8 Ghat(s) at the chain rungs 16, 32, 64 and beats the cited polynomial ceiling on Ghat for all large s (PROVEN given the ceiling); the sum form is false at seven steps and the max form is a floor; the weighted run itself, computed exactly, sits at 0.83 of its allowance at s = 16 and (M8) is exactly where yesterday left it, OPEN. | D | [attack-0830-doubling-killrun.md](history/staging/attack-0830-doubling-killrun.md) |
| `Q-embed-backlog-0829` | PARTIAL | How much of the embed backlog (legacy scripts with no OUTPUT block, readings not traceable to their block) could be closed in one pass, and what did the fresh runs contradict? | MEASURED. embed-backlog fell 218 -> 189 findings in one pass: no-output-block 34 -> 5, readings-not-traceable 181 -> 181 (untouched by design), hand-pasted-tail 3 -> 3. Twenty-nine legacy scripts were bound with node research/qc/embed.js, zero --force was used, and one legacy reading is contradicted by its own fresh output (attack-beta2-03-exact-strata reading 8, "1.04 to 1.07 across y = 7..23" against a printed 1.102 at y = 7). | none | [embed-backlog-0829.md](history/staging/embed-backlog-0829.md) |
| `Q-embed-binding` | ANSWERED | What does the embed fingerprint actually bind, and what does it leave loose? | It binds the code to a claim about the output and does not bind the output block to anything: code-sha256 covers every byte above the banner, out-sha256 is only ever compared against another run, timeouts and failures write nothing, a prose line can unbind a tail and one did during this pass, and 37 cited scripts have no output custody at all. | none | [verify-the-verifier-embeds.md](history/staging/verify-the-verifier-embeds.md) |
| `Q-endpoint-fourier` | ANSWERED | Does a complete Fourier truncation budget and a matched Kloosterman-fraction theorem control any further part of the actual endpoint sum when its small prime-power coefficients are combined first? | A written classical-input derivation controls the rectangle d in (floor(x^(27/100)),2floor(x^(27/100))], e in (floor(x^(46/100)),2floor(x^(46/100))] to O_H(x/log^H x) for every fixed H. Its product is of order x^(73/100), outside the previously controlled region eventually. The aggregated Fourier exponent is 1989/2000; the full Vaaler tail and gcd=2 branch are included. This is a regional estimate, not a full residual bound or twin theorem; finite algebra and saved-factor checks are separate validation. | C | [endpoint-fourier.md](endpoint-fourier.md) |
| `Q-endpoint-pairing` | ANSWERED | Does retaining the difference of interval endpoints improve the complete Fourier budget, and are the lowest frequencies actually the next obstruction on the squarefree pilot rectangle? | A written derivation controls the full rectangle d~x^(11/40), e~x^(93/200) to O_H(x/log^H x), with product of order x^(37/50). The sufficient first exponent becomes 3/20+(7/10)(a+b)+(1/4)max(a,b), equal to 3999/4000 there. On the a=b=517/1000 pilot, this transition-frequency budget is 20061/20000, not the separate-endpoint 20163/20000; prime-dispersion.md now controls that pilot with a different estimate. Finite identities and exact exponent checks validate the implementation, not the asymptotic theorem. No uniform product cutoff or twin lower bound follows. | C | [endpoint-pairing.md](endpoint-pairing.md) |
| `Q-endpoint-target-audit` | ANSWERED | Does the endpoint reduction require a fixed positive fraction of the expected twin count, and do recorded uniform-gap theorem failures exclude its weaker consumer? | No fixed fraction is required: for every fixed H the reduction has error O_H(x/log^H x), so C2*x+E_>(x)>=c*x/log^K x on unbounded dyadic scales suffices, as does a stated logarithmically rescaled average. These implications are derived from named inputs; their endpoint hypotheses remain OPEN. The recorded uniform-gap theorem comparison has different quantifiers and does not establish an obstruction for this consumer. | C | [endpoint-target-audit.md](endpoint-target-audit.md) |
| `Q-erdos-map` | ANSWERED | Does the two-class object already occupy a numbered slot on somebody else's map of open problems? | It has no problem number and no name on erdosproblems.com, Ben Green's list or the OEIS citation graph, but it is not unposed: Erdos posed it himself in one sentence in the same paragraph as the $1000 offer, and our object is the r = 2, difference-2 instance of his own stated extension of #687. | none | [attack-erdos-map.md](history/staging/attack-erdos-map.md) |
| `Q-excess-chain-c` | CLOSED | Does the excess chain's constant c pin to 1.074 via a compressed-tail max correction? | NO: for any FIXED correlation length the derived family tends to 1 and both named corrections lower the maximum, so 1.074 is not derivable from a compressed-tail max correction; c measures 1.05 +/- 0.07 (sd) over x = 17..31, MEASURED, which does not separate 1.05 from 1.074. | 10 (retired) | [excess-chain-c.md](history/staging/excess-chain-c.md) |
| `Q-exponent-control` | PARTIAL | What is the growth exponent of G2, measured against a control that knows its own answer? | MEASURED 1.50 +/- 0.05 stat on 22 trusted terms after control correction, systematic unquantified; the raw fit's bias grows and sticks at +0.28, exponent 2 stays disfavoured but is not excluded, and the question is bias-limited rather than data-limited. | none | [exponent-control.md](exponent-control.md) |
| `Q-external-data-audit` | ANSWERED | Where is the corpus limited by external data it could simply adopt? | Findings are candidates, not verdicts: the highest settles an open reading for free, since dividing the two now-trusted series moves the G2/h ladder maximum from x = 37 to x = 79 and reverses the fall at x = 53, killing "peaks at x = 37"; the rest tighten quoted constants or retire stale limitation sentences. | none | [external-data-audit.md](history/staging/external-data-audit.md) |
| `Q-f-census` | PARTIAL | What does the grain census law give for f, the qualifying-gap fraction, and where does it structurally stop? | DEFECT-carrying: every census point from x = 37 up is aliased, so the 42-point table above x = 31, both regressions, the factor 170 and the x = 1000 extrapolation must be re-read against the corrected law; the staircase theorem (treads are exactly the twin pairs), Lemma B, the comb coefficient and everything at x <= 31 are UNAFFECTED, and the growth law is a fit and not a theorem. | none | [a3-03-f-from-census.md](a3-03-f-from-census.md), [f-decays.md](f-decays.md) |
| `Q-f4weak` | PARTIAL | What is the weakest sufficient form of F4 that could be proven, given rms <= z^(3+o(1))? | The mode-count/degree bound is NOT the theorem (sqrt(N)*rms grows at z^8.174 +/- 0.249 against the z^4.26645 ceiling and is dead from z = 31); one new PROVEN finite-z clearing survives z = 47 at a 5.0 percent margin but converges onto the trivial bound; the weakest law-shaped form found is MV(alpha), a mean value over modes, MEASURED slope 4.214 +/- 0.304 with beta2 inside the bar. | none | [attack-f4weak-01.md](history/staging/attack-f4weak-01.md) |
| `Q-fdecay-deep` | ANSWERED | Does the fitted f decay law hold out of sample at deep levels? | It holds as a band, nine of nine deep levels inside the four-specification band, but the residual trends against the central specification at t = -7.08; the test also found what it was not looking for, that the 42-point exact census is wrong from x = 37 upward by a factor rising to 1.63 at x = 199, from a 32-bit shift alias. | none | [fdecay-deep.md](history/staging/fdecay-deep.md) |
| `Q-fdecay-out-of-sample` | OPEN | Does the 42-point decay law for f, the qualifying-gap fraction, survive out of sample, given that every downstream reading extrapolates it three to thirty times past its range? | Pre-registration only, written before any producer for the pass exists on disk: four specifications are refit on the 42 exact census points as a transcription check and their projections are frozen, and nothing here is measured. | none | [fdecay-deep-prereg.md](history/staging/fdecay-deep-prereg.md) |
| `Q-fekete-1d-defect47` | PARTIAL | Does the bounded-defect Fekete route survive a probe at 47#? | The defect at 47# is ordinary and the 47# enumeration cannot move item 1d's TPC threshold whatever value it returns; the bounded-defect Fekete lemma is stated exactly and proved with every hypothesis except the candidate itself discharged, so the route reduces to one named inequality and is neither closed nor open beyond that. | 1d | [fekete-1d.md](history/staging/fekete-1d.md) |
| `Q-fixed-endpoint-discrepancy` | PARTIAL | After the accepted truncation to odd moduli e<x^(1/2+eps), what exactly is the fixed-endpoint centered discrepancy D^(e_1) below and above the level x^(1/2-eps'), which piece does an existing theorem estimate, and what single input would close D^(e_1)>=-4x/25+o(x)? | Reviewed 2026-09-09 after the coprimality repair: T_I^low=O_(A,eps')(x/log^A x), hence S=C_2x+B+O_A(x/log^A x), with B the exact Type II plus band sum (2.9). The untruncated modulus bound was false; g<=(log x)^(A+13), both tails, the coprime density and the weighted BV multiplicity now pay the estimate. Review corrects harmless log powers and the power-of-two atom over the full eps' range. D^(e_1)>=-4x/25+o(x) is equivalent to B+2C_2M>=-4x/25+o(x); it implies, but is not equivalent to, B>=-(C_2-1/200)x+o(x). The latter and H_B are sufficient OPEN margins. The absolute band statement (4.9) is one stronger sufficient input, not a necessary condition. No inspected source estimates the remaining actual signed B. Twin-prime infinitude remains OPEN. | C | [fixed-endpoint-discrepancy.md](fixed-endpoint-discrepancy.md) |
| `Q-fkmpt-corrigendum` | ANSWERED | Does the 2023 FKMPT corrigendum change anything the corpus depends on? | Clean bill of health: the corrigendum changes four numerical constants and the parameter M, every one already carried at its corrected value here; the loudest finding is the opposite of the expected one, since the premise that nothing in this repository has read it is false and has been since 2026-08-18. | none | [verify-fkmpt-corrigendum.md](history/staging/verify-fkmpt-corrigendum.md) |
| `Q-fold-arithmetic-bridge` | PARTIAL | Does one parity-table bridge from the anchored fold ledger yield a sufficient twin lower bound with named arithmetic inputs? | Exact identities retained. The one unread sieve input of the pricing, Bombieri--Vinogradov for k-fold X^(1/u)-rough products, is derived from Wu's Lemma 2.3 (section 3a); the same input, sieved in the composite variable, gives the contamination aggregate constant 4 for each fixed k,u, replacing the displayed 12.86 to 19.72. With these inputs, elementary bounds give Q_cov(u)<1 and c*_real(u)<4 for every u>4 (section 4a, independently reviewed 2026-09-09 with rational certificates), so neither sufficient ratio test succeeds at any depth. This closes the two tests, not the decorrelation hypotheses, and supplies no twin estimate. | C | [fold-arithmetic-bridge.md](fold-arithmetic-bridge.md) |
| `Q-fold-profile` | ANSWERED | Where does a fold by p land its damage inside the original tile stretch [0, W)? | The counting half is a theorem with an effective constant (Level Ledger PROVEN, Mirror Ledger VERIFIED 45 of 45) and the survival law is scale free (MEASURED), but the quantity controlled here is provably uninformative about L and kappa(m), so it buys nothing against the Zone Postulate route. | none | [FOLD-PROFILE.md](FOLD-PROFILE.md) |
| `Q-fold-succession` | CLOSED | Does folding in succession damp the multiplier, giving a lower L than the sum of per-fold jumps? | No: the succession-damping route closes empirically at both reachable scales against a calibrated null, the only damping present is what level-tracking forces and the only extra structure present is cooperative, matching the structural closure by super-additivity. | none | [fold-succession-autocorr.md](history/staging/fold-succession-autocorr.md) |
| `Q-foldL-amortized` | CLOSED | Can the fold multiplier L be bounded by charging kill-runs to the birth of the gaps they consume? | The accounting does not close on the tile: the Consumption Identity makes the charge exact and the bound is then only as good as X = 2Q0 + Q+ + Q-, and supply against demand fails on the tile at every x by exactly the factor ln^2 x; it closes in a localized window from p about 421 on, which is a statement about a bounded population only. | none | [attack-foldL-04-amortized.md](history/staging/attack-foldL-04-amortized.md) |
| `Q-foldL-bridge` | ANSWERED | Does the bridge from a fold's kill count to L hold, and what is the sharpest transportable ceiling it gives? | The bridge is PROVEN and was already in the corpus, so the job was custody rather than a new theorem; the new pair-window rung is exact at all eight diagonal cells, and the best fully-proven transportable ceiling stays near 0.18p and beats the requirement nowhere. | none | [attack-foldL-02-bridge.md](history/staging/attack-foldL-02-bridge.md) |
| `Q-foldL-extinction-scaling` | ANSWERED | Does the multi-kill extinction law predict windows it was not fitted on? | CONFIRMED under the pre-registered rule at Y = 2e7, 2e8 and 2e10 from the Y = 2e9 calibration alone, with the run-length extension REFUTED exactly as pre-registered; this promotes a law candidate on measurement, not a proof. | none | [attack-foldL-06-scaling.md](history/staging/attack-foldL-06-scaling.md) |
| `Q-foldL-maxsum-direct` | CLOSED | Can maxsum_m(T_x), plain and residue-deleted, be bounded above by an argument that never counts kills? | The brief's premise contradicts the corpus's own Bridge Floor (maxsum_k >= maxsum_1 = G2(T_x) for every k), so the bridge cannot convert far enough however good the bound is; all four routes close (R1 partial then closed, R2 tautological and quantitative, R3 busts the budget), and the order-m object is in print, so item 0c's absence sentence has to change. | 0c | [attack-foldL-05-maxsum-direct.md](history/staging/attack-foldL-05-maxsum-direct.md) |
| `Q-foldL-run-census` | PARTIAL | What ceiling on L does the channel-compatible run census force, and is that ceiling forced or a bridge? | Channel compatibility is exact and cheap but buys little: 3 in 71 at kappa(1) = L, the forced ceiling is a presence-relaxation rather than a multiset-exact bound, exact tiles stop at T_29, and the angle's own verdict sends it to TODO 0c, bounding a residue-deleted maxsum, which this pass did not attempt. | none | [attack-foldL-01-census.md](history/staging/attack-foldL-01-census.md) |
| `Q-foldL-transport` | ANSWERED | Is there a third invariant of the tile's gap alphabet that provably survives the fold recursion, alongside the sum rules and the maxsum family? | Yes: the tail-count profile transports (the Tail-Count Transport, PROVEN, verified to T29 at 214,708,725 twin slots) and is sharper per fold than the standing route by a factor of three to eight in nats, but it does not chain, dying on the same accumulating index gate-multiplies.md closes. | none | [attack-foldL-03-transport.md](history/staging/attack-foldL-03-transport.md) |
| `Q-foldL-window5` | MIXED (foldL-window5-prereg.md: OPEN; foldL-window5.md: ANSWERED) | Does the fold extinction law score one decade blind at W = 2e11? | HIT on all four pre-registered criteria (last fold with L >= 2 measured 631 against band [571, 877]; both counts inside their bands), with the hot systematic now confirmed at five of five windows at measured over predicted about 0.82, which by the prereg's own clause belongs in the law as a known overprediction rather than in the acceptance band. | none | [foldL-window5-prereg.md](history/staging/foldL-window5-prereg.md), [foldL-window5.md](history/staging/foldL-window5.md) |
| `Q-ford-halberstam` | CLOSED | Does Ford and Halberstam's dual decomposition beat Brudern-Fouvry's (2.6), as its authors said it should? | No: the dual is the same inequality, verified to 3.553e-15 at r = 2 and 6.821e-13 at r = 2..7, and their estimation step is better than they claimed, the Rosser boundary layer making their absolute-value bound an identity with loss 0.000000000 at z = 20, 30, 42; the shortfall is the freedom the step gives up, one level per component and no lower sieve. | none | [attack-ford-halberstam.md](history/staging/attack-ford-halberstam.md) |
| `Q-fractional-retention` | CLOSED | Do Brady and Li's fractional retention rules at kappa = 2 open the adjacent door sift-limit-attack section 7c named? | Do not pursue: the door is real, applies to our system and carries no regress, but half the rule family cannot be applied at kappa = 2 and the applicability window there is empty, both settled from the sources; the unlooked-for find is that Brady's thesis is prior art for our object. | none | [scope-fractional-retention.md](history/staging/scope-fractional-retention.md) |
| `Q-frontier37` | ANSWERED | What do the fold-L wave's three exact instruments give one level deeper, at fold 37? | The prior-art check moved the target first: the ninth diagonal L(T_31, 37) = 4 and the maxsum_m(T_31) table for m <= 8 were already embedded in the corpus, so this is a re-measurement, not a first; M_alt = G2 is measured at eight folds and proven at none, and the transport ratio's rise 0.8881 to 0.9477 has no mechanism attached. | none | [frontier37.md](history/staging/frontier37.md) |
| `Q-full-coefficient-average` | PARTIAL | Can aggregating the complete coefficients before a correlation theorem remove the explicit cofactor count, and what additional estimate is needed? | Exact factor and rounded-endpoint Fourier identities retained, with c_(i,0)=3/5 and an explicit composite-filtered weighted sum. The full family is not 1-bounded, but the sufficient phase condition admits at least k=0,+/-1 on the left and l=0,+/-1,...,+/-6 on the right for every Mellin twist; the earlier zero-only claim is corrected. Composite filtering and the required correlation rate remain unmatched. Proposition 6.5, independently reviewed including on 2026-09-09, proves coefficient norm at least (log x)^(2/5) for representations by 1-bounded functions on all smooth inputs. This does not exclude density-one representations, paid growing components or a jointly treated Fourier sum. No sufficient signed twin margin follows. | C | [full-coefficient-average.md](full-coefficient-average.md) |
| `Q-g2-43-term` | ANSWERED | What is the fourteenth exact term of the G2 ladder, past 41#? | G2(43#) = 618, at least position 830,330,079,152,051 and attained at 8 positions of the period, confirmed by two independent enumerations over disjoint natal masks agreeing on value, multiplicity, position and survivor count; 47# is priced by direct probe at 1.49 days per run and stays out of session reach. | none | [phase1-T2b-exact-ladder.md](history/staging/phase1-T2b-exact-ladder.md) |
| `Q-g2-falls-decision-rule` | PARTIAL | Does G2(x#)/x^2 fall, and what pre-registered decision rule would settle it? | The instrument is calibrated and sharp, resolving the one-class control at 11.6 sigma on the same nine points where it returns 0.9 sigma on G2, and the honest band on the slope is +/-0.117 at nine terms, so the rule is registered; but the power analysis puts separation at x = 53 only if the falling law is x ln^2 x and at x = 151 if it is x ln^3 x, so phase 1's extra terms settle nothing and no reachable exact ladder does either. | 1d | [phase1-T3prep-decision-rule.md](history/staging/phase1-T3prep-decision-rule.md) |
| `Q-g2-provenance-x37` | ANSWERED | Does the headline G2 exponent depend on the eight terms this repository has never reproduced, and does any instrument without G2(37#) inside it flag x = 37? | MEASURED, both largely negative: the custody-only refit lands at 1.533 against the headline 1.498 and no provenance-block drop moves the corrected central by more than 0.035 (Ghat(64) alone moves it 0.002), while no G2-free instrument flags 37 in the high direction, the one \|z\| past 2 being h(37#) at -2.20 in the low direction and range-dependent; the blind extreme-value forecast of G2(37#) does overshoot at z = +6.58, unexplained. | 0 | [measure-g2-provenance-0829.md](history/staging/measure-g2-provenance-0829.md) |
| `Q-g2-state` | PARTIAL | What is known about G2, the two-class maximum twin-slot gap, and at what calibration? | The gap is unchanged through roughly fifty recorded passes: the proven upper bound is exponent 4.26645 against a target of 2, and this file consolidates the map rather than computing anything new. | none | [G2-STATE.md](G2-STATE.md) |
| `Q-gap-spectrum` | ANSWERED | What is the full gap-length distribution of twin slots over one period of the tile, what does the excess functional \|B_N\| = sum_{g>N}(g-N) read on an x^s grid, and where does the empirical minimum window count leave zero? | The distribution is exact at nine levels to x = 31 and the pre-registered renewal null FAILS in the light direction at every one: the tail is uniformly steeper than exponential (body slope -1.3302 against -1), no power law survives (the power-law slope moves by a factor 17), the maximum is 2.087 to 2.241 BELOW the renewal maximum, and \|B_N\| sits at 0.0245 to 0.7436 of the null and is exactly zero at s = 1.75 where the null predicts 6.5262e+5 empty windows; so no heavy-tail mechanism for a super-linear G2 exponent exists at any computable level, the identity G2 <= N + \|B_N\| is proven but degenerates to G2 <= N on this grid, and the sifting onset is flat at 1.63 to 1.70 against a sieve bound f2 that is zero everywhere the grid reaches. | 0 | [gap-spectrum-01.md](history/staging/gap-spectrum-01.md) |
| `Q-gate-multiplies` | ANSWERED | Does "the gate multiplies" close the entire u-frame recursion branch, or only the merge chain? | Only the merge chain and one relative of it: the no-fixed-point argument does not reach TODO 0b at all, though 0b is wrong as stated for an unrelated reason and the error is a factor of ln u; what survives is the copy theorem for maxsum (VERIFIED 40 of 40), which needs a residue-deleted maxsum bound that does not pass through a kill count. | 0b | [gate-multiplies.md](gate-multiplies.md) |
| `Q-gate-repair` | ANSWERED | Were the verify-the-verifier repairs landed with the gate ending fully green? | COMPLETE: node research/qc.js --full reads FULL GATE PASSED at the close, TOTAL 0 across the 11 checks, selftest 39 known positives firing and 32 controls silent, audit-numbers 246/246, and no bound tail left amber. | none | [gate-repair-finale.md](history/staging/gate-repair-finale.md) |
| `Q-global-cutoff-averaging` | PARTIAL | Does the wider corpus suggest changing the global decomposition before extending the small-cofactor estimate, and can that change be made without an unpaid transition or outside term? | Derived: independently averaging the two initial Mobius cutoffs over fixed exponent intervals gives S=C2*x+sum G_L(n)G_R(n-2)+O_A(x/log^A x), uniformly on dyadic scales, with all cofactor and prime-power branches included. Each full G has squared norm O(x log x). The existing sharp-corner lower norm then forces cancellation between the corner coefficient and the rest at the same input. This does not estimate their shifted product. The global signed residual was already O(x) by the sieve upper bound and positivity; the new norm representation is not an improved signed bound. Prefer a bounded attempt on this global coefficient pair and a one-sided consumer; the twin margin remains OPEN. | C | [global-cutoff-averaging.md](global-cutoff-averaging.md) |
| `Q-global-factor-signs` | PARTIAL | Which full factor configurations cause negative global products, can prime-power exceptions be paid, and does a pair-trigger upper bound control the negative part? | Derived: G_i(n)=Lambda_(>W_i)(n)-F_i(s_i(n))*log t_i(n)-E_i(n), with all small-prime factors in s_i and all primes of t_i exceeding W_i. The correction is supported on a small-prime power exceeding W_i; its full shifted effect is O_epsilon(x^(39/40+epsilon)). After also paying proper prime powers, the residual is a composite-filtered signed smooth/rough cofactor sum. A ten-small-prime cell has F=-84 although every pair lies below a, refuting the proposed pair-trigger majorant. Prime filters contribute explicit terms when bounding the negative part; dropping them is an upper bound, not an identity. No scale-x signed improvement or twin margin follows. | C | [global-factor-signs.md](global-factor-signs.md) |
| `Q-global-smooth-majorant` | PARTIAL | Can a higher-order majorant control the complete global coefficient pair at scale x while retaining every factor configuration and the prime filters? | Derived using the corrected Henriot upper theorem: a C3 probability average of the same admissible initial cutoffs gives a full residual with sum \|Ghat_L(n) Ghat_R(n-2)\|=O(x). The three-smallest-prime majorant has bounded harmonic mass and meets the source growth class uniformly, despite not being multiplicative. All prime-power exceptions are paid. This replaces the O(x log x) absolute budget for the earlier logarithmic profile by O(x) for a different admissible profile representing the same signed residual to arbitrary logarithmic precision. The implied constant is not compared with C2 and no improved signed lower bound or twin margin is supplied. | C | [global-smooth-majorant.md](global-smooth-majorant.md) |
| `Q-greedy-oracle` | ANSWERED | Is the corrected greedy a G2 oracle? | ORACLE ESTABLISHED, 13 of 13 exactly-known terms hit with minimum ratio 1.0000, so the greedy RULE is an exact solver where the answer is checkable at x <= 41; the rider matters more, the search budget needed grows 3.31x per additional prime and two objects whose truth reaches further show the same estimator's fidelity DECAYING, so nothing is established for the greedy AS RUN on the ladder. | 1b (retired) | [greedy-oracle-validation.md](history/staging/greedy-oracle-validation.md), [phase1-T1-greedy-oracle.md](history/staging/phase1-T1-greedy-oracle.md) |
| `Q-grouped-divisor-moment` | ANSWERED | Does the full gcd-normalized moment proposed by the literature audit hold, and what exact portion of the twin-prime remainder does it control? | The proposed moment is derived from classical completion with all coefficient sectors and uniform twists included. Full rectangles are controlled when delta<19/25 and delta+3nu<161/100, in addition to the preceding region. A concrete extra cut d<=floor(x^(151/200)), de^3<=floor(x^(321/200)) controls the entire d~e~x^(2/5) benchmark and leaves an explicit smaller-domain endpoint remainder. The uniform product threshold stays below 19/25. At delta=8/25,nu=9/20, the next deficit is confined to small-common-divisor nonzero kernels; their required saving and the global twin margin remain OPEN. Finite validation does not prove asymptotic rates. | C | [grouped-divisor-moment.md](grouped-divisor-moment.md) |
| `Q-growth-law` | ANSWERED | What does G2(x#) actually grow like? | MEASURED about 0.762 * x ln^2 x * lnln x over x = 11..79 (18 terms, ten log-linear families AICc-ranked), with the honest statement being the band and not the winner; the pure power law is excluded against a control that knows its own answer, and G2/h costs one further logarithm. | none | [attack-growth-law.md](history/staging/attack-growth-law.md) |
| `Q-h2-extension` | CLOSED | Is extending A288815 (h2) past its 21 terms the high-value computation it was taken for? | No, on both halves, and it is recorded in OUTCOMES.md as WITHDRAWN: term 22 is a roughly four-year single-thread computation for the specialists' own tuned code, all three cheaper proxies fail downward and growing (the direction that fakes a smaller exponent), and the control measured one extra term moving a ten-term exponent fit by 0.022. | none | [h2-scoping.md](h2-scoping.md) |
| `Q-handoff-review-0906` | ANSWERED | Does the handed-back arithmetic campaign survive an independent check of its main regional estimate and the conclusions used to choose the next research direction? | The bounded handoff audit is completed in reports 20 and 21: the checked local reduction and regional mechanisms survive, named source statements were verified, and the consumer, corner support, rate, shrinking-margin and identity-piece overclaims were corrected. Joint Cauchy is now priced and adds no region. The multiplicative band transfer has a separate PARTIAL owner with a weaker continuous-scale payoff. Imported deep theorems remain imports; this is not corpus-wide certification or a twin margin. | C | [handoff-review-0906.md](handoff-review-0906.md) |
| `Q-hawkins-read` | ANSWERED | Does the Hawkins random-sieve tradition, read at source, hold a two-class variant, a stage-to-stage moment identity, or an answer to the analogue question? | NOT FOUND for a two-class or k-residue variant; the moment identity is found in the null and not in the fold; and the tradition raises the analogue question repeatedly and answers it only as a missing constant. Two primaries stayed paywalled, so the absence claims rest on the rest of the bibliography. | none | [hawkins-read.md](history/staging/hawkins-read.md) |
| `Q-head-remainder-0830` | PARTIAL | Does the 5.3 percent remainder that Hardy-Littlewood leaves in the head's endpoint deficit Delta = 2 - beta derive by a route that is not HL: the frozen-sieve first-survivor object, a level-of-distribution correction, or the exact tile-ensemble head? | No route that is not HL closes it, and the remainder as recorded is not what it was taken to be. The record's Delta_meas = 0.6214 at [1e7,1e8) pools a decade over which the prime density falls ten percent, and the OLS intercept absorbs the gradient (a Simpson-type effect, sign derived): the two half-decades read 0.6848 and 0.6500, the four quarter-decades 0.7203 to 0.6565, and pooled minus the gap-weighted mean of the halves is -0.0378, -0.0455, -0.0524 at the three decades, so the same-sign 5.3 percent miss is the pooling. At half-decade resolution HL's pipeline prices Delta to 1.2 and 0.4 percent at the top two windows, inside one standard error, and the sign of the miss alternates. That agreement is a near-cancellation of two four-percent effects: the pipeline under-predicts its own rotation ensemble by 3.6 to 4.9 percent (pipe/ens 0.951 to 0.964 across y = 313 to 19997, MEASURED by exact CRT sampling; 1.049 to 0.958 at y = 11 to 23 by full enumeration), an ensemble quantity that derives by finite count with no prime input and whose sign is opposite to hl3 section 2's guess; and the anchored window's deficit sits 2 to 5 percent below its gap-scale-matched ensemble (Delta_meas/Delta_ens 0.878 to 0.995 over six half-decades, 0.954 to 0.995 on the four with more than 13,000 gaps), the anchoring part, which is a three-point prime correlation in a short window and is HL-strength by every route named. The head is a slack field and nothing here touches Z2. | Z4 | [attack-0830-head-remainder.md](history/staging/attack-0830-head-remainder.md) |
| `Q-head-residual` | PARTIAL | What is the head's residual prime-origin factor h/R = 1.09 -> 1.03, and does it derive? | h - R decomposes exactly and A_forced derives; h/R -> 1 follows from beta CV^2 being bounded, beta CV^2 -> 2 controlling the RATE and not the limit (under it h - R -> D = -0.95, so +8.4661/ln^2 p cannot be the limit law); R is the continuum functional and the integer-origin null sees R + 1/2 exactly, so h - R = 5.679 depends on the unstated null population, reading 5.179 discrete-uniform and 2.925 coprime-to-30; the mod-30 answer is NO by a valid route, class term -0.0001; Delta = 2 - beta is priced by HL to 5.3 percent with nothing fitted and HL's own 1/ln x term absorbs the miss, so the 5.5 s.e. framing is dropped; the asymmetry-as-mechanism claim and the [0.289, 0.361] bracket are refuted, hl3's 16 percent standing; beta_null is 1.898 for the discrete-consistent null and 2 in the continuum; the 72/28 split reads 81/19 in the other exact order; c = 0.844 is 0.722 on a subset, pinned to 15 percent; Delta_HL ln p/lnln p = 4.02 is a property of the prediction; and the N4 plateau is not OPEN, needing beta CV^2 = 2.71 rising to 6.63. | Z4 | [head-residual-factor.md](history/staging/head-residual-factor.md), [head-residual-hl3.md](history/staging/head-residual-hl3.md), [head-residual-null.md](history/staging/head-residual-null.md) |
| `Q-heath-brown-edges` | ANSWERED | Does the a=1 edge, and hence the corner S_0, come from the particular two-cutoff Vaughan identity in prime-detection-spec.md and shifted-prime-decomposition.md, or does an equivalent edge reappear under Heath-Brown's identity and the other standard decompositions of Lambda? | The exact identities and exponent simplex leave a=1 in separately bounded formal pieces, including Heath-Brown's balanced j=K configuration. This does not prove an intrinsic edge after identity-piece cancellation. The bounded-cofactor object has affine dilations, not literally F(n)F(n-2). Linnik's fixed truncation has a large term-wise absolute tail by an elementary counting proof; its signed tail is not thereby bounded below. Heath-Brown K=3 narrows the classical split band, with coefficient and Type I normalization obligations retained. No full alternative reduction, new region or twin margin follows. | C | [heath-brown-edges.md](heath-brown-edges.md) |
| `Q-history-dial` | ANSWERED | Does revealing the scour primes' classes concentrate the floor on a bounded set of strike locations, and what is the history dial worth? | Disconfirming: the class axis is linear at 2.90 survivors per prime read, so no bounded set of strike locations carries the floor, and the touch-count ceiling is proven and tight; deliverable (1) of the brief already existed as canonical state (the forcing ladder 16 -> 45 at @11), so nothing new was bought there. | A | [attack-history-dial.md](history/staging/attack-history-dial.md) |
| `Q-hm-basis` | ANSWERED | Does the u_sup divergence survive the change to the natural (h,m) basis? | It survives: the two bases are nested rather than rivals, the natural one is the outer and weaker member, and the gap between them is a flat factor of 7.26 across nine levels, so the divergence that closed u_sup runs in both bases. | none | [attack-hm-basis.md](history/staging/attack-hm-basis.md) |
| `Q-holt-2605` | ANSWERED | Does the fifteenth Holt manuscript, arXiv:2605.19165, contain anything that touches our record? | No: it carries no twin, no max-gap bound and no G2, its \|s\|/2 threshold restates the 2603.25915 / 1408.6002 inequality, and the interaction check is negative, our extinction law diverging from his by a factor 396 across three decades of W; the sweep is now complete at fifteen of fifteen. | none | [holt-2605-sweep.md](history/staging/holt-2605-sweep.md) |
| `Q-hsub-reductions` | PARTIAL | Can (H-sub) be proven or refuted, and what does the fold machinery reach? | Neither, but the statement is smaller: three reductions of the hypothesis are proven, the lemma consuming only power pairs so that it weakens to (H-sub-pow) with the conclusion unchanged, the fold machinery's inability to reach any of them is made exact, and the hunt over all 111 reachable pairs found no drifting family and no counterexample. | 1d | [attack-hsub-01.md](history/staging/attack-hsub-01.md) |
| `Q-hsubpow-K` | CLOSED | Can (H-sub-pow) be proven with an explicit K in the legal zone? | NO by three mechanisms: the CRT lift (K* >= pi(y') - pi(y) diverges), anchored caps (diverge at every base), Iwaniec at two classes (it IS beta2-note); TODO 1d's legal zone is mis-stated, the trusted zone is [1.3946, 11.3568). | 1d | [hsubpow-explicit-K.md](history/staging/hsubpow-explicit-K.md) |
| `Q-hsubpow-K-0829n` | OPEN | Can (H-sub-pow) be proven with an explicit K inside the trusted legal zone [1.3946, 11.3568) by a mechanism the 2026-08-28 pass did not close? | No K is proven at any base; the single open inequality is the uniform-in-k ratio cap G(b^(k+1))/G(b^k) <= e^K G(b), which is a proof gap at a fixed base and a possible truth gap across bases, since for any law G ~ c n^beta (ln n)^delta the all-bases hypothesis holds with finite K if and only if delta >= 0. | 1d | [attack-0829n-hsubpow-K.md](history/staging/attack-0829n-hsubpow-K.md) |
| `Q-hybrid-bound` | CLOSED | Does an exactly-handled head of small primes plus a sieved tail improve the certified exponent? | The glue closes and is a real theorem, and it buys one factor of 1.93 in x and nothing asymptotic: the window where the bound beats 4.2665 widens from x <= 227 to x <= 439 and never returns, the head can only reach x0 = O(ln x), and the literal glue the brief named (A144311 as base case) is dead on a type mismatch. | none | [attack-hybrid-bound.md](history/staging/attack-hybrid-bound.md) |
| `Q-identifications-prior-art` | ANSWERED | Who owns the three identifications that were banked without a prior-art search? | All three are OWNED in their conventions: the complementary-window duality, maxsum_m as the largest m-spacing of a scan statistic, and the alternation language as a textbook charge constraint; the exponent law H = a + b ln D and the H* Shearer-threshold ladder come back NOVEL-SO-FAR on four calibrated channels. | none | [identifications-prior-art.md](history/staging/identifications-prior-art.md) |
| `Q-import-bfree` | ANSWERED | Does the ergodic theory of B-free systems - Mirsky measures, Toeplitz structure, tautness, heredity, entropy - say anything about the twin comb? | It lands as an exclusion: the comb is exactly the object the field's newest generalisation is built for and that generalisation names the comb's own regime as the one it declines to study, the limit comb is the single point {-1} so every ergodic statement about it is vacuous, and the yield is a corrected address for the walls plus one live external open problem. | none | [import-bfree.md](history/staging/import-bfree.md) |
| `Q-import-boolean-analysis` | CLOSED | Does the analysis of Boolean functions reach the anchored bias? | Five things that had to hold do not, starting with the product space eating the statement worse than C^pi(x); the forced degree saturates at 2 and the globality hypothesis fails at q1, so the row supplies a wall address rather than a route, and every figure is SCRATCHPAD-GRADE and may not be quoted until re-derived inside an embedded producer. | none | [import-boolean-analysis.md](history/staging/import-boolean-analysis.md) |
| `Q-import-bridge` | CLOSED | Do Ojaroudi's Bridge and collision lemmas certify a number the corpus lacks? | Both lemmas are true and both proofs go through in three lines here, and the answer to the question the import was raised for is no: the certified-number verdict is zero by an identity rather than by a margin, and the per-prime nature is what stops it. | none | [import-bridge.md](history/staging/import-bridge.md) |
| `Q-import-bridge-prereg` | SUPERSEDED | Do Ojaroudi's two elementary lemmas, imported onto our tile, beat the incumbent per-prime discrepancy numbers? | Pre-registration only, sealed before any number was computed: the predictions, the incumbents, the win condition and five declared traps are fixed here, and the null result is the expected result because P4 is an identity; the outturn is import-bridge.md. | none | [import-bridge-prereg.md](history/staging/import-bridge-prereg.md) |
| `Q-import-chaining` | CLOSED | Can Dudley's entropy bound or Talagrand's generic chaining beat the union bound over positions on the maxsum law? | No, and the reason is geometric rather than probabilistic: the entropy integral of the true increment metric is already 1.054-1.099 times rms*sqrt(2 lnW) at its lower branch and 1.484-1.545 at its upper, flat across z = 13..23, so chaining's ceiling with a perfect universal constant sits below the union bound's floor; the honest constant-carrying chain measures 2.878 to 3.027. | 0c | [import-chaining.md](history/staging/import-chaining.md) |
| `Q-import-distortion` | CLOSED | Does the distortion method of covering systems speak at two classes per modulus, and what does it certify on the window? | It does speak at two classes, and the row's expected blocker was the wrong one: its economy sum 4/p^2 converges (sup 0.364545) where the union bound's sum 2/p dies at x = 13, but it charges in ambient length, its measures living on a CRT product so the certified window is at least a primorial and the only published bridge back to an interval is exponential in the number of progressions. | none | [import-distortion.md](history/staging/import-distortion.md) |
| `Q-import-distortion-prereg` | ANSWERED | What does the distortion method certify on our window, and does it speak at one class per modulus or at two? | Sealed before any line of the producer existed; scored in import-distortion.md, where the deciding question comes back opposite to the row's expectation: BBMST's criterion carries no distinctness, multiplicity or minimum-modulus hypothesis, so the method speaks at two classes and the one-versus-two-class wall is not its wall. | none | [import-distortion-prereg.md](history/staging/import-distortion-prereg.md) |
| `Q-import-entropy-decrement` | CLOSED | Does Tao's entropy decrement argument, the one place a parity-type obstruction was circumvented for a two-point correlation, transfer to the tile's census? | It does not: the engine runs on multiplicativity at small primes and the census is defined by the absence of small prime factors, Tao scopes twin-prime sums out himself in print, and the census sits on the structured side of the pretentious dichotomy; all figures SCRATCHPAD-GRADE. | none | [import-entropy-decrement.md](history/staging/import-entropy-decrement.md) |
| `Q-import-fracparts` | ANSWERED | Does Saffari-Vaughan Theorem 10 cover the branches carrying the Skeleton door's mass? | Prediction HIT: the covered branches carry at most 8 percent of the mass; anchor and a sharper wall-address banked; the THEOREM column is struck, not merely overpriced, because Theorem 10's range condition is x^{6/11+eps} < y, which fails at fixed M; no route; no cap-36 line is upgraded. | 4 (retired) | [import-fracparts.md](history/staging/import-fracparts.md) |
| `Q-import-hypergraph` | MIXED (import-hypergraph-prereg.md: OPEN; import-hypergraph.md: ANSWERED) | Does hypergraph covering (Pippenger-Spencer / FGKMT) apply to the adversary's construction? | The covering theorem is class-count-agnostic and the analogy is EXACT at the hypothesis level, leaking at exactly one named place, the edges the machine needs as input; Branch A landed a theorem-provenance lower bound G2(x#) >> x ln x (HELD), Branch B died as predicted with a sharper wall than the registered one, and none of the three pre-registered kill lines fired. | none | [import-hypergraph-prereg.md](history/staging/import-hypergraph-prereg.md), [import-hypergraph.md](history/staging/import-hypergraph.md) |
| `Q-import-interp` | ANSWERED | Does the Bayati-Gamarnik-Tetali interpolation method reach the G2 Fekete object? | No: BGT closes on hypothesis H1, since the constraint count never splits (pi(st) - pi(s) - pi(t) is zero at no pair with st >= 25, minimum 2, maximum 12, VERIFIED on 104 pairs), and the one coordinate that does split has limit +infinity; the row lands as WALL-ADDRESS plus the identity that the submultiplicativity defect is the Overshoot slack. | 1d | [import-interp.md](history/staging/import-interp.md) |
| `Q-import-interp-prereg` | SUPERSEDED | Does the interpolation method (Bayati-Gamarnik-Tetali, Proposition 5) transfer to the G2 ladder, and in which coordinate? | Pre-registration only, committed alone before any producer existed, with the source verified at page images first (Proposition 5 is a special case of de Bruijn-Erdos, by the authors' own attribution); the predictions and the meaning of each outcome for the map are fixed here, and the outturn is import-interp.md. | none | [import-interp-prereg.md](history/staging/import-interp-prereg.md) |
| `Q-import-kw-zonegap` | ANSWERED | What does the graded Kourbatov-Wolf row buy the Z2 programme, and does the flagged 0.7574 against 0.7504 agreement corroborate anything? | A split-cell circularity verdict: the trend formula's raw performance is real, G/Tbar inside [0.78, 1.05] over thirteen decades with zero fitted parameters, but the flagged agreement is adjudicated a range accident, and since Theorem occurs zero times in the source the row can only be priced PUBLISHED-ANCHOR plus WALL-ADDRESS, whose wall is a quantifier: an almost-all over a log-sparse record sequence cannot deliver an every-zone statement. | none | [import-kw-zonegap.md](history/staging/import-kw-zonegap.md) |
| `Q-import-l1l2` | CLOSED | Does an l1 -> l2 conversion on the (e,a) coefficient sum buy the needed sqrt(log)? | The pre-registered kill line (rho >= 0.5 at every level) does NOT fire, rho falling 0.4352 to 0.0645 at z = 13..41, and the programme dies anyway on what the decay measures: \|\|Theta\|\|_1/\|\|Theta\|\|_2 grows by 2.01 per added prime against 2.0516 for S_sat, so the l1/l2 gap is not a proxy for the C^{pi(z)} price, it IS that price; rows 5 and 6 retire together. | none | [import-l1l2.md](history/staging/import-l1l2.md) |
| `Q-import-l1l2-prereg` | CLOSED | Does the l1 to l2 conversion on Theta_e(a) reach the threshold the import map set? | Sealed before any number was computed; scored in import-l1l2.md, where the pre-registered kill does not fire and the programme dies anyway: rho falls monotonically from 0.4352 to 0.0645 over z = 13..41, never reaching the map's 0.5 line, and what the conversion outputs is the sharp maximal law. | none | [import-l1l2-prereg.md](history/staging/import-l1l2-prereg.md) |
| `Q-import-map` | PARTIAL | Which foreign mathematics is worth aiming at this object, and what did each landed import actually buy? | Nineteen landings, zero routes opened on the exponent; every one banked a proven identity, a derived constant, a published anchor or a wall address, which is why payoff is graded by TYPE rather than by probability, and the map is live with rows still unrun. | none | [IMPORT-MAP.md](IMPORT-MAP.md) |
| `Q-import-map-construction` | ANSWERED | What was searched, what was rejected, and at what verification level, in building IMPORT-MAP.md? | The reconnaissance record behind the map: candidates rejected with reasons (hypergraph containers for want of a supersaturation input; determinantal processes by a proof-level obstruction, the twin tile failing the pair inequality at d = 6), a per-attribution SOURCED / SOURCED-BIB / MEMORY ledger, and two results derived here and offered for adjudication. | none | [import-map-construction.md](history/staging/import-map-construction.md) |
| `Q-import-maxplus` | ANSWERED | Do max-plus (tropical) spectral theory and subadditive ergodic theory bound the fold recursion's growth exponent? | The mapping is exact rather than an analogy - the fold is p-fold cyclic duplication followed by max-plus state elimination and the copy theorem is a semiring identity, verified at 6 of 6 folds - but the tropical Perron root of the tile is the mean gap mbar, not G2, so the import delivers a structural negative, a sharpening of A5's Theorem A, and refuses the growth exponent. | none | [import-maxplus.md](history/staging/import-maxplus.md) |
| `Q-import-proof-complexity` | CLOSED | Does proof complexity supply the barrier that wall-note Face 4 wants? | The row is VOCABULARY-ONLY and is recommended for rejection at the gate: the shared word is parity naming two different objects, a degree bound is a pseudo-expectation whose finite exact instance the corpus already refuted, and any unconditional barrier would imply Siegel-zero finiteness; the payoff is Tao and Brady 2014 read at source as a published anchor and a wall address, not a theorem. | none | [import-proof-complexity.md](history/staging/import-proof-complexity.md) |
| `Q-import-repulsive` | CLOSED | Does any repulsive point-process model (determinantal, Coulomb gas, hyperuniform) reproduce the twin tile's sub-Poisson counts? | NO, two-sided: g(2) = 0 kills positively-associated models and g(6) = 2.66 (g never in (0,1); support 6 \| d, g >= 2.38) kills Hermitian determinantal and negatively-associated ones; the Gibbs extension is withdrawn; every fixed level is periodic hence class I hyperuniform and the statement is empty, while along the diagonal family L = y^u no member approaches a hyperuniform limit in Var/E, which is a statement about the family and not a class for any one tile; the determinantal row's quoted product evaluates to 0 and its obstruction distance is 6 not 2. | none | [import-repulsive.md](history/staging/import-repulsive.md) |
| `Q-import-rough-anatomy` | ANSWERED | Does the analytic theory of rough numbers derive the depth law's drift, and is u = 2 a singular point of the dimension-2 sifting functions? | SCRATCHPAD-GRADE throughout, and leaning on three never-red-teamed premises: the drift is derived to 0.16 per cent by exact Mertens products and NOT by any published next-order term (the one in print is the wrong term for this object), and u = 2 is one identity seen four times rather than a singular point of the dimension-2 sifting functions. | none | [import-rough-anatomy.md](history/staging/import-rough-anatomy.md) |
| `Q-import-rows-15-17` | ANSWERED | Which three new fields deserve import-map rows, and at what price? | Row 15 is a wall address and a published anchor and NOT a theorem, since Theorem 10 requires x^{6/11+eps} < y and fails at every fixed M; row 16 is stale, its experiment already executed by record-location-null.md and its prior-art half closed by lit-kourbatov-shortfall.md; row 17 lands as priced; six fields rejected with pointers and one promoted to row 17. | none | [import-map-rows-15-17.md](history/staging/import-map-rows-15-17.md) |
| `Q-import-scanstat` | ANSWERED | Does the extreme-value theory of scan statistics settle the disputed sqrt(m) claim of IMPORT-MAP row 1? | The identity offered for adjudication is true and its conclusion is false - Sum gamma(k) = 0 is trivial while the step to Var(S_m)/m tending to 0 is refuted by a free permutation counterexample - the Leadbetter half of the row is confirmed as written and the pre-registered kill criterion passes at both target levels, one of them blind; the adversary pass corrected the claim that T29 had never been computed here to a reproduction. | none | [import-scanstat.md](history/staging/import-scanstat.md) |
| `Q-import-scanstat-prereg` | OPEN | What is the maxsum exponent at T_23 and T_29, predicted from a T_13/T_17/T_19 fit before the run? | Machine-written pre-registration only: the extrapolation laws, the grid and the kill criterion (Model A must beat Model B on the ln-RMS of excess_m at T_23) are fixed before any scoring, so part 4 cannot be scored against a prediction chosen after the fact. | none | [import-scanstat-prereg.md](history/staging/import-scanstat-prereg.md) |
| `Q-import-shearer` | ANSWERED | Where does Shearer's region actually end for the fold read as a repulsive lattice gas? | SURVIVES WITH CORRECTIONS under the 2026-08-19 adversarial pass: the complete-graph identity is verified by independent-set enumeration at n = 2..8, H* = 35..481 reproduce exactly and the 2/sqrt(e) floor is sound, but the tightness witness's disjoint-intervals sentence is false exactly where invoked and the atomicity lemma's hypothesis is load-bearing and not shown, the closure surviving instead on the sequel's gamma_i >= mu(f_i). | none | [import-shearer.md](history/staging/import-shearer.md) |
| `Q-import-shearer-prereg` | ANSWERED | Where does Shearer's region actually end on the repulsive lattice gas model of our window? | Sealed before any line of the producer existed; scored in import-shearer.md, where the exact criterion says the local lemma is the union bound on a complete dependency graph, and the two levels it buys over the local lemma's own sufficient condition are the only thing it buys. | none | [import-shearer-prereg.md](history/staging/import-shearer-prereg.md) |
| `Q-import-sofic` | ANSWERED | Does constrained coding and symbolic dynamics identify the Alternation Lemma's shift, and does the import map's shape claim survive? | The identification is exact and better than the map states - the shift is strictly sofic, two states, four edges, Perron root exactly 2, and the graph's own per-step rate is 2/p rather than the 3/p the map divides by - and the pre-registered ratio test then kills the map's literal formula while the graph-corrected one survives only as a small-D transient spent by fold 37; the shape claim does not stand, and it fails in the corpus's favour. | none | [import-sofic.md](history/staging/import-sofic.md) |
| `Q-import-sofic-prereg` | OPEN | Does the constrained-coding presentation of the fold predict the exact per-fold L, and is the shift sofic? | Pre-registration only, and declared weaker than the G2(41#) case because the nine exact L values were already published in the corpus: what is fixed here is the estimator, the exclusion rule, the trend statistic and the kill thresholds, plus a soficity verdict written before the check, strictly sofic and not of finite type. | none | [import-sofic-prereg.md](history/staging/import-sofic-prereg.md) |
| `Q-import-stein` | CLOSED | Does Stein's method for Poisson approximation derive the extinction law's constants and the ~3.8 joint deficit? | The pre-registered kill fires at both targets for one structural reason: each object is driven by exactly one shared uniform draw, so the non-neighbourhood indicators reconstruct it and b3 climbs to its own ceiling, measured at 0.850 to 0.9998 of that ceiling and 200 to 800 times b1 + b2; with no error term there is no Stein derivation, and the first-moment arithmetic banks the (A, c) pair anyway, relabelled. | none | [import-stein.md](history/staging/import-stein.md) |
| `Q-import-stein-prereg` | CLOSED | Does Stein's method for Poisson approximation bound the extinction law or the ~3.8 constant? | Sealed before any producer ran; scored in import-stein.md, where the pre-registered kill criterion fires at both targets for one structural reason, that both objects are driven by exactly one shared uniform draw, which is precisely the dependence the b3 term measures. | none | [import-stein-prereg.md](history/staging/import-stein-prereg.md) |
| `Q-import-suen` | ANSWERED | Do Suen's inequality, Janson's inequality and the Lovász Local Lemma family supply the missing proof for the anchored delta? | No inequality can: the import lands and what it certifies is that the target was never a lemma, the NOT-REACHED item being the Twin Prime Conjecture wearing a percentage; what it does deliver is the constant in the sharp form and the wall's address in local-lemma coordinates. | none | [import-suen.md](history/staging/import-suen.md) |
| `Q-import-thinning` | ANSWERED | Do point-process thinning and interval coalescence give H'' a null model? | Yes and exactly: the fold recursion is an exactly solvable thinning whose gap pgf transforms by a Mobius map fixing 0 and 1, so under independent thinning the gap word of T_x is exactly geometric with mean mbar/6 at every rung with no error term, which turns both of the record's fitted parameters into derived ones. | 0b | [import-thinning.md](history/staging/import-thinning.md) |
| `Q-import-transference` | CLOSED | Does the transference principle and relative Szemeredi theory reach the twin pattern? | VOCABULARY-ONLY and closed by an exclusion in print: the founding paper names our configuration as out of scope in one printed sentence, the theorem degenerates at k = 2 which is the case we want, and the W-trick removes the tile before the argument starts; re-entry costs a finite-complexity system whose solvability implies the Zone Postulate. | none | [import-transference.md](history/staging/import-transference.md) |
| `Q-import-vc-nets` | CLOSED | Does VC dimension, epsilon-net or set-cover duality bound G2? | VOCABULARY-ONLY, at a self-set 0.2 per cent confidence of opening the 4.2665 -> 2 gap and with every number SCRATCHPAD-GRADE: the range space's VC dimension is small and its growth is O(log log L) (proven), but the dual shatter function is exponential, the interval formulation's hypothesis contains its conclusion, and the full-period formulation is clean, free and on the wrong side of the inequality. | none | [import-vc-nets.md](history/staging/import-vc-nets.md) |
| `Q-ioslack-survey` | CLOSED | Does any instrument in the corpus carry a sharp-level signature that would let the infinitely-often slack be spent? | None does: 23 instruments surveyed and 19 eligible, smallest per-instrument p_FWE = 0.1082 and 0.8865 after Šidák, so dial 4's fourth channel closes and the dial is finished; the second finding is that maxsum_{L+1} is sharp exactly when L = 1. | 0e (retired) | [ioslack-survey.md](history/staging/ioslack-survey.md) |
| `Q-joint-correction-source-audit` | ANSWERED | Does completing the supported prime-partner correction yield cancellation beyond the existing Vaughan reduction, and which literature inputs actually justify that completion? | CHECKED prior-art matches for subset convolution, complementary sieve sums and signed smooth-number distribution. DERIVED reconstruction identifies the unrestricted factor weight with an existing short divisor approximant, up to the paid prime-power error. Its supports are x^(12/25) and x^(1/10). Reassembling the entire joint correction returns the already-open Vaughan remainder and supplies no new signed bound. A formal factor-vector control distinguishes the unrestricted logarithmic weight from the selected prime-cofactor branch. The matched general sieve theorems require inputs not supplied here. Literature novelty is unestablished; twin infinitude remains OPEN. | C | [joint-correction-source-audit.md](joint-correction-source-audit.md) |
| `Q-joint-factor-estimate` | ANSWERED | Can an additional estimate for actual factor configurations control the full signed balance of the C3 residual? | DERIVED: for the single-large-prime delta-rough family F, the residual splits exactly as R_F = C2*x*H_delta - Z_F^p + o(x), where the Type I part C2*x*H_delta is evaluated by ordinary prime BV on each cofactor interval and the twisted Mobius constant 2C2 (corrected 2026-09-08 after V2: Wu Lemma 2.3 is squarefree-only and did not cover the non-squarefree b_R moduli; prime BV covers all moduli), and Z_F^p is the signed prime-partner sum. The complement carries the opposite Type I part -C2*x*H_delta, so grouping by factor configuration transfers Type I mass and leaves the twisted prime correlation B_L unchanged. With the matched upper sieve the family bound is C2*x(1+H_delta-(40/9)H^+), certified below -2/5 C2*x: INSUFFICIENT BOUND. Even a sieve constant 2 in place of 40/9 needs H^abs<1 and leaves the complement unpaid. Independently reviewed 2026-09-09 with the uniform delta-range and complement corrections below. Twin infinitude and every sufficient margin remain OPEN. | C | [joint-factor-estimate.md](joint-factor-estimate.md) |
| `Q-k4direct-swap` | ANSWERED | Does swapping the shipped Monte Carlo estimator for k4direct meet the @13 gate, and is the x3600 on record a speedup? | The swap meets the gate by x3632, but the margin on record is an ACCURACY margin and not a speedup: k4direct is a 4x to 8x SLOWDOWN, 93.5 s against 11.7 to 23.4 s, and the 198.9 s on record for it is 2.1x too expensive, which drags the @17 extrapolation from 8.5 days on ten cores to about 4.4. | none | [verify-k4direct-swap.md](history/staging/verify-k4direct-swap.md) |
| `Q-kappa-not-L` | CLOSED | Can L, or its generalisation kappa(m), be bounded well enough to be the route's target? | L is not the target: three bounds on L are PROVEN through the Alternation Lemma and transfer to kappa(m), but the wall is located precisely and the lower bound never becomes exact, so L cannot be made irrelevant; closed 2026-08-19, L has no law of its own, being G2 divided by the block's own spacing and super-additive on disjoint sets. | none | [kappa-not-L.md](kappa-not-L.md) |
| `Q-kernel-sign-control` | ANSWERED | At delta=8/25, nu=9/20, is the moment Mfrak and its small-common-divisor kernel X_small measurably smaller with the actual coefficient b_u=A_right(gu) than with \|b_u\| or with \|b_u\| times an independent seeded random sign, and does the actual/random ratio decrease with x over the feasible dyadic range? | MEASURED, negative. Over seven dyadic scales j=18..30 and four boxes, the pre-registered slope of log2(actual/random) for X_small has mean + sd >= 0 in all four families, so the run gives no heuristic support for extra Mobius-sign cancellation in the small-j kernel. The actual coefficient's \|X_small\| ranks like one more random draw. The measurement is weak where it matters: the finite moment is 97.66-102.58 percent equal-frequency class, X_small carries 0.02-2.88 percent, J0=floor(x^(1/20)) is 1 at j=18 and 2 at j=20..30, and Z=2 collapses the prime-power sector of (13) to r=2. Equation (21) and the global twin margin remain OPEN and untouched. | C | [kernel-sign-control.md](kernel-sign-control.md) |
| `Q-kk-substitution` | ANSWERED | Does the Kalmynin-Konyagin construction survive substituting the two-class set Omega_p = {a_p, a_p - 2}, and what lower bound does it give? | STANDS WITH CORRECTIONS: G2(P(y)) >> y (ln y)^3 (lnlnln y)^2 / (lnln y)^4 for y >= y0 survives every attack made here, including an exhaustive brute force of the Proposition itself over four million values of i; five corrections follow and none touches the exponent. | none | [attack-kk-substitution.md](history/staging/attack-kk-substitution.md), [verify-kk-substitution.md](history/staging/verify-kk-substitution.md) |
| `Q-klz-forward-walk` | ANSWERED | Does the forward citation graph of arXiv:2205.08273 hold a two-class or k-class complexity result, and is Part II out? | The forward graph has exactly one member on three independent indices and it never treats word complexity; no citing work goes beyond one class per prime, Part II is NOT OUT as of 2026-08-19, the owning convention was OEIS A023192 all along, and the comparison is APPLES-TO-APPLES so the exponent-shape sentence needs no heredity caveat. | none | [klz-forward-walk.md](history/staging/klz-forward-walk.md) |
| `Q-kstar-drift` | ANSWERED | Is the drift in K* across doubling steps structural, and how far past the scannable levels does the certificate reach? | Structural and it lands early: K* is now enumerated at 16 doubling steps against 11, the raw drift slope steepens from 0.6881 +/- 0.1328 to 0.8184 +/- 0.0908, and the period-free certificate touches K*+1 = 18, 93.5% of 2^beta2 = 19.2455, at the base-2 chain step s = 16 itself. | none | [attack-kstar-01.md](history/staging/attack-kstar-01.md) |
| `Q-kstar-prereg` | OPEN | What is K* at the three next doubling steps, predicted before any period walk? | Pre-registration only, committed alone: the predictions, the scoring rule and the growth-type verdict thresholds are fixed in advance, with the inclusion-exclusion engine validated against an independent scan engine on all eleven known steps first. | D | [attack-kstar-01-prereg.md](history/staging/attack-kstar-01-prereg.md) |
| `Q-l1-residue` | CLOSED | Is the L = 1 residue count an open counting hypothesis whose proof would deliver the Zone Postulate? | REFUTED as a hypothesis: restore the dropped L >= 2 terms and it IS the Zone Postulate, so the chain is a tautology, and leave them out and what remains is provably no stronger than the target; Lemma A (inside B(p) the residue condition is the kill condition) is PROVEN and VERIFIED at 237 folds, and the route lands back on the residue-deleted maxsum without advancing it. | none | [attack-l1-residue.md](history/staging/attack-l1-residue.md) |
| `Q-lambda-ledger` | CLOSED | Does parity information survive in the lambda-weighted fold ledger? | REJECT, against a pre-registered threshold fixed before the producer existed: the lambda multiplier exists and is parity-free, so the ledger is blind at its design point rather than at its margins; two columns are pinned by proof, and nothing here is novel mathematics. | Z5b (retired) | [attack-lambda-ledger.md](history/staging/attack-lambda-ledger.md) |
| `Q-ledger-extraction` | ANSWERED | Can the QC engine's three suppression ledgers be moved out of the checks and into data? | Moved: all three now live in research/qc/ledgers.js, the fast gate and the selftest are byte-identical to their pre-change output, and all 25 entries were verified verbatim against git HEAD by key, order and reason text. | none | [audit-ledger-extraction.md](history/staging/audit-ledger-extraction.md) |
| `Q-ledger-forced` | ANSWERED | Which properties of the fold ledger's columns are FORCED rather than expected? | Fourteen forced constraints, all identities or wrong-direction bounds; by_new is forced only in the prime gap (its O(1) is MEASURED); nothing forces net from below. | Z5b (retired) | [fold-ledger-forced.md](history/staging/fold-ledger-forced.md) |
| `Q-left-divisor-signs` | PARTIAL | Can the Möbius structure of the left coefficient A_left(gm) replace the first Cauchy inequality, so that its sqrt(M) loss is not paid, and what does that buy at the target box (delta,nu)=(8/25,9/20) and at the corner a=b=1? | Partly, and not where it is needed. Two lemmas are derived: a Type I bound with no zero-frequency budget, usable at the target box whenever the arbitrary block is shorter than x^(1/4), and a Type II bound that is uniform in the Perron twist heights. Applied to the actual coefficient they confine the target-box deficit to sectors with left prime power r>=x^(43/200) and right prime power q>x^(3/100), and lower the worst block exponent there from 103/100 to 41/40. The corner a=b=1 is untouched: grouped, Type I, Type II, Bettin-Chandee/Wright and even a hypothetical per-block square-root bound all exceed 1 there. No region is added, E_dagger and the consumer (20) are unchanged, and the global twin margin remains OPEN. | C | [left-divisor-signs.md](left-divisor-signs.md) |
| `Q-lemmaV-meansquare` | PARTIAL | Does the mean-square-in-x form of Lemma V hold, and what does the proof cost? | Proved unconditionally, <R^2>_H <= B(z,s)*H for every H, z and level s, and the proof stops at exactly one place, B(z,s) bounded: B(z,3.0) measures 1.3833 to 1.4883 at z = 13..37, flat to 8 per cent over the whole computable range, which is a measurement and not a bound. | none | [attack-beta2-01-lemmaV-meansquare.md](history/staging/attack-beta2-01-lemmaV-meansquare.md) |
| `Q-lemmaV-neighbours` | ANSWERED | What do the five Lemma-V-adjacent instruments give when read at source, and which hypothesis do we violate? | The right instrument is Maynard's Lemma 6.12, owned by Deshouillers-Iwaniec 1982 Theorem 12 and sharpened by Pascadi's Corollary 18 in exactly the term that binds us; the hypothesis violated is narrower and sharper than the corpus expected, since all three papers allow arbitrary rough coefficients in three of five variables and what they require is smoothness where we have none. | none | [lemmaV-neighbours.md](history/staging/lemmaV-neighbours.md) |
| `Q-lemmaV-usup` | ANSWERED | Does u_sup plateau below beta2, or diverge? | It rises at every added level, 2.0617 at z = 13 to 3.2026 at z = 43: a plateau below beta2 is rejected and so is the fast divergence attack 1 feared, leaving "plateau above beta2, or divergence", which for this route is the same verdict (divergence since REFUTED at fixed s by attack-0829n-rml-proof.md section 4.1, adjudicated in verify-0830-usup-convention.md). | none | [lemmaV-sup-extension.md](history/staging/lemmaV-sup-extension.md) |
| `Q-level-ledger-tight` | PARTIAL | How much of the Level Ledger's 2*3^{pi(x)-1} class-discrepancy bound can be taken back? | The sup-versus-variance gap is not closed, and section 4 shows no L1 Fourier method can close it, since such a bound is already >> 2^{pi(x)} from its own j = 1 term; what replaces the exponent is an exact reduction to one finite quantity, computed by exhaustion to y = 19, and a proven CONSTANT factor 81.0 uniform in x, p and a (53.9 from the cheap y = 17 seed), which does not grow. | none | [level-ledger-tight.md](level-ledger-tight.md) |
| `Q-lichtman-decomp` | ANSWERED | What is the wall's published constant 3.29956 made of, and is there technique slack a method of this class could spend? | The split is multiplicative, 3.2995525 = 2 x 1.649776 with the second factor an equidistribution deficit, so the brief's "remaining 1.65 of technique" has no referent and category (b) is empty; the floor for this class is 2 on Type-I data and still 1.122919 at unlimited level, all arithmetic SCRATCHPAD-GRADE. | none | [attack-lichtman-decomp.md](history/staging/attack-lichtman-decomp.md) |
| `Q-lit-evans` | ANSWERED | Does Evans, Correlations of almost primes, reach y about x^0.28, does it ever fix h, and is there a secondary term to harvest for the depth law? | None of the three, and the item named the single highest-value unread item in the survey yields nothing for the depth law: over the whole 35-page extraction Buchstab, rough, sifting and omega(u) each occur zero times, so the paper has no sieve-depth coordinate, and its object is E2 numbers, a multiplicative condition rather than a roughness one. | none | [lit-evans.md](history/staging/lit-evans.md) |
| `Q-lit-fgkt-maier` | ANSWERED | Do the corpus's FGKT and Maier quotations hold against the PDFs of record? | The quotations are VERBATIM where checked, including at the sub/superscript level HTML destroys, and the defects are in the claims built on them: a Buchstab dimension error at four sites, one of them publication-track and self-contradictory, and two provenance errors (the Maier-Pomerance equality form and the FGKT/FGKMT R-statement); Cheer-Goldston was not obtained, so one quotation stays unverified. | none | [lit-pdf-fgkt-maier.md](history/staging/lit-pdf-fgkt-maier.md) |
| `Q-lit-fkmpt-quotes` | ANSWERED | Do the corpus's FKMPT quotations hold against the journal PDFs of record? | All three quotations are VERBATIM or CONFIRMED and two of the three surrounding claims are supported; the third is not, the cited section 1.3 does not exist (the passage is 1.1) and the connective overreaches, and five corrections are drafted including one silent elision inside a block labelled verbatim. | none | [lit-pdf-fkmpt.md](history/staging/lit-pdf-fkmpt.md) |
| `Q-lit-halberstam-richert` | ANSWERED | Do the Halberstam-Richert and DHR citations in dhr-verification.md and two-class-lower-bounds.md check out against primary sources? | Mostly reachable, against the brief's expectation: seven claims verbatim against source including beta2 about 4.266 at the book page itself, one UNREACHABLE (HR Corollary 2.4.1), the meaning of DHR and the Friedlander attribution both settled, and 4 defects among 21 further attributions swept. | none | [lit-pdf-halberstam-richert.md](history/staging/lit-pdf-halberstam-richert.md) |
| `Q-lit-kalmynin-konyagin` | ANSWERED | Do the corpus's Kalmynin-Konyagin citations hold against the PDF of record? | Item 2 is clean, reproducing their Theorem 1 at l_f = 2, h_f = 0, M(f) = 2 exactly; item 1 is MISROUTED, the quote being FKMPT's Definition 1 rather than K-K; and the word twin appears zero times in every version, with the calibration running opposite to expectation, since they delete two or more residue classes per prime and run a dimension-2 Mertens ledger, which our own absence rows still call ABSENT. | none | [lit-pdf-kalmynin-konyagin.md](history/staging/lit-pdf-kalmynin-konyagin.md) |
| `Q-lit-kourbatov-grob` | ANSWERED | Do the Kourbatov and Grob quotes on which the ZONE-POSTULATE retraction rested hold against the PDFs of record? | They hold: four verification items land VERBATIM against the published article and Grob's three negatives are confirmed, so the retraction was justified and a true claim was not retracted on false evidence; the corpus under-reports Grob in two places. | none | [lit-pdf-kourbatov-grob.md](history/staging/lit-pdf-kourbatov-grob.md) |
| `Q-lit-pdf-bft` | ANSWERED | Do our Banks-Ford-Tao quotations survive checking against the PDFs of record? | All three quotations VERBATIM, checked by scripted normalised diff rather than by eye; one was misattributed by the brief and not by the document (it is Maier-Pomerance), the demotion resting on their model R stands, and the corrections owed to the record are listed. | none | [lit-pdf-banks-ford-tao.md](history/staging/lit-pdf-banks-ford-tao.md) |
| `Q-lit-pdf-holt-rudd` | ANSWERED | Do our Holt and Rudd citations survive checking against the arXiv PDFs of record? | Every quotation VERBATIM with no misquotation found, but Lemma 3.1 is not the lemma the demotion needs, the 2p spacing result carries no numbered theorem of that name, several attribution defects and two internal conflicts are ours to settle, and the absence claim remains an absence claim. | none | [lit-pdf-holt-rudd.md](history/staging/lit-pdf-holt-rudd.md) |
| `Q-lit-scourfield-2008` | ANSWERED | Does Scourfield, Smooth divisors of polynomials (LMS Lect. Note Ser. 352, CUP 2008, 286-311), supply the divisor-distribution estimate that varE-theta2-proof.md section 6 leaves open? | DOES NOT DELIVER, at SECOND-HAND rung, and the chapter is still UNREAD at the page: ten channels were attempted, nine answered, and every one that answered is closed, degraded or paywalled, but the author's own restatement of the 2008 theorem, read at the page image of Scourfield, Funct. Approx. 55.1 (2016) 84 eq. (1.1), counts divisors m <= x of f(n) for n <= x with weight 1, for f a product of pairwise coprime irreducible factors each of degree at least 2, and the open step needs divisors n > 2L above the window, carrying a branch-dependent weight of total mass 4^omega, for the product of three LINEAR factors C(C-2)(C+2). Two gaps each independently fatal, plus a third that is AMBIGUOUS between two author-sourced statements and does not carry the verdict. One correction to lit-smooth-divisors.md is earned: the precision register of the owning convention is not uniformly (log y)^{o(1)} or order-of-magnitude, since (1.1) is an asymptotic with relative error O(1/log x), which is the right register and one epsilon short of the o(1/ln y) the open step needs. Step 1 of Var/E does NOT become conditional on a citation, and no absence may be written, since the chapter's interior lemmas were not read. | 9 | [lit-scourfield-2008.md](history/staging/lit-scourfield-2008.md) |
| `Q-lit-siebert` | ANSWERED | Is Siebert's 1983 result stated for general sieve dimension kappa, or for kappa = 1 only, and does it therefore already contain the kappa = 2 extremal example that SEARCH-CONVENTIONS section 3 records as not found? | kappa = 1 ONLY, on three independent statements of the theorem (the chapter's own publisher abstract, Granville 2020 section 1, Friedlander-Iwaniec 2022 page 20), all naming the LINEAR sieve and the Jurkat-Richert f and F; the chapter's full text was NOT reached, so this is testimony not primary reading, and the SEARCH-CONVENTIONS section 3 "no published kappa = 2 extremal example" row needs no correction. | 0 | [lit-siebert-1983.md](history/staging/lit-siebert-1983.md) |
| `Q-lit-wu2004` | ANSWERED | What is H_theta(2) in Wu 2004, and what does the source say about theta approaching 1? | The source does not answer it: Wu never parameterises H by a level of distribution at all, so the theta to 1 reading is not in the paper; three defects follow in what attack-lichtman-decomp.md quotes, one of them a wrong inference built on a wrong table row, and the only proven cap is H <= 1. | none | [lit-wu2004.md](history/staging/lit-wu2004.md) |
| `Q-localized-gap` | CLOSED | Does the Localized Merge Lemma close a chain from the localized twin-slot gap to a bound on the maximal gap? | The chain does not close, and it fails on a one-line averaging argument rather than on any sieve question; what survives is the growth law of maxsum_m and the boundary question, closed at (a)/(b) = (a)/(c) = 1.0000 at every x and every m <= 1024. | none | [LOCALIZED-GAP.md](LOCALIZED-GAP.md) |
| `Q-lp-push-x43` | ANSWERED | Does the level-D LP's DP1 > DP3 inversion survive being pushed to x = 43? | Yes, and the correction strengthens it: the two statistics still climbing at x = 23 stop climbing, the pooled floor moves UP from 3.1945 (16 readings) to 3.3152 (33 readings), DP1 reads 2.32 of the 3.2665 against DP2+DP3's 0.95, and every one of the 33 pooled readings clears the (1 + beta_2)/2 = 2.6332 the inversion needs, the tightest at 2.6692. | none | [lp-push-x43.md](history/staging/lp-push-x43.md) |
| `Q-maier-matrix` | CLOSED | Can the Maier matrix transfer exact residue-level knowledge about twin slots into an interval statement, and if not, where does it stop? | It stops at a scale collision: at q = x# the matrix is the identity 0 = 0, at q = y# with y < x the transfer identity is PROVEN and VERIFIED 20 of 20 but is a first-moment identity only, almost-all would need the second moment which is the localized twin-gap problem itself, and Granville-Soundararajan Corollary 1.4 is vacuous at every computable scale. | none | [maier-matrix.md](maier-matrix.md) |
| `Q-maxgap-law` | ANSWERED | Does maxgap ~ c*mbar*lnD survive far enough to contradict Maier-Pomerance, and why did two agents measure two constants? | It does not, and not because the law breaks late: it was never an extreme-value law but a curve through a two-dimensional surface, and the two agents sat on different curves without recording which; on the diagonal c really is flat over a lever 46 times long with an estimator demonstrably able to see Maier-Pomerance growth, and one repo projection is REFUTED by the audit. | none | [maxgap-law.md](maxgap-law.md) |
| `Q-maximal-law-tpc` | ANSWERED | Is the SIEVE Gaussian maximal law TPC-implying? | YES in the only form that would deliver anything: stated for the operative remainder R_H, need/z^2 runs 0.49 to 0.61, flat and below the zone budget at every z from 13 to 43, which is the Gap Reformulation, hence the Zone Postulate, hence TPC, so no soft argument can prove it; the published above-2 theta column is not the maximal law's verdict but the law plus two lossy steps. | 0 | [phase1-T4-maximal-law.md](history/staging/phase1-T4-maximal-law.md) |
| `Q-maxsum-growth-law` | CLOSED | What is the growth law of maxsum_m, and is there a constant C that closes the localized chain? | The chain has no chance, and for a reason cheaper than the sieve wall: the gate grows like ln x per fold while the bound it must stay under grows by at least 2.4 ln^2 x, a deficit that is unconditional in C and in the sifting parameter, and the Deficit Lemma kills the weaken-the-gate repair because the gate feeds back. | none | [localized-04-maxsum.md](localized-04-maxsum.md) |
| `Q-maxvr-uniform` | CLOSED | Is there a level-uniform bound on max VR, and what would an all-x form need? | No level-uniform bound: all three candidate bounds are killed by the numbers, and the all-x form needs a second ingredient the Status sentence does not name, an analytic lower bound on Sbar, the count of n with both n and n+2 free of prime factors in (x, sqrt(N)]; a max VR bound is in any case not TPC-strength, and no REFUTED.md row covers the route. | none | [attack-maxvr-uniform.md](history/staging/attack-maxvr-uniform.md) |
| `Q-measure-0904-argmax` | PARTIAL | Where inside the tile is G2(x#) attained, with what multiplicity, and how thick is the near-maximal tail? | The multiplicity half was NOT open, and is reproduced here rather than found: exact-g2-ladder.js, measure-g2z2-0829.js and ATTACKS3.md already carry it at every level to x = 43, so object-g2-read-0829.md:1000's "unknown" is wrong. What is new, MEASURED exhaustively over the whole period at x = 11..37 by a third independent engine: the argmax set is tau-invariant with no fixed-point hit at all eight levels and carries ZERO congruence pairs from x = 23 up (refuting this note's own F7 at four scored levels), while 58 to 82 percent of the near-maximal windows ARE exact congruence translates of another by a multiple of W/p, at 10^6 to 10^8 times the uniform null; at x = 37 the maximum is 2 positions of 7,420,738,134,810 and only 6 gaps of 217,929,355,875 sit within 10 percent of it; four of eight pre-registered forecasts failed (F3, F5, F6, F7) and two falsifiers fired (F5, F7), and the exponent is untouched. | none | [measure-0904-argmax.md](history/staging/measure-0904-argmax.md) |
| `Q-measure-g2-generic` | ANSWERED | Where does G2(x#) sit in the distribution of the same maximum gap taken over other two-class configurations with the same census, and is the constant-shift family generic inside the free-pair family? | G2 is GENERIC in this coordinate on the registered rule, MEASURED: the midrank percentile of G2 in the census-matched two-class ensemble reads 20.00, 18.06, 26.35, 17.14 exhaustively at x = 11..19 and 13.70 sampled at x = 23, all inside the registered [5, 95] band so the falsifier does not fire, while sitting about one ensemble sd below the mean at all five levels; and the free-pair and constant-shift ensembles are PROVEN identical up to translation, so killer 1 gains no target in the class positions at these levels. | 0 | [measure-g2-generic-0829.md](history/staging/measure-g2-generic-0829.md) |
| `Q-measure-g2z2` | ANSWERED | What is G2(x#)/Z2(x) at every level where both exist, where does the tile's least attaining position sit, and how often does a zone hold exactly two pairs? | MEASURED at 22 levels: G2/Z2 rises 1.00 to 8.1429 with its maximum 8.3214 at x = 71, is lossless only at x <= 7, and no gap of length G2 lies inside the zone for x = 11..79 (PROVEN there from Z2 < G2 plus the Zone Restriction Lemma); R0's tight case k = 2 occurs at 0 of 27,291 zones above the degenerate first one; the fourteen custody ratios reproduce digit for digit and Z2 = env at 27,292 of 27,292 zones; the pre-registration scored three of five with one pre-registered theorem refuted (the Poisson miss is 1.518e-1 over p >= 3, corrected from a mislabelled 4.177e-1); no upper bound on G2/Z2 is claimed or in evidence. | none | [measure-g2z2-0829.md](history/staging/measure-g2z2-0829.md) |
| `Q-minus-half` | ANSWERED | Is the -1/2 anticorrelation constant of the abutting-window covariance exact, or only equidistribution-conditional? | For the flat spectral functional the -1/2 is EXACT, a two-line consequence of the mod-30 difference set, verified to relerr <= 1e-15 on the full spectrum at x = 7 and 11; the whole equidistribution question compresses exactly into two residue-class correlation sums, and the residual all-x statement reduces to G30_agg(x) < 1/2. | none | [natal-cap-26-minus-half.md](natal-cap-26-minus-half.md) |
| `Q-mismatch-adjudication` | ANSWERED | What is the true value behind each of readings-traceability's 56 mismatches, and where does each repair land? | All 56 adjudicated with old and new recorded: 33 READING-FIXED, 5 OUTPUT-FIXED-REBOUND, 2 awaiting re-embed, 5 DOC-FIXED, 4 UNTRACED-MARKED and 7 HOLDS-AS-IS; nine were repaired by making a script produce a figure it had only described, and three of those reproductions turned up a second defect. | none | [mismatch-adjudication.md](history/staging/mismatch-adjudication.md) |
| `Q-mobius-bv-derivation` | ANSWERED | Is there a published theorem statement of Bombieri-Vinogradov for the Mobius function at level T^(1/2)/log^B T with a maximum over coprime classes, and if not, does that estimate follow from published theorems by a derivation whose every hypothesis is checked? | No published theorem statement was located in five channels searched in the owning convention named in research/SEARCH-CONVENTIONS.md; the closest is Granville-Shao's published assertion that the result is known, which carries no proof locator for the Mobius case. The estimate is derived here from four numbered results of Koukoulopoulos, GSM 203 (Corollary 13.4, Theorem 26.2, Theorem 26.6, equation (26.3)) plus Vaughan's identity for mu, with B(A)=A+6 and an ineffective constant. This is a derivation from published theorems, not a refereed theorem, and it is read from the author's preliminary version of that book. | C | [mobius-bv-derivation.md](mobius-bv-derivation.md) |
| `Q-mod30-tail` | ANSWERED | Are the BV survey's S1 (mod-30 tail) and S2 (fixed truncation and depth) provable as stated? | Both PROVEN at short-note grade (no second reader) once S2's freshness factor is corrected to one class per prime, which needs only P^-(m) >= q > q_i and so holds at every scour prime, not only in the prime regime; tail constant 2 ln 2 -> (ln 2)/2; nothing in the head. | 11 (retired) | [thm-mod30-tail.md](history/staging/thm-mod30-tail.md) |
| `Q-monotonicity-sweep` | ANSWERED | Does anything in the corpus assume certificate validity is monotone in L? | One unsound artifact and one invalid inference: attack-beta2-04-loss-budget.js section 6 bisects on a predicate measured not upward-closed and is wrong at 3 of 5 levels, true first-crossings 30/72/132/174/210 against the reported 36/72/144/174/354, and redteam-DP1-certificate.js draws a global minimality conclusion from a two-point local check; corrected, worst-casing certifies within 1.00 to 2.00 of true G2 and the exponent penalty runs 0 to 0.27 and falls with x. | 3 (retired) | [monotonicity-sweep.md](history/staging/monotonicity-sweep.md) |
| `Q-moving-cutoff-parity` | ANSWERED | Does a proof-level reading of the shifted-Mobius sieve give a valid, explicit error-tolerant arithmetic target, and does its divisor switching preserve the moving boundary? | CHECKED prior art: Murty--Vatwani already supplies the conditional squarefree/parity mechanism and fixed-residue reduction. Its printed p. 654 swap omits n+h>ey; an exact finite counterexample verifies failure of that equality. DERIVED dyadic repair keeps the boundary and gives S=C2*x-2*C2*M+D_y+O_A(x/log^A x). A one-sided D_y>=-4*x/25+o(x) on unbounded dyadic scales is sufficient, using the certified margin C2*(1-A2)>33/200. That discrepancy estimate remains OPEN. Vatwani's recovered author preprint clarifies the one-odd-exponent cases and unfilled near-level-one hypotheses. No new signed bound is obtained; literature novelty is unestablished. | C | [moving-cutoff-parity.md](moving-cutoff-parity.md) |
| `Q-mp-derivation` | ANSWERED | Can the fold-factor field M_p be derived rather than merely measured? | Its comb structure derives: M_p is about k*W1(theta_p)*exp(-delta*theta_p/mbar_p) with W1 the exact endpoint comb at zero parameters, blind-validated at a second fresh anchor; (k, delta) remain fitted, so this is a zero-parameter derivation of the field's comb structure and not of M_p, and nothing here proves H-double-prime or touches the exponent. | none | [mp-derivation.md](history/staging/mp-derivation.md) |
| `Q-mp-window-prereg` | OPEN | Do the M_p FORMULA bands hold at a second fresh anchor? | Pre-registration only, sealed and committed alone before the measuring producer exists: the window, the population, the zero-new-parameter formula, all 37 band pairs, three scoring criteria and the consequences are fixed here, pinned to the v1 producer's embed fingerprint; nothing is measured. | none | [mp-window-prereg.md](history/staging/mp-window-prereg.md) |
| `Q-multiplicity3` | CLOSED | Does the m >= 3 multiplicity instrument buy anything for the anchored deficit? | Closed as an instrument: at @17 the m >= 3 statistic sees the anchored deficit worse than the pair statistic it was to replace (anchored z -0.23 against -2.71 for the overlap credit X), the Bonferroni depth ladder buys one place and dies, and multiplicity 3 in moment order buys a factor 1.3 that does not reach the anchor. | none | [attack-multiplicity3.md](history/staging/attack-multiplicity3.md) |
| `Q-natal-cap-campaign` | ANSWERED | What is the mathematical upper limit on the number of Natal@5 slots a prime q can remove from an X-tile as the Scour drags across it? | Per-prime removal is boxed by four instruments (max overshoot +7.7% over the fair share 2N/q, worst conceivable dilation +0.7% at @17 over 92,160 tuples, certified Selberg caps 1.13-2.5x truth, and a proven prime-counting cap for q > W^(1/3)), but no per-prime cap, even an oracle, closes the first-order union bound for x >= 13 because Sum 2/q crosses 1 between @11 and @13. | none | [NATAL-CAP-CAMPAIGN.md](NATAL-CAP-CAMPAIGN.md) |
| `Q-natal-cap-overlap-sign` | CLOSED | Is the sub-CRT overlap bound S2 <= sum of 4N/(q q') provable, per pair or in aggregate? | REFUTED as an inequality at every granularity, with 40 to 53 percent of pairs sitting above CRT at x = 11 through 23 and named exhibits at each level; what survives is proven structure, an exact per-pair-computable aggregate deficit, with the remainder a sign-alternating discrepancy at noise scale. | none | [natal-cap-12-overlap-sign.md](natal-cap-12-overlap-sign.md) |
| `Q-natal-cap-sieve-cap` | ANSWERED | What is the rigorous sieve upper bound on how much a single scour prime can remove, and does it certify the zone? | Certified Selberg and Bonferroni caps run 1.60 to 2.36 times N over x = 7..17 with the fluctuation factor at 1.000, gross(q) hugging 2N/q to three decimals, but from x = 13 the harmonic factor alone exceeds 1, so Sum gross > N and even exact-truth caps fail. | none | [natal-cap-10-sieve-cap.md](natal-cap-10-sieve-cap.md) |
| `Q-natal-discrepancy-lemma` | PARTIAL | Can the rotation ensemble's class discrepancy be controlled strongly enough to feed Freedman's inequality? | Lemmas 1 to 4 and Theorem 5 are stated and machine-checked (1,954 assertions, zero failures) and Proposition 6's stopped Markov-union-Freedman chain is rigorous, but none of it touches the anchored problem: the anchored path's per-step conditional variances are ensemble-typical (mean ratio 0.93 to 0.99), so the anchored side remains 100 per cent drift against the Mertens/2C2 wall. | none | [natal-cap-14-discrepancy-lemma.md](natal-cap-14-discrepancy-lemma.md) |
| `Q-natal-onset` | ANSWERED | Does Chris's q^2 destruction-onset staircase hold, and does the onset lens open a mechanism at x = 37? | The staircase is VERIFIED over 1..10000 after aborting-on-mismatch against his three hand anchors, the three onsets collapse to two and the naive 50:50 A/B split is refuted by derivation; the x = 37 fourth lens is a clean negative and the fourth mechanism family closes. | none | [natal-onset-01.md](history/staging/natal-onset-01.md) |
| `Q-next-correlation-source-map` | ANSWERED | Is there a primary-source statement with stronger scale or coefficient quantifiers than the ones the prime-band transfer actually consumed? | Scoped negative for the inspected statements: function-class and rate mismatches remain. The coordinating review withdraws the all-scales/dyadic-omitting requirement as a necessary gate, since bounded-interval stability yields a weak dyadic scale average from the existing input. No sufficient rate or full-coefficient theorem is matched. Proper-prime-power terms are already negligible on the fixed corner; other prime-r cofactor branches remain open. | C | [next-correlation-source-map.md](next-correlation-source-map.md) |
| `Q-next-transfer-review` | ANSWERED | Does prime-band-transfer.md (1)-(6) follow at exactly its stated scope, and does any step fail against an adversarial reading of its hypotheses? | The derivation (1)-(6) survives at its stated continuous-average scope. The coordinating round review corrects check l: interval stability additionally gives a dyadic scale average, with a further exponent loss. There is no every-dyadic estimate, o(N), full-corner control or twin margin. Proper-prime-power branches have a separate negligible fixed-corner bound. | C | [next-transfer-review.md](next-transfer-review.md) |
| `Q-novelty-postaudit` | ANSWERED | Of the ten results never covered by the 2026-08-13 prior-art audit, which are novel? | None survives as fully novel: two are outright prior art (one published thirteen years earlier with its headline claim contradicted by the source's own table), one is a two-line classical theorem mis-calibrated as a measurement, five are restatements or special cases of standard objects, and one names a lemma that does not exist. | none | [audit-novelty-postaudit.md](history/staging/audit-novelty-postaudit.md) |
| `Q-np-licenses` | ANSWERED | What does NP-completeness license here, and is Brady's Problem 3 the G2 covering problem? | The corpus sentence "his Problem 3 IS the G2 covering problem" is false as written and must be withdrawn (one class per prime and an arbitrary finite set, against two classes at locked separation 2 on an interval); NP-completeness licenses four statements about computation and none of the five mathematical ones. | none | [attack-np-licenses.md](history/staging/attack-np-licenses.md) |
| `Q-null-limsup` | MIXED (null-limsup-prereg.md: OPEN; null-limsup.md: ANSWERED) | Does the thinning null's maximal gap disagree with Neudecker's limsup law, which would retire the extinction half? | The trigger does not fire: the closed form is the exact law, the reduction returns Hawkins' own constant, and the real fold's record gap lands within 2 sigma of the null, so the extinction half survives and the null now supports the ceiling argument rather than threatening it; the limsup itself is not measurable and cannot be. | none | [null-limsup-prereg.md](history/staging/null-limsup-prereg.md), [null-limsup.md](history/staging/null-limsup.md) |
| `Q-object-bridge-read` | PARTIAL | What sits between Z2(p) and G2(x#), which inequalities between them are proven and in which direction, and is the information the Gap Reformulation discards provably needed? | Map only, nothing computed: the reduction discards the origin to buy rotation invariance at a loss measured at G2/Z2 = 4.12 by p = 43, and the discarded information is PROVABLY not needed for the implication (a rotation-invariant statement, G2 < x'^2 - 2, does reach the zone statement), MEASURED to be worth about one unit of exponent against a deficit of 2.2665, and OPEN as to whether any proof needs it, with no separation theorem on record on either side. | none | [object-bridge-read-0829.md](history/staging/object-bridge-read-0829.md) |
| `Q-object-g2-read` | PARTIAL | What is actually known about G2, at what calibration, where do the corpus's documents disagree about it, and which questions about it have not been asked? | The band is unchanged: exponent 4.26645 proven above, 2 needed, and the reading found no document that moves it; what this note adds is a variant table, a legal open set for section 4, seven drift items including one live target that is TPC-strength and unlabelled, and eight unasked understanding questions. | none | [object-g2-read-0829.md](history/staging/object-g2-read-0829.md) |
| `Q-object-models-read` | PARTIAL | For G2(x#) and Z2(p), what does each null model in the corpus predict, which measured deviations from those models are real, and does any of them carry interval-level (wall-relevant) information? | Nothing found that carries interval-level information: seven of the nine real deviations are residue-level by the THE-LENS section 5 rule, Kourbatov's b is interval-level in form but blocked by a log-sparse quantifier and unexplained as a mechanism in both corpora, and the sub-Poisson rough-pair dispersion is classified interval-level in form and elementary in content (division with remainder, not placement) by the independent-thinning null that ran 2026-08-29 (measure-roughpair-null-0829.md), which also weakened the sub-Poisson reading since that null's own chi-squared per degree of freedom is 1 minus p rather than 1. | none | [object-models-read-0829.md](history/staging/object-models-read-0829.md) |
| `Q-observations` | PARTIAL | Which sightings from the bench survive being stated precisely enough to check, and at what rung? | A running log, each entry carrying its own rung: the mirror-centre and divisor-landmark items stand as VERIFIED, the closed form for the half word is REFUTED as a route (max of the half equals max of the whole at every level), and the compounding window is PROVEN to close only to U = 30. | none | [OBSERVATIONS.md](OBSERVATIONS.md) |
| `Q-obstruction-audit` | ANSWERED | Is the wall named parity the right name for what blocks G2(x#) < x'^2 - 2? | Read at source, the audit's central reason does not survive: Tao's forbidden is defined extensionally rather than intensionally, so the primality-detection step in the reduction does not put the method class outside the obstruction, and where the wall sits on our own reduction moves accordingly; the proposed text for paper/wall-note.md is left unapplied. | none | [attack-obstruction-audit.md](history/staging/attack-obstruction-audit.md), [lit-tao-parity.md](history/staging/lit-tao-parity.md) |
| `Q-oeis-G2-submission` | CLOSED | Should the twin Jacobsthal function G2 be submitted to OEIS as a new sequence? | DO NOT SUBMIT: it duplicates A144311 (Carter, September 2008), which is G2 - 1 on the same fixed classes with no free translate and carries 22 terms to our fourteen, all fourteen agreeing; five waves missed it because every search was run on G2 and never on G2 - 1. | none | [oeis-G2-submission.md](oeis-G2-submission.md) |
| `Q-oeis-g2-absence` | ANSWERED | Is the G2 ladder absent from OEIS at fourteen terms? | Falsified: the ladder has been in OEIS since 2008 in the run-length convention G2 - 1, as A144311 carrying 22 terms to our 14, with the search channel calibrated live in the same session on two known-positive probes. | none | [audit-oeis-14term.md](history/staging/audit-oeis-14term.md) |
| `Q-oeis-seam-submission` | PARTIAL | Is the seam twin-pair count sequence absent from OEIS, and is the draft ready to submit? | Status DRAFT. The source records twenty DATA terms plus ten further verified terms available for the submitter. CROSSREFS now includes A367739 and A384545, so the old missing-neighbour objection is resolved. Before submission still identifies the LINKS entry as a path rather than a public URL, with the publication moratorium unresolved. No new OEIS absence search or submission is claimed. | none | [oeis-seam-submission.md](oeis-seam-submission.md) |
| `Q-ojaroudi-read` | ANSWERED | Does Ojaroudi's Zenodo preprint prove an unconditional twin-prime theorem, and is anything in it importable? | No: the fatal step imports a Selberg quadratic-form LOWER bound from Opera de Cribro Chapter 7 where none exists, and a second independent gap leaves the Kloosterman hypothesis never checked; the venue is an unrefereed self-deposit, and the only payoff is two elementary lemmas that are importable onto our tile. | none | [ojaroudi-read.md](history/staging/ojaroudi-read.md) |
| `Q-omega-floor-blind-0830` | ANSWERED | Does the local log-slope of the pointwise floor Omega(z) of attack-0830-rec-cheapest.md (exact to z = 73, certified 2+4-chain family to z = 5e5), extended blind to new levels under a sealed forecast, behave as the DERIVED growth law Omega >> z^{16s/9}/ln^8 z predicts at s = 2.698721, and at what z would the test be decisive? | MEASURED, blind, on the derived law only: 18 of 22 sealed rows HIT; the certified 2+4-chain family at p* = (47, 43) runs 5e5 -> 1e9 (A1A2 = 8.863e17 -> 9.351e32, exact integers) with its step slope falling 4.85 -> 4.38 through every sealed band onto the law's log-corrected slope, the decisive decade 1e8 -> 1e9 reading 4.410 against 16s/9 - 8/ln z = 4.389 (HIT, kill rule not triggered at 4.452 +/- 0.011); the 4 MISSes are the ratio to z^{16s/9}/ln^8 z sitting at 2.00-2.14 above the sealed cap of 2 at z >= 1e8, the pre-declared non-adverse direction; the exact floor is extended 73 -> 113 (251 -> 1980, equal to the hill-climb floors at 89 and 101), where the law predicts nothing; no exponent moves and the law stays DERIVED and HELD. | 0 | [blind-0830-omega-floor.md](history/staging/blind-0830-omega-floor.md) |
| `Q-operator-pair-count` | ANSWERED | Can the histogram transfer operator and the pair count be evaluated exactly at any level with no tile in memory? | Both instruments are exact and neither needs a tile resident: the operator is PROVEN and VERIFIED exactly at six folds and the pair count at every fold; the tail carries a FIT beside them that must not be used past the range it was fitted on. | none | [operator-and-pair-count.md](operator-and-pair-count.md) |
| `Q-origin-excess` | ANSWERED | Can the Origin Excess Lemma be pushed to S = x'^2, and is the scale collision genuine or an artifact of that one argument? | It cannot, and the collision is genuine: the origin's excess is exactly a ratio of two values of the survival curve rho at the same window and two sieving levels, and the Zone Postulate asks for that ratio at u = 2, where rho takes its minimum, so no better lemma moves the boundary; three candidate mechanisms fail, each for a different reason, one of them working against us. | none | [origin-excess.md](origin-excess.md) |
| `Q-packing-two-class-priorart` | PARTIAL | Does the two-class (twin) analogue of the Hensley-Richards packing function exist in print? | Not found, on an uncalibrated search in our own wording with no owning convention recorded, so this is the reach of the search rather than an absence; the classical one-class theory is well developed, and against A008407 the two-class ladder is bounded below by the minimal admissible 2k-tuple diameter. | none | [natal-cap-04-packing-notes.md](natal-cap-04-packing-notes.md) |
| `Q-paired-factor-budget` | ANSWERED | Does averaging the proposed two-small-prime loss and three-small-prime gain using existing distribution theorems make their net contribution sufficient for the current twin consumer? | DERIVED from the matched classical inputs, with finite rational enclosures VERIFIED: the explicit positive family has liminf P3/(C2*x)>1, but liminf (N2-P3)/(C2*x)>11/10. Keeping only these families and the main term therefore fails at the current cutoffs. Pan--Ding supplies aggregate level x^(9/20), stronger than the earlier per-cofactor application; the complete signed margin remains OPEN. The aggregation machinery is prior art and literature novelty of this application is unestablished. | C | [paired-factor-budget.md](paired-factor-budget.md) |
| `Q-paper-iii-restructure` | ANSWERED | Is Paper III restructured around the proven model theorem? | Yes. paper/variance-note.md now carries four new sections in place of its fit narrative: sec.8 the proven spectral form (Var/E = delta X, delta ln^2 W -> 16 C_2 e^{-2gamma}/3 = 1.109905, the Montgomery-Soundararajan main term exactly L prime by prime, so all of Var/E is discrepancy), sec.9 the decoupled model with Theorems 7 and 8 and Lemmas 9-11 written out with proofs and the closed form lambda_2(2) = 1 - e^{-2gamma}(9/2 - 4 ln 2) = 0.45546 plus the theta = 1 identity with Gorodetsky, sec.10 Conjecture 1 (delta(X - X_dec) -> 0) with eight exact ratios, two of three lag groups closed and the third named as a divisor-distribution statement not yet searched, and sec.11 the 0.611 refutation as a short calibration paragraph; sections 1-5 are untouched, the abstract and section 6's open question are rewritten to match, and the "u = 2 exactly" defect in section 7 is corrected. | 9 | [paper-iii-restructure.md](history/staging/paper-iii-restructure.md) |
| `Q-paper-kk-draft` | ANSWERED | Is the K–K two-class lower bound written up as a refereeable draft? | Yes. paper/kk-lower-bound.md, self-contained at INFERRED grade, carrying Theorem B (the substitution), Theorem A (the published-ingredient x ln x chain) and Proposition 2 (the free G2 >= g transfer), with every constant, every consumed hypothesis, the y0 = 10^134.1 floor, the three residuals, and a per-number provenance appendix; nothing in it is new mathematics and nothing in it is refereed. | none | [paper-kk-draft.md](history/staging/paper-kk-draft.md) |
| `Q-parity-adversary` | ANSWERED | Does a parity adversary built on our own stretches survive at every level, and what precision class does a certificate need? | It does NOT survive: the exact-data adversary dies at D* about Q^1.18 (MEASURED, exact arithmetic, 43 anchors Q <= 200), and the certificate that kills it is itself destroyed by 0.30 of one count per modulus, so Z2's precision class is now measured rather than described; it is PROVEN not to be a proof ingredient. | Z2 | [attack-parity-adversary.md](history/staging/attack-parity-adversary.md) |
| `Q-parity-dstar-law-0829n` | CLOSED | Does the exact-data parity adversary's killing level D*(Q) follow D* ~ Q^c with a stable c on the decades past Q = 200, and is c distinguishable from the independent-thinning null's? | No law in Q and CLOSED by the sealed kill rule (score 5 HIT, 1 MISS): MEASURED on 271 anchors 211 <= Q <= 13679, the Q-slope moves 1.446 to 1.204 to 0.575 across ranges while ln D* on ln width holds slope 1.097 +- 0.012 with a quarter of the scatter, D*/width about 0.5, and the independent-thinning null reproduces the width law within 0.025 in slope; the mechanism is that D* is where a modulus first reads a single position of the window, which is the wall survey's remainder statement in the stretch coordinate and names nothing new. | Z2 | [attack-0829n-parity-dstar.md](history/staging/attack-0829n-parity-dstar.md) |
| `Q-perfold-error-model` | ANSWERED | What is the per-fold error model behind the extinction law's +/-3 sqrt(lambda) failure at 43.2 per cent? | X_p ~ Poisson(lambda_model(p, Y) M_p) with M_p a deterministic factor of the fold, the same number at every window length from 2e7 to 2e11 and at every anchor, MEASURED and not derived, and it holds on a sealed blind test at a fresh anchor. | none | [perfold-error-model.md](history/staging/perfold-error-model.md) |
| `Q-perfold-window` | ANSWERED | Does the negative-binomial per-fold error model's band hold at a fresh blind anchor, after the extinction law's +/-3 sqrt(lambda) clause failed at the fifth window? | The preregistered blind window [6.6e10, 6.6e10+2e9) is scored HIT: 33 of 37 folds inside the sealed 90% bands (needed >= 28), 0 outside the 99.73% bands (allowed <= 1), with an independent re-sieve/re-score in redteam-0820-empirical.md section T1.b. The producer is attack-perfold-02-blindwindow.js Stage D; perfold-error-model.md sections 0 and 5 records the outcome. This is finite blind validation of a MEASURED error model, not a derivation, aggregate-law upgrade or twin-prime result. | none | [perfold-window-prereg.md](history/staging/perfold-window-prereg.md) |
| `Q-phase1-W1b` | ANSWERED | Which unapplied wave-6 findings on the research notes were still live, and what did applying them change? | Most of wave 6 was already applied, so the yield is the residue plus one code defect nobody had fixed: a3-05-bound-L.js's truncated cyclic replay was printing a FALSE PASS on kappa(m) <= L+2 at fold 7, and fixing it kills a claim; the gate reads 0 findings across all seven checks at hand-back. | none | [phase1-W1b-applied.md](history/staging/phase1-W1b-applied.md) |
| `Q-polylog-fold-transfer` | ANSWERED | Can the fixed-fold calculation be made uniform at growing depth, and transferred to the actual bilinear remainder with an adequate error? | The local bilinear model is O_H(x/log^H x) uniformly for polylogarithmic squarefree moduli. Its absolute reconstruction error is at least (1/2+o(1))*x. The needed signed reconstruction bound remains OPEN, so this model does not establish the twin-prime lower bound. | C | [polylog-fold-transfer.md](polylog-fold-transfer.md) |
| `Q-prime-band-completion` | ANSWERED | Can the remaining squarefree correlation be localized to simpler prime and harmonic bands, and does completion then permit a direct general bilinear Kloosterman estimate? | The pilot reduces, with power-saving endpoint errors, to p in (x^0.235,x^0.24], q in (x^0.045,x^0.05] and positive h in (x^0.029,T], with T=O(x^0.0342). Both primes exceed 2h eventually. Completion is exact but produces coupled h-dependent coefficients on every dual residue modulo q. Its full-frequency Kloosterman matrix has norm exactly q, so a uniform power saving by an arbitrary-coefficient operator bound is impossible at that scope. This completion alone leaves the 61/20000 budget deficit; prime-dispersion.md controls the pilot using a different second moment. No twin lower bound is established. | C | [prime-band-completion.md](prime-band-completion.md) |
| `Q-prime-band-transfer` | PARTIAL | Can the nonmultiplicative prime-band weight be represented by bounded multiplicative functions, and what does an available quantitative correlation theorem actually give after all scale and normalization costs? | A smooth Fourier superposition represents mu(n)L_B(n)/log X exactly on n<=2X+2. The quantitative non-pretentious input and a mesh give a continuous scale-average saving for the exact s=s'=1 windows. The round review additionally derives a dyadic scale-average saving by bounded-interval stability, with exponent c_*/2. Neither estimate gives an every-dyadic bound, o(N), full-corner control or a twin margin. The extension in cofactor-progression-transfer.md now estimates a growing polylogarithmic cofactor family; the full remainder remains open. Proper-prime-power branches have the separate bound in corner-correlation §1.1. | C | [prime-band-transfer.md](prime-band-transfer.md) |
| `Q-prime-detection-inputs` | ANSWERED | Can we give a locally correct positive comparison sequence, justify the ordinary arithmetic inputs, and prove exactly what one additional estimate would buy? | Yes: the comparison sequence and Type I estimates are derived, and a classical Vaughan decomposition gives S(x)=C2*x+B(x)+O_H(x/log^H x) for every fixed H. A fixed one-sided saving over B>=-C2*x+o(x) implies twins on unbounded scales. This is a fully specified classical reduction, not a new cancellation estimate or proof mechanism. | C | [prime-detection-spec.md](prime-detection-spec.md) |
| `Q-prime-dispersion` | ANSWERED | Can a second moment retaining two right primes control the remaining localized squarefree pilot after its actual conductor and coefficient costs are included? | Yes at this rectangle: aggregation in m=dp before Cauchy gives a logarithmically bounded coefficient on a long interval. The only zero-phase pairs are identical (q,h). Distinct primes give modulus e*q1*q2 with gcd loss at most O(A*Z); completion and Weil bound all off-diagonal terms. The diagonal has exponent 1989/2000 and the largest off-diagonal exponent is 1173/1250 before an arbitrarily small loss. The remaining high-frequency polynomial is O(x^(199/200)); consuming the previous reductions gives R_IJ=O_H(x/log^H x) at D=x^0.277, E=x^0.467. This is a full rectangle at product scale x^0.744, not a uniform product cutoff or a twin lower bound. | C | [prime-dispersion.md](prime-dispersion.md) |
| `Q-prime-power-dispersion` | ANSWERED | Does the repeated-prime structure control the BB contribution beyond its two-norm bound, and can a prime-power moment include every harmonic uniformly? | The decomposition leaves an exceptional coefficient with norm at most sqrt(D) times logarithms; its odd prime-power core has a derived all-harmonic dispersion bound. The same bound for first powers removes the former left-prime cutoff and unpaired diagonal constraint. Two strict inequalities control a region including d~x^0.247, e~x^0.612 at product scale x^0.859. Their product-exponent supremum is 5757/6700, not a uniform product cutoff or a twin lower bound. Exact finite checks run separately from this classical-input derivation. | C | [prime-power-dispersion.md](prime-power-dispersion.md) |
| `Q-prior-art-audit` | PARTIAL | What in this programme is rediscovery, and what might be new? | Rediscovery, prolific and correct, spanning 170 years (Smith 1857 to Tafula 2015); three candidate novelties survived the 2026-08-13 audit and item 1 was cut back on 2026-08-18 by OEIS A144311 (Carter 2008), and several negatives were run in our own wording rather than the owning convention, which is worth little. The 2026-09-06 global smooth majorant uses an explicitly matched prior-art finite-difference mechanism; literature novelty of the complete application is unestablished. | none | [PRIOR-ART.md](PRIOR-ART.md) |
| `Q-prior-art-last-ground` | ANSWERED | Is MathSciNet reachable, and does the two-class upper-bound absence survive a complete title enumeration? | MR Lookup answers author/title/journal/year queries free (bibliographic fields only, no review text or MSC), so SEARCH-CONVENTIONS section 5 needs correcting; the standing sentence survives, since the complete MathSciNet title record for Jacobsthal contains every published upper bound and every one is one class per prime, and Holt's 2022 book is in no bibliographic database. | none | [attack-prior-art-last-ground.md](history/staging/attack-prior-art-last-ground.md) |
| `Q-proposals-prior-art` | ANSWERED | What is the prior-art risk for the six candidates in the paper-proposals registry? | None is clean: three are ADJACENT with the boundary drawn Holt-style (one of them breaking a sentence the corpus rests on), the thinning null is PRIOR ART FOUND under Hawkins' random sieve with the Fold Moment Identity NOT FOUND, and only the reverse-direction Suen import reads NOVEL-SO-FAR; every verdict names what was not searched. | none | [proposals-prior-art.md](history/staging/proposals-prior-art.md) |
| `Q-qc-arch` | ANSWERED | Is the corpus's architecture, ordering and file layout readable by a fresh agent at minimum context cost? | Diagnosis only, no existing file edited: the restructure plan of section 2 was accepted over the shepherd's, and the leading verdict is to leave OBSERVATIONS.md exactly as it is, in place, unsplit and off the reading path, taking out only four inbound citations that name it as the home of something it does not own. | none | [qc-arch.md](history/staging/qc-arch.md) |
| `Q-qc-campaign` | ANSWERED | What did the 2026-08-17 consistency campaign run, find, decide and apply? | The shepherd's ledger: Chris's duplication rule and splitting ruling recorded in his words, the qc framework and the provenance index delivered in wave 1, and every partition's results with the decisions that settled them, including two novelty verdicts flagged as publication-track changes. | none | [qc-CAMPAIGN.md](history/staging/qc-CAMPAIGN.md) |
| `Q-qc-checks-9-10` | ANSWERED | What do the provenance and search-convention gate checks find, and why are they held out of the default gate? | Both are built, calibrated and in the selftest but deliberately behind --pending because they fire on live claims an attack agent is mid-flight against: provenance reads 8 findings and search-convention 75 on the 2026-08-18 corpus, the flip to default is one line, and what could not be mechanised is stated. | none | [qc-checks-9-10.md](history/staging/qc-checks-9-10.md) |
| `Q-qc-compound` | ANSWERED | Which named claims are compounds whose parts carry different calibrations, and how should each be decomposed? | Twelve compounds decomposed and eight examined and left whole, with about 90 corpus sites needing rewording; the test each decomposition must pass is that Proven: <parent> becomes unwritable rather than merely wrong, and the sharpest finding is that natal-cap-28's fully analytic certificate law has no markdown home at all, which is why its status is unfindable. | none | [qc-compound.md](history/staging/qc-compound.md) |
| `Q-qc-history-migration` | ANSWERED | Which body text is history and should move to CHANGELOG.md or history/? | The headline is a negative and it is the most useful thing in the report: no body file is a session record that should move wholesale, so what moves is per-section, and the pass leaves an ORPHANED-CLAIM list of live errors plus per-file findings over all 63 body files. | none | [qc-history.md](history/staging/qc-history.md) |
| `Q-qc-numbers` | ANSWERED | Do two places in the corpus ever give the same number for the same object, and does each remote quotation carry the caveat its home document requires? | 16 findings organised by quantity, led by the rho disagreement between U-FRAME:646 and gate-multiplies:360; diagnosis only, no existing file touched, and arithmetic-per-number is audit-numbers.md's axis rather than this pass's. | none | [qc-numbers.md](history/staging/qc-numbers.md) |
| `Q-qc-papers2` | ANSWERED | Do the paper suite's five doors and four faces restate their research homes correctly? | Fifteen findings in sections 7 and 7A plus a suite sweep: a door resting entirely on a column its own cited file disclaims as invalid, whose corrected computation reverses the reading; a degree-4 certificate credited with a result needing moments through order 6; and the same paper contradicting itself forty lines apart on the anchored calm. | none | [qc-papers2.md](history/staging/qc-papers2.md) |
| `Q-qc-queue-9-10` | ANSWERED | Can the provenance and search-convention queues be cleared without suppressing anything? | TOTAL 84 to 0 with nothing suppressed and every finding resolved in the corpus: all six not in OEIS claims were FALSE, since the G2 ladder is A144311 + 1 and PRIOR-ART.md already recorded the find 270 lines further down; the honest remainder is that five of 75 were resolved by rewording a sentence that was never a literature claim. | none | [qc-queue-9-10-worked.md](history/staging/qc-queue-9-10-worked.md) |
| `Q-qc-refs` | ANSWERED | Are the corpus's external citations and its quotations sound? | Nine dead quotations and eight wrong external citations, the worst being that the corpus sits on the retracted FKMPT constant, an OEIS crossref off by one twice in a document addressed to an OEIS editor, and a false premise ("Kanold, Stevens and Paseman all give exponent 2 + eps") under an open TODO item. | none | [qc-refs.md](history/staging/qc-refs.md) |
| `Q-qc-scope-R` | ANSWERED | Where does the summary layer restate a result with the scope its home document attaches dropped? | Fifteen findings, 2 HIGH, 3 MEDIUM-HIGH, 4 MEDIUM, 6 LOW: one HIGH is a false statement in README.md Status introduced by this campaign's own wave 2, the other is both papers giving a false reason for the X-limitation theorem's scope, and the coverage statement at the end is short and matters. | none | [qc-scope-R.md](history/staging/qc-scope-R.md) |
| `Q-qc-scope-T` | ANSWERED | Does the surface partition R left unswept carry the campaign's dominant defect, a scope dropped in restatement, or a false absence claim? | Fifteen ranked findings plus the TA, TB and TC blocks: a scoreboard still logging the rich vein as the campaign's one unexplained novelty after a same-day follow-up solved it, a fourth copy of the retired sifting limit, and a largest-single-event superlative refuted by the event log it is read from; adjudication only, nothing edited. | none | [qc-scope-T.md](history/staging/qc-scope-T.md) |
| `Q-qc-scripts-S1` | ANSWERED | Do the 37 natal-cap scripts' READINGS blocks hold against their own output and against the documents citing them? | Twenty-six of 37 are consistent and eleven carry a defect, none of them contradicting the summary layer on a status claim: a false promise of a record with no READINGS block, a reading refuted by its own printed output, an absence claim at the site a whole wave read as absolute, and a Miller-Rabin bound wrong by nine orders (3.186e14 for 3.186e23) at three sites. | none | [qc-scripts-S1.md](history/staging/qc-scripts-S1.md) |
| `Q-qc-scripts-S2` | ANSWERED | Do the fold-profile and attack script families say what their own outputs say? | Thirteen defects over 34 scripts and 5,673 lines, five of them HIGH: an untested identification two later scripts had already killed, a printed reading refuted by its own table, a section that has printed only its header since it was written, and a reproduction pointer to a scratchpad that is gone; script-side ones fixed, document-side ones left as evidence, gate 0 on all seven checks. | none | [qc-scripts-S2.md](history/staging/qc-scripts-S2.md) |
| `Q-qc-scripts-S3` | ANSWERED | Do the 57 non-campaign research scripts' banners, embedded OUTPUT blocks and READINGS agree with each other and with the documents citing them? | Defects ranked by consequence, the leading one a3-02-diagonal-f.js carrying the refuted L scanner while naming as its source the sibling that had been repaired underneath it, the two state machines disagreeing at exactly one cell, L(T23, 29) = 3 against the true 2, now fixed; the partition ends with qc.js at 0 on all seven checks and audit-numbers.js 78/78. | none | [qc-scripts-S3.md](history/staging/qc-scripts-S3.md) |
| `Q-qc-shepherd` | ANSWERED | What does the wave-1 shepherd find on the corpus's own structure? | The largest structural defect is that U-FRAME is organised by campaign rather than by claim, with five whole sections of process record sitting in working documents, a PROVEN lemma quoted without the hypothesis that makes it non-vacuous, and three documents disagreeing about how many hypotheses that lemma has; the claim-status register across named objects was not covered and is named as the highest-value remaining axis. | none | [qc-shepherd.md](history/staging/qc-shepherd.md) |
| `Q-qc-slopes-K` | ANSWERED | Are the three fits at slopes 1.062, 1.451 and 1.2992 numerically inconsistent? | There is no numerical inconsistency: the seven tile points are seven of the 42 census points with f agreeing to printed precision, restricting the 42 to the seven's x reproduces 1.062 exactly, and the two estimates are statistically indistinguishable (seven-point 95 per cent interval [0.32, 1.81]); but the corpus's stated reason is wrong, the comb does not explain it, and the coefficient is range-dependent under every specification, so no single slope exists. | none | [qc-slopes-K.md](history/staging/qc-slopes-K.md) |
| `Q-qc-status` | ANSWERED | Is any named object's claimed status inflated, contradicted or misattributed? | Thirteen findings, 12 with replacement text: the worst scope inflation is the Fused-Window Calm Lemma listed as proven when two of its four legs are not, and "the matching lower bound" claims a sharpness the corpus explicitly disclaims; on attribution the corpus is in better shape than the brief assumed. | none | [qc-status.md](history/staging/qc-status.md) |
| `Q-qc-transfers-J` | ANSWERED | Are the thirteen transfers findings real defects or benign restatements? | Adjudicated by word diff with the diff pasted under each finding: 11 KEEP, 2 DEFECT, both in gate-multiplies.md and both one root cause, 0 false positives, and nothing needing compute or a human decision. | none | [qc-transfers-J.md](history/staging/qc-transfers-J.md) |
| `Q-qc-wave6-U` | ANSWERED | Do ATTACKS.md and ATTACKS2.md say what the corpus above them says? | Fifteen findings on 57 lines, led by a campaign verdict awarding theorem-grade to a curve its own home marks MEASURED and Hardy-Littlewood-conditional, the rich vein still logged as an unexplained novelty, and the anchored-window programme called unexplored where a research note and a 34 kB paper exist; six of the fifteen turn on a frozen-record-versus-current-state decision nobody has made. | none | [qc-wave6-U.md](history/staging/qc-wave6-U.md) |
| `Q-qc-wave6-V` | ANSWERED | Do the sixteen fold-profile scripts carry auditable evidence, and what do they show when run? | All sixteen were run and now carry a real OUTPUT block and a numbered READINGS block, each verified by re-running and diffing; eighteen findings follow, the highest being a lemma quoted as proven that is false as written in two documents while three scripts in this partition print the counter-example. | none | [qc-wave6-V.md](history/staging/qc-wave6-V.md) |
| `Q-qc-wave6-W` | ANSWERED | Do the three expensive natal-cap artifacts reproduce? | All three re-run, after the complete @41 march log turned up on disk outside the repo in a place no wave had cited; a three-way tally per file, with the .md disagreements logged rather than edited and the coverage limits stated. | none | [qc-wave6-W.md](history/staging/qc-wave6-W.md) |
| `Q-qc-wave6-Y` | ANSWERED | Do the eight run logs, the three committed .txt outputs and the leaf-note residue say what the corpus above them says? | Findings on all three surfaces, including a stated bound on sup\|R\|/(H*M) that the log's own full-period block violates by 5.6x, an S6 block produced by a function the repo has since flagged wrong while the log stays unflagged, and a false absence claim in G2-STATE that the same document refutes 162 lines later; line numbers were taken against a tree being modified concurrently. | none | [qc-wave6-Y.md](history/staging/qc-wave6-Y.md) |
| `Q-qc-wave6-absence` | ANSWERED | Do the corpus's [ABSENT], [INFERRED] and [UNVERIFIED] markers survive a check against fetched primary sources? | First web-enabled pass, no repository file edited: the exact-terms OEIS absence for the seam count sequence survives on both range conventions but a concept neighbour, A367739, goes unmentioned in the draft's crossrefs, and the note closes with an explicit list of what it could not reach, led by the MathSciNet citation graph of Iwaniec 1978. | none | [qc-wave6-X.md](history/staging/qc-wave6-X.md) |
| `Q-quadpoint-blind-31607-0830` | ANSWERED | Does the zero-parameter depth law y*(Q), stated on the set where T(Q) >= 1 and on both the 1/(2e^gamma) = 0.280730 and the u*omega(u) = 2 (1/u* = 0.280438) forms with and without the finite-size Mertens factor, survive a sealed blind test on the bands past Q = 10007, and can that decade tell the two asymptotes apart? | MEASURED, blind, and it decides nothing asymptotic: on 8363 new anchors 10009 <= Q <= 100003 the 76 sealed rows score 64 HIT and 12 MISS with every MISS on the two naked asymptotes as pre-declared, the two finite-size zero-parameter comparators HIT every row at every band (residual on ln y*/ln h -0.00022 to -0.00002 against C2), K*/pool falls 0.032 -> 0.026 -> 0.020 -> 0.016 -> 0.013 with no bend and a quiet sup, and the band means sit 0.0017 to 0.0037 below both asymptotes, six to twelve times their 0.000291 difference, so which limit the deficit tends to is set by the comparator and not by the data. | Z2 | [blind-0830-quadpoint-31607.md](history/staging/blind-0830-quadpoint-31607.md) |
| `Q-quadpoint-c1c2-0830` | ANSWERED | Does the fourth decade's post-hoc, unsealed preference for the omega-form comparator C2 over the exact-Mertens comparator C1 (C1 above the data by 3.46 and 8.83 se at B11 and B12, C2 within 2.82 se) survive a sealed blind test at the fifth decade, Q in (100003, 316243], and what does that say about which mechanism explains the depth law's drift? | MEASURED, sealed before the run and scored blind on 17702 new anchors, and it decides nothing asymptotic: the sealed D1 row HITs at both B13 and B14 (C1 above the data by 13.33 and 23.82 se, C2 within 1.26 and 1.82 se), so by the sealed rule the omega-at-finite-u crossing of import-rough-anatomy.md §2.1 is CONFIRMED over the exact-Mertens product of u2-engine-depth.md §5 as the depth law's main term at the sampling scale, while both still HIT every ±0.0015 row, the kill rows on C2 all HIT, K*/pool falls 0.013 -> 0.010 -> 0.008 with no bend, and the band means sit 0.0012 to 0.0018 below both asymptotes, so the two constants 0.280438 and 0.280730 stay unseparated by the pre-declared rule and the run separates two mechanisms, not two limits. | Z2 | [blind-0830-quadpoint-c1c2.md](history/staging/blind-0830-quadpoint-c1c2.md) |
| `Q-quadpoint-prior-art` | ANSWERED | In the owning conventions, who holds the rough-pair census, the capture identity and the crossing law, and is any of it ours? | The object and the identity are standard (the dimension-2 twin sifting function plus Buchstab's identity; ADJACENT-STANDARD, no verbatim carrier, no novelty language); only the comparison X(y) < T and the crossing law stay ABSENT-PER-CONVENTION, and the Buchstab correction is 6.6% of the top-band residual, not 2%. | Z2 | [quadpoint-prior-art.md](history/staging/quadpoint-prior-art.md) |
| `Q-quadpoint-transplant` | ANSWERED | Does the anchored-cap family transplanted onto the stretch window S_Q certify every anchor, and what does the depth cost do with height? | Pre-registration for the decade extension, committed ALONE before the segmented producer existed: it fixes the FALL trend line, the registered band readings, the kill rule and a digit-exact calibration gate that must abort before any new figure prints, and states that a falling K*/pool over two decades would still be only a measurement. | Z2, Z1 (retired) | [attack-quadpoint-01.md](history/staging/attack-quadpoint-01.md), [attack-quadpoint-02.md](history/staging/attack-quadpoint-02.md), [quadpoint-decade-prereg.md](history/staging/quadpoint-decade-prereg.md) |
| `Q-quartic-fourth-moment` | PARTIAL | Can the fourth moment of rho-tilde, attack-rhoms-01's named stopping object, be bounded? | Not yet: the genuine quartic correlation is small (OFF/m2^2 measured -0.0454, -0.2767, +0.0101, -0.0446 at z = 13..23), the resonance condition is proved to be a local covering condition, and the whole question transfers by two exact identities onto a Lambda(4) inequality for one explicit cosecant sum whose constant is flat; the new increment rung clears z = 47. | none | [attack-quartic-01.md](history/staging/attack-quartic-01.md) |
| `Q-reachability-coverage` | ANSWERED | Which part of the original divisor domain can no improvement to the grouped moment's nonzero kernel reach, in either orientation, and what would a uniform saving on that kernel actually buy? | For a prescribed fixed exponent margin eta0, the zero budgets leave S_0={p<2eta0,q<2eta0} below that required margin regardless of the nonzero-kernel saving. Uniform gamma=2 covers its complement at that prescribed margin. Smaller positive margins can reach fixed interior points of S_0; only p=q=0 remains at zero budget one for every margin. The proposed eta0~loglog x/log x substitution is not justified by estimates carrying x^epsilon losses; its box count is geometry only. The sufficient twin margin remains OPEN. Independent review F3 and F5 correct the quantifiers and the prime-power tail proof; round-review-0906 corrects the diagonal scope, fixed-margin bulk claim and six-cut separation. | C | [reachability-coverage.md](reachability-coverage.md) |
| `Q-readings-traceability` | ANSWERED | What is the source of each of the 1,592 figures that appear in a script's READINGS and not in its own OUTPUT block? | The running record: nothing in the pass changes a number, 56 mismatches are classified in eight kinds for adjudication elsewhere, and the advisory count rises when the work is done right because a provenance declaration is prose that carries printed values. | none | [readings-traceability.md](history/staging/readings-traceability.md) |
| `Q-rec-cheapest-0830` | PARTIAL | At the cheapest legal point of REC(s, u0), s -> 1+sqrt(e) and u0 -> beta_2, where the saving asked over the triangle inequality is only z^{1.031}, does any of the five dead routes close, does a mixed mean-square-plus-cap strategy close, and is the failure a proof gap or a truth gap? | No route closes and the failing step is yesterday's statement, so PARTIAL on the routes; but the step is located as a TRUTH gap, not a proof gap, asymptotically: the certificate's own value at a CRT-planted doubly-smooth window is cc(r) = -(A1A2 + A1B2 + B1A2) with every term a count of exit chains of the Rosser supports (PROVEN, checked exhaustively at z <= 73), the window bound T <= cc(r) + H - 1 is exact, and the exit-chain count is DERIVED (held) to grow like z^{16s/9 - o(1)} at four primes and z^{2s - o(1)} in the limit, so REC(s, u0) is false for every u0 < 16s/9 = 4.7088 at s -> 1+sqrt(e), the whole legal band (2, beta_2] included, and RML(alpha) with it; at every computable z it is a proof gap (Omega(z) exact to z = 73 reads 251 against z^{u0} = 1.05e6, and a certified lower bound 8.86e17 at z = 5e5 sits a factor 1.2e6 under z^{u0}); no exponent moved. | 0 | [attack-0830-rec-cheapest.md](history/staging/attack-0830-rec-cheapest.md) |
| `Q-recon-0828-covering` | ANSWERED | Does the interval-covering, automated-proof or extremal-combinatorics literature hold a method that bounds the length of an interval covered by two residue classes per prime, or that turns the exact G₂ ladder into a statement at all x? | No route. Fifteen angles examined, fourteen dead on arrival or already closed here; the best interval-covering bound in print is Crittenden-Vanden Eynden's own Lemma 2, which reads 1.02e12 against G₂(79#) = 1710 and is 8181x weaker than the corpus's own 4.2665 sieve bound at the same level; the one survivor, transplanting Costello-Watts's recurrent certificate to two classes, is a computation that certifies finitely many levels and whose analytic half is Erdős #970 at one class. | 0 | [recon-0828-covering.md](history/staging/recon-0828-covering.md) |
| `Q-recon-0828-farfields` | ANSWERED | Do any of the fields still absent from IMPORT-MAP.md hold a theorem whose hypothesis the tile satisfies exactly and whose conclusion is a lower bound on a periodic set's count in every window, a maximal-gap bound for a product-structured periodic set, or a positivity statement at a distinguished point? | No route from any of the sixteen candidates priced; two reach STRONG-ANALOGY or better and CLEAN and both bank only a closure or a wall address, the Fourier one by a one-line non-vanishing proof that empties the Donoho-Stark/Tao/Meshulam family on this object, and Janson's lower tail by saturating at exp(-1/c) >= 0.0805 against the 1/W a position union bound needs, short by 3.6e2 at x = 11 and 2.8e13 at x = 41. | 0 | [recon-0828-farfields.md](history/staging/recon-0828-farfields.md) |
| `Q-recon-0828-jacobsthal` | ANSWERED | Does the 1978-2026 literature on upper bounds for Jacobsthal-type functions and maximal gaps in sieved sets hold anything that lowers G2 or Z2? | No route. Thirteen angles graded, ten dead on arrival (eight already closed in this corpus, two on their own structure), three surviving and none of them lowers an exponent: a kappa=2 extremal candidate built from an exceptional character rather than from Liouville, which can only close the band faster; an unread 1983 Siebert chapter that could already contain it; and one published anchor. Z2 has no non-TPC band at all. | none | [recon-0828-jacobsthal.md](history/staging/recon-0828-jacobsthal.md) |
| `Q-recon-0828-rough` | ANSWERED | Does the 2000-2026 literature on y-rough numbers, sifted sets and short intervals hold any theorem that lowers Z2 or G2, meaning any control on the largest gap or the minimum count of a sifted set in EVERY short interval, or any structure of rough numbers a gap bound could use? | No. Ten angles examined, ten killed for this purpose; the strongest every-interval statement in print for one-class rough numbers is Iwaniec's S(x,y,z) >= (4y/log^2 y)(log(y/z^2) - O(1)) for y >> z^2, uniform in x, giving J(P(z)) << z^2, and it is the linear sieve run exactly at its sifting limit beta_1 = 2 with no slack outside it; no two-class analogue exists in print at any exponent, the corpus's own x^4.2665 is beta_2 by the same mechanism, and every remaining branch of the field (Matomaki-Radziwill, Gorodetsky, Friedlander-Iwaniec Cor 6.28, Gafni-Tao) carries the almost-all quantifier, which a second-moment statement can never convert into a bound on one empty window. | Z2, 0 | [recon-0828-rough.md](history/staging/recon-0828-rough.md) |
| `Q-recon-0828-sieve` | ANSWERED | Is there anything in the 2008-2026 sieve literature, or in the parity-breaking literature, that lowers beta_2 = 4.26645 or supplies a consumer for a level theta > 1 on the two-class comb? | No route. Twenty-one angles examined, nineteen dead on arrival, nothing in print beats 4.26645 at kappa = 2 at any level on four calibrated channels; the two survivors are an owning-convention row and one unresolved hypothesis in a five-page 1990 announcement whose stated requirement beta < 3 excludes beta_2 = 4.26645. | 0, Z2 | [recon-0828-sieve.md](history/staging/recon-0828-sieve.md) |
| `Q-recon-0829-escapes` | ANSWERED | Each of the three killers is an obstruction shape that occurs elsewhere in mathematics; where has each shape been beaten in print, by what mechanism, under what hypothesis, and does that hypothesis hold for the tile and zone objects? | Of nineteen escapes read, fourteen fail a hypothesis check (twelve on a fact already in this corpus), four fail some other way and one (the decoupled vector sieve) stays OPEN as the programme's existing road, so no route opens; Granville-Soundararajan's uncertainty principle is NOT killer 3 in print, is adverse-direction, and is already cited here twice. | 0 | [recon-0829-escapes.md](history/staging/recon-0829-escapes.md) |
| `Q-recon-0829-farfields2` | ANSWERED | Do any of eight fields still absent from IMPORT-MAP.md and from the three 2026-08-28 recon notes hold a theorem whose hypothesis the tile or the zone satisfies exactly and whose conclusion is a lower bound on a periodic set's count in every window, a maximal-gap bound for a product-structured periodic set, or a positivity statement at a distinguished point? | No route from any of the eight; the pass banks one PUBLISHED-ANCHOR (Holt and Rudd's transfer matrix has its full spectrum in print, second eigenvalue a2 = prod_{17<=q<=p}(q-3)/(q-2), printed 0.10206751799779 at p = 999999999989, decaying only like 2.82/ln p, and this corpus's prior-art record names the eigenstructure and the binomial eigenvectors but carries the per-prime eigenvalue (p-j-1)/(p-2) at lit-pdf-holt-rudd.md line 259 but no product-over-primes closed form, no numerical value and no rate), one CLOSURE with mechanism (Beurling-Selberg is the proof device behind the large sieve, whose constant N-1+1/delta is an l2-to-l2 statement and whose error 1/delta exceeds the window at the operative theta_total > 2, so the whole extremal-function family reproduces a row already rejected), and three wall addresses; two angles are TPC-strength at the form that would pay and are labelled (ii). | 0 | [recon-0829-farfields2.md](history/staging/recon-0829-farfields2.md) |
| `Q-recon-0830-rec-killrun` | ANSWERED | Does the literature hold, in its own conventions, a theorem whose hypotheses REC(s, u0) (the sup-versus-rms recovery of the level-D signed remainder over all positions, attack-0829n-rml-proof.md section 3) or the weighted kill-run K*(s) (the longest run of level-s slots the primes in (s, 2s] can kill, attack-0829n-doubling-bridge.md sections 0 and 3) satisfies as stated, or a Maier-type theorem that makes REC false for two-class sifted sets at some u0 below beta_2? | No theorem applies to either object as stated, on four calibrated channels searched in the owning conventions; every neighbour is graded NEAREST with its unmet hypothesis named, and neither object is on any refuted row. On the Maier question the answer is negative for REC as stated (the Maier family bounds the COUNT, i.e. the full-level remainder, never a level-D truncation) but carries one calibration: at one class and full level the REC-shaped inequality is FALSE asymptotically, by Buchstab's origin ratio against the Montgomery-Vaughan full-period variance ceiling, and the embedded arithmetic puts the level where that falsity first shows at log10 z between 16 and 141 depending on u0 and epsilon, so a finite-z margin of the kind the corpus measures cannot see a failure of this type; at two classes the same full-level statement is HL-conditional at u0 = 2 and unlocated in print at any u0. No exponent moved. | 0, D | [recon-0830-rec-killrun.md](history/staging/recon-0830-rec-killrun.md) |
| `Q-recon-0830-smooth-aps` | PARTIAL | Does any theorem on y-friable integers in arithmetic progressions (Granville, Fouvry-Tenenbaum, Soundararajan, Harper, Drappeau, Drappeau-Granville-Shao) supply the uniform o(1) equidistribution that attack-0830-varE-identification.md section 4 leaves open, for moduli up to y^(4/5) with the lam1 weight and the squarefree restriction? | NONE APPLIES AS STATED, and the step stays open; lim Var/E = 0.45546 stays HEURISTIC. Read at the page (eleven sources, arXiv text layers and the Acta Math. page image): every pointwise asymptotic is O(log q / log y)-precise (Granville 1993 Thm 1) or hypothesises log x / log q -> infinity, and every beyond-square-root level (Fouvry-Tenenbaum 1996, Drappeau 2015, Drappeau-Granville-Shao 2017, Pascadi 2023/2025) hypothesises y <= x^delta, i.e. u -> infinity, against our u in (1.2, 2]. NEAREST: Harper arXiv:1208.5992 (2012, a preprint with no journal version found) Theorem 2, the Barban-Davenport-Halberstam form, whose range (log^K x <= y <= x, Q <= Psi/log^A x, bounded u in the ineffective form) covers d up to L^(1/2)/log and whose weight (1 on all friable n, no squarefree restriction, no max over x' <= x) is unmet. The record's quantifier is also refined: the cell needs the lam0-weighted AVERAGE over d, not uniformity. PROVEN given the weighted form (H_w) of that theorem, derivation mine and unreviewed, with its two identities checked numerically in the producer: every two-branch cell of Xmix, both mirror cases, all bands, balanced blocks included, is o(ln^2 y), so the Bettin-Chandee kernel separation is not on this route; the reduction of (H_w) to Harper's theorem is OUTLINED and not written, and the three-branch type (measured -0.0002 at x = 19, trivial bound O(ln^3 y)) is untouched. Not TPC-strength. | 9 | [recon-0830-smooth-aps.md](history/staging/recon-0830-smooth-aps.md) |
| `Q-recon-0904-sifting-limit-floor` | PARTIAL | What is actually known, in the owning convention and at the page, about LOWER bounds on sifting limits at dimension kappa > 1, and is the class-blind cap at beta_2 = 4.26645 a barrier or a method artefact? | Both. The corpus's [ABSENT] is wrong for lower bounds and right for extremal examples: Selberg's Lectures section 17 and Brady's 2017 Corollaries 1 and 3 ARE lower bounds on beta(kappa) at kappa > 1, invisible because Selberg's convention is the reciprocal a_k = 1/beta_kappa so his lower bounds are titled "upper bounds for sifting limits", while no kappa > 1 extremal example exists and Halberstam's own 2003 review says so; the best floor on beta(2) resting on a citation is 1.8394 from Brady's reduction evaluated at kappa = 2, unconditional and below the band, and beta(2) >= 2 follows from monotonicity by a padding argument DERIVED here and probably folklore; the cap at 4.26645 is a METHOD ARTEFACT at rung MEASURED, since the level-D LP is exactly the axiom-only information class and its calibrated floor of 3.3152 sits about 18 per cent below the DHR value and passed, 0 of 15, its first external test against the published beta_3 and beta_4; the band (2, 4.26645] is untouched by anything proven. | 0 | [recon-0904-sifting-limit-floor.md](history/staging/recon-0904-sifting-limit-floor.md) |
| `Q-reconcile-bind` | ANSWERED | Can the unbound script tails be reconciled against their code and then bound by embed.js? | Six producers came back CLEAN-BOUND and one REBOUND with two documented label supersessions and identical results; nothing was DEFERRED and nothing DRIFTED outside the one pre-registered band move, fdecay-band-01's point 35.5 to 33.9 and band [30.8, 42.9] to [29.6, 38.3]. | none | [reconcile-bind.md](history/staging/reconcile-bind.md) |
| `Q-record-deficit` | MIXED (lit-kourbatov-shortfall.md: ANSWERED; record-location-null.md: PARTIAL) | Does the 6.0 percent record-location deficit survive the corrected null, and what is it? | Survives (z = -3.3, five window cuts); Z5's premises on 'location' and on n_eff were wrong; corrected-null formula in §4. | Z5 | [lit-kourbatov-shortfall.md](history/staging/lit-kourbatov-shortfall.md), [record-location-null.md](history/staging/record-location-null.md) |
| `Q-record-mechanism-0830` | PARTIAL | Which of three candidate mechanisms (sub-Poisson gap dispersion, the tile's exact gap law, Kourbatov's k = 1 conspiracy heuristic transported to k = 2) carries the residual 0.78 to 0.97 of Kourbatov's b, at what derived size, and what fraction of b is left? | The residual is carried by the twin-prime gap law AT HEIGHT and by nothing else tried: a new sieve to 1e11 measures that law under-dispersed (CV^2 rising 0.7276 to 0.9295 over seven decades) with a far tail steeper than exponential (log-slope 1.0638 at the top decade), and fed into the record null it carries 95.7 to 99.8 percent of the residual (d b_z = 1.0370 and 1.0806 +- 0.0014 against 1.0833, MEASURED on a model, paired, 2000 replicates); the tile's period-wide law (d b_z = 8.10) and Kourbatov-Wolf's k = 1 bin-count heuristic (4.20) overshoot by 4 to 7x and are closed as posed; the transport of a bare CV^2 is family-dependent (0.62 against 1.06 at CV^2 = 0.93), so "computable from Var/E" is false as stated; Kourbatov-Wolf's second-order scale a_c/abar tracks the measured CV^2 to within 0.04 at every decade with no parameter and is an ansatz, not a derivation; the shape statistic moves a third of the way toward the data (z_D from -1.64 to -0.97); what is left with no derivation is the gap law itself, and the top height band's b (0.937 measured against 1.69 to 1.98 predicted on 17 records) is the open falsifier. | Z5 | [attack-0830-record-mechanism.md](history/staging/attack-0830-record-mechanism.md) |
| `Q-record-null2` | ANSWERED | How much of Kourbatov's shortfall coefficient b does an inhomogeneous-intensity record null carry, how much does a 6Z-latticed null carry, and what is the residual? | The inhomogeneous null carries essentially none of b (d b_z = -0.0012 +- 0.0001, MEASURED); the 6Z lattice's share is LAW-DEPENDENT, +0.1113 +- 0.0003 under the memoryless rounding-up law against -0.0060 +- 0.0003 under rounding to nearest, so the null side is a bracket of 16.1 to 25.1 percent of b and three quarters or more stays a residual with no mechanism; record-location-null.md section 8's argued 1.7e-4 lattice bound is wrong but no single number replaces it; the 15 percent estimator disagreement is pinned as an exact weighting identity; and the shape assumption behind every b reading is measured at 1.6 sigma and stays open. | Z5 | [measure-record-null2-0829.md](history/staging/measure-record-null2-0829.md) |
| `Q-records-placement` | ANSWERED | Do the seven unswept twin-gap records 76-82, above 2^53, land uniformly inside their stretches, or is there square-anchor coupling in record-start placement? | Sealed alone before the producer existed: the uniform band, the fixed definitions, the registered readings, the calibration abort gate and the riders are all fixed here and no placement fraction, q or stretch boundary was evaluated; scored in records-placement-01.md. | Z6 (retired) | [records-placement-01.md](history/staging/records-placement-01.md), [records-placement-02.md](history/staging/records-placement-02.md), [records-placement-prereg.md](history/staging/records-placement-prereg.md) |
| `Q-redteam-0818` | ANSWERED | Do the six headlines of 2026-08-18 survive being checked by someone other than their author? | Four CONFIRMED, two WEAKENED, one REFUTED: the second instrument's independence claim is refuted, the growth law weakens to G2 = x ln^{2+o(1)} x with the o(1) positive, and B is polylog, Brady's Problem 3 and DP1's consumer stand. | none | [redteam-2026-08-18.md](history/staging/redteam-2026-08-18.md) |
| `Q-redteam-0820-empirical` | ANSWERED | Do the two held empirical headlines, perfold-error-model and item-x-offset, survive an adversarial pass before integration? | Both SURVIVE: every decisive statistic reproduced digit-for-digit on independent code, the blind window was re-sieved and re-scored 33/37 with independently re-derived bands, and the cofactor purity claim is certified; two sentences are weakened (the anchor-direction identical is only bounded at 6-10 per cent, and the @31 sigma calibrated claim outruns its controls) and one sentence is refuted as stated. | none | [redteam-0820-empirical.md](history/staging/redteam-0820-empirical.md) |
| `Q-redteam-0820-math` | ANSWERED | Do fekete-1d, smoothness-front and import-hypergraph survive an adversarial pass before integration? | Mostly CONFIRMED, with one REFUTED as stated (import-hypergraph's "the engine can never carry a ln-power" is false for bounded-size edges, though the row's verdict survives for FGKMT-sized edges) and one WEAKENED (the freeze survives, the frozen value does not, under the trusted ladder). | none | [redteam-0820-math.md](history/staging/redteam-0820-math.md) |
| `Q-redteam-0820-night` | ANSWERED | Do the night's two staged headlines, mp-derivation.md and rho-maximal-law.md, survive an adversarial re-derivation before integration? | Both survive: every decisive number reproduced on independent code, the fresh window re-sieved with a different engine reproducing all 37 X, the prereg custody at commit 303711b confirmed with the anchor genuinely fresh, and all 37 sealed (mu, lam) values and all 74 band integers reproduced exactly. | none | [redteam-0820-night-empirical.md](history/staging/redteam-0820-night-empirical.md) |
| `Q-redteam-0820-night-proofs` | ANSWERED | Do the two proof-heavy held headlines of the 0820 night, anchored-01 and hsub-01, survive independent re-derivation? | Both stand: zero refutations and zero corrections to any quoted number, with every digit re-derived from the staircase-note's own lemmas or recomputed from the definitions in independent code; the doubling inequality itself was not attempted and remains posed, open and trap-free. | none | [redteam-0820-night-proofs.md](history/staging/redteam-0820-night-proofs.md) |
| `Q-redteam-0820-structural` | ANSWERED | Do the Mirror-Sweep Lemma and its palindrome, and the advmin@11 = 16 headline, survive an adversarial replay? | Both CONFIRMED on independent re-derivation with zero shared code, advmin@11 = 16 re-proven end to end so that 16 < 34 kills every class-uniform cap; the correction that matters is one quantifier made explicit in the inversion sentence, since a family whose conclusion reads the chosen classes is not capped by 16 at the anchored point, and two precision defects sit in a Thorne citation. | none | [redteam-0820-structural.md](history/staging/redteam-0820-structural.md) |
| `Q-redteam-0821-exponent` | ANSWERED | Do attack-rhoms-01's exponent claim and attack-doubling-01's certificates survive independent re-derivation? | No numerical discrepancy anywhere in either target, every re-derived figure reproducing to the printed digit; the 3.5+o(1) cap survives the attack it was most likely to die to but is not an unconditional bound on G2, and two wordings that run ahead of their custody grades are WEAKENED. | none | [redteam-0821-exponent.md](history/staging/redteam-0821-exponent.md) |
| `Q-redteam-0821-structure` | ANSWERED | Do the W1/HL identity and the anchored-02 ladder survive re-derivation from the definitions on independent code? | Both headlines survive with zero refutations and all ten sub-claims CONFIRMED, carrying two recorded corrections: the -0.33 se figure's sign is presentation-dependent, becoming +0.32 se when duplicate-theta folds are collapsed, and the shadow guarantee is stronger than sold, a one-line theorem rather than a 76/76 empirical. | none | [redteam-0821-structure.md](history/staging/redteam-0821-structure.md) |
| `Q-redteam-0821-wave2` | ANSWERED | Do the three held analytic attacks, b2mean, f4weak and quartic, survive an adversarial re-derivation? | All three survive with every load-bearing number re-derived independently, including four full N_k curves on a different inclusion-exclusion implementation and a c1 column from a freshly fetched OEIS b-file; two sentences are weakened, the cert/C2 widening being non-monotone, and no claim is refuted. | none | [redteam-0821-wave2-analytic.md](history/staging/redteam-0821-wave2-analytic.md), [redteam-0821-wave2-structural.md](history/staging/redteam-0821-wave2-structural.md) |
| `Q-redteam-0828-census` | ANSWERED | Do destroyer-census-01.md, stretch-01.md and records-placement-01.md survive an independent re-derivation of every load-bearing claim, and may they leave HELD? | All three survive on arithmetic, every decisive number reproducing exactly on an independent engine; one sealed reading (records READ-3) is REFUTED as vacuous and four sentences need correcting before integration. | Z0, Z4, Z6 (retired) | [redteam-0828-census.md](history/staging/redteam-0828-census.md) |
| `Q-redteam-0828-closures` | ANSWERED | Do the five 2026-08-28 closure notes stand, and do they stand for the reasons they give? | Three stand on corrected sentences (1d, Z5b, 0); one stands in half (10, the 1.074 counter-claim does not); one does not stand for its stated reason (1c, closed on a narrower window than the prior work's significant one, and its CLOSED has overwritten a PARTIAL in the generated index). | 10 (retired), 1c (retired), 1d, Z5b (retired), 0 | [redteam-0828-closures.md](history/staging/redteam-0828-closures.md) |
| `Q-redteam-0828-engine` | ANSWERED | Do the five 2026-08-28 certificate-engine notes survive an adversarial re-derivation, and does the one-class freshness factor correction hold before it reaches a live document? | The one-class factor holds and is stronger than either note states; four numbers are refuted (first s>=10.82 is x=263 not 239, first non-empty kappa=1 level is @37 not @53, rho*g_max is off by one gap, the @17 certified share and per-term constant carry the wrong convention) and one proof step needs the max-over-y form of BV; the cluster's shared verdict stands. | 11 (retired), 8 | [redteam-0828-engine.md](history/staging/redteam-0828-engine.md) |
| `Q-redteam-0828-head` | ANSWERED | Do the three 2026-08-28 head-residual notes survive an adversarial re-derivation of every load-bearing claim on independent code? | Mostly yes on the numbers and no on two framings: "h/R -> 1 iff beta CV^2 -> 2" is REFUTED (the limit needs only boundedness, the product controls the RATE), and 9 to 59 percent of the quoted h - R is the choice of comparator, since R is the continuum functional and a discrete uniform origin sees R + 1/2 exactly. | Z4 | [redteam-0828-head.md](history/staging/redteam-0828-head.md) |
| `Q-redteam-0828-litimports` | ANSWERED | Do the six notes of 2026-08-28 survive an adversarial pass, and which of their load-bearing claims are wrong? | Every measured number reproduces on independent code; Saffari-Vaughan Theorem 10's range exponent is 6/11 not 1/11, which voids import-fracparts's one banked THEOREM at fixed M and corrects row 15 twice; four further weakenings, one refuted verdict line, no note refuted whole. | Z5, 4 (retired) | [redteam-0828-litimports.md](history/staging/redteam-0828-litimports.md) |
| `Q-redteam-0828-quadpoint` | ANSWERED | Do the four HELD quadpoint notes of 2026-08-22 survive an adversarial pass: the capture identity's proof line by line, the depth law and its asymptote, the sealed prereg scoring, and the prior-art citations at page level? | The identity is PROVEN once its window convention is written down and holds at every K of 50 anchors under an independent implementation; four load-bearing sentences are wrong (section 4's gloss on Sum capU, v1 section 2's limit, the prior-art note's 2%, and the note's unconditional y* sentences), and none of the four defects opens or closes a route. | Z0, Z2 | [redteam-0828-quadpoint.md](history/staging/redteam-0828-quadpoint.md) |
| `Q-redteam-0828-varE` | ANSWERED | Does the 2026-08-28 chain from the exact comb variance to lim Var/E = Pr[GD(2) > 2] = 0.45546 survive an adversarial re-derivation, and does the refutation of the 0.611 reading hold? | The constant survives at HEURISTIC and the 0.611 refutation is CONFIRMED and strengthened (the frozen out-of-sample half of the protocol also fails on the control); the correction is that TWO steps are open, not one, and that the theta=1 branch is an exact identity with a read theorem rather than a second-hand numerical match. | 9 | [redteam-0828-varE.md](history/staging/redteam-0828-varE.md) |
| `Q-redteam-0829-measure-a` | ANSWERED | Do the three held measurement notes of 2026-08-29 (g2z2, g2-generic, provenance/x37) survive an independent re-derivation of every load-bearing claim, a custody and pre-registration audit, and a label audit against the wrong-direction scheme? | 96 load-bearing claims checked, 88 CONFIRMED on independent code or by hand, 7 WEAKENED, 1 REFUTED; the one refutation is a label, not a result: the g2z2 note's M2 and its producer's printed block both call 4.177e-1 the summed Poisson probability of a two-pair zone over p >= 3, while the code sums every decade including p = 2, whose single contribution is 2.6586e-1, so the true p >= 3 figure is 1.518e-1 and the MISS verdict is unchanged; no pre-registration in any of the three shows any sign of a prediction edited after its run, and birth-time evidence puts the note file before the producer file in two of the three, with the generic producer's inode anomalous and its claimed timestamps uncorroborated. | none | [redteam-0829-measure-a.md](history/staging/redteam-0829-measure-a.md) |
| `Q-redteam-0829-measure-b` | ANSWERED | Do the three 2026-08-29 HELD measurement notes (measure-roughpair-null-0829, measure-record-null2-0829, zone-tail-02-0829) survive independent re-derivation of their load-bearing claims, their custody and pre-registration integrity, their (i)/(ii)/(iii) labels, and their proposed edits to other documents? | 59 load-bearing claims checked, 44 CONFIRMED, 13 WEAKENED, 2 REFUTED, no data defect found and all three producers bit-honest under embed --check; the worst finding is custody clerical rather than numerical, measure-roughpair-null-0829.md:161 quoting code-sha256 4813584b against the producer's banner 5caaa5173b4c1561, a hand-transcribed hash that does not bind the artefact it names; the second is zone-tail-02's scope claim that every head bootstrap in the corpus is three times too narrow, REFUTED as written because destroyer-census-01.md publishes no bootstrap at all and head-residual-factor.js bootstraps over gaps rather than zones, while the defect itself is CONFIRMED on an independent engine (1,910 distinct a_first among 17,700 top-band zones reproduced exactly) and is LARGER than stated, a cluster bootstrap giving an inflation factor of 4.10 against the note's implied 3.04; measure-record-null2's exact cov identity reproduces to 1.4e-15 from the OEIS ladder and its lattice arithmetic reproduces at every row, but its headline "wrong by about three orders in b units" is unit-inconsistent and contradicts its own section 3e's "about one order below the effect"; no pre-registration shows any sign of post-run editing and none of the three can be shown NOT to have been, because all three preregs live inside note files whose mtimes necessarily postdate their producers'. | none | [redteam-0829-measure-b.md](history/staging/redteam-0829-measure-b.md) |
| `Q-redteam-0829-measure-c` | ANSWERED | Do the load-bearing claims of measure-tail-deficit-0829.md, lit-scourfield-2008.md, recon-0829-farfields2.md and recon-0829-escapes.md survive independent re-derivation at the record, and are their custody, prereg, provenance and (i)/(ii)/(iii) labels intact? | No verdict of the four notes is overturned; of 61 load-bearing claims 38 CONFIRMED, 14 WEAKENED, 6 REFUTED, 3 UNVERIFIED. Worst: lit-scourfield-2008.md line 79 quotes lit-smooth-divisors.md section 6 as saying the convention has "no asymptotic machinery in this range at all", a string absent from the repository and contradicted by that section's own words, and uses it to justify a correction; measure-tail-deficit-0829.md section 2 describes a superseded embed and does not disclose the --force the header records, although embed.js --check passes on all three hashes; and note 1's reported M-P1 failure at 19 -> 23 is a single-draw artefact, reversed here on 40 draws (shuffled 296.1 sd 29.1, Markov 264.0 sd 18.4, share 34.9 percent inside the registered band). Note 2's precision correction inverts a quantifier, the open step needing o(1/ln y) against Scourfield's O(1/log x); note 3's corpus does hold the per-prime eigenvalue at lit-pdf-holt-rudd.md line 259; note 3's section 3c re-prices a family already resident as the Vaaler completion of its own Lemma V remainder. Every verdict, and most of the arithmetic, otherwise reproduces on an independently written engine. | none | [redteam-0829-measure-c.md](history/staging/redteam-0829-measure-c.md) |
| `Q-redteam-0829-objects-gb` | ANSWERED | Does every load-bearing claim of the two 2026-08-29 object reads (G2 and the bridge) survive independent re-derivation at the cited record? | 60 load-bearing claims re-derived at the record: 47 CONFIRMED, 8 WEAKENED, 1 REFUTED, 4 left UNCHECKED and marked so; the refutation is the G2 note's L5 formula, which pairs the corrected trusted zone K in [1.3946, 11.3568) with the superseded single-base expression (ln 66 + K)/ln 16, an expression that evaluates to 5.607 above beta2 at the top of its own stated range, and the three live-layer edits already applied by the orchestrator are correct as written. | none | [redteam-0829-objects-gb.md](history/staging/redteam-0829-objects-gb.md) |
| `Q-redteam-0829-objects-zm` | ANSWERED | Do the load-bearing claims of z2-state-draft-0829.md and object-models-read-0829.md survive independent re-derivation at the record, and is the Z2 draft fit to become research/Z2-STATE.md? | 96 load-bearing claims re-derived at the record, 84 CONFIRMED and 11 WEAKENED and 1 REFUTED; the one refutation is a custody label, since the Z2 draft grades as unstamped hand arithmetic a table that sits in an embedded producer's OUTPUT block, and the draft is fit to become Z2-STATE only after eight named line fixes. | none | [redteam-0829-objects-zm.md](history/staging/redteam-0829-objects-zm.md) |
| `Q-redteam-0829-theorem1` | ANSWERED | Is Theorem 1 of attack-AB-bounded.md (B <= 9 A(z)^2 (E(z)-1) = O((log z)^8)) a theorem, and at what rung does the corpus carry it? | PROVEN, and the scope now covers the whole chain: the L1 to L5 mean-square derivation and Theorem 1's bound on B are each re-derived here with no hypothesis, so <R^2>_H <= 9 A(z)^2 (E(z)-1) H holds for every z, s and H as a mean over one period, the record's [INFERRED] is an under-grade, and the live layer's "published as Opera de Cribro 6.18" is wrong on two counts and must be replaced. | none | [redteam-0829-theorem1.md](history/staging/redteam-0829-theorem1.md) |
| `Q-redteam-0830-doubling` | ANSWERED | Do attack-0829n-doubling-bridge.md and attack-0830-doubling-killrun.md survive an adversarial re-derivation on an engine sharing nothing with their producers, and do REFUTED rows 94 and 98 stand as worded? | The mathematics survives: the maxsum certificate Ghat(2s) <= maxsum_{K*+1}(T_s) and the product composition K*+1 <= prod(1+L_j) are each re-derived here and hold, the second at 21,641,346 nesting links over 6,012,804 killed runs with zero failures including the zero-kill fold, and every quoted figure reproduces digit for digit on a fresh engine (K*(16) = 17; G2(31#) = 348 @ 8813641451 x4 from both base tiles; sup msc 6.6364; the diagonal cells; the 2^N ratios 1.226/1.481/41.348). Row 94 STANDS and is if anything under-claimed, but its attribution is wrong in one direction: Lemma 1 at s = 128 alone clears the whole band, so the s = 16 walk corroborates rather than carries it. One statement is falsified: the bridge note's NOT-REACHED line puts 19#->37# out of reach, but column-major it returns here, reproducing the ladder row x = 37 and adding a FIFTEENTH step at s = 19, 20 (K* = 13, N = 4, C2 3.5200, certificate 3.8000), so the enumerable range ends at s = 20, not s = 18. Row 98 STANDS on its mathematics and is WEAKENED on one clause: "the truth sits under it everywhere (sup w/a = 0.8295)" attaches the CERTIFICATE's ratio to the word truth; the truth's sup is 0.6591. | D | [redteam-0830-doubling.md](history/staging/redteam-0830-doubling.md) |
| `Q-redteam-0830-engine` | ANSWERED | Do attack-0830-buchstab-deep.md, attack-0830-comb-tail.md and attack-0830-anchored-ladder-17.md survive an adversarial re-derivation on code that shares nothing with their producers, and does REFUTED row 97 stand as worded? | Every headline number in the three notes reproduces exactly on independent code (26 of 26 comparisons, including F2/f2 = 3.6682 at sigma = 4.7088 by a near-analytic route, the 0-of-1512930 pair count, the tail defect at five levels, the full 419328-term Legendre split, and the whole @23 anchored ladder including K* = 27, floorU = 5364, truth 597475 and the minimal pool 1543 proven exact); one load-bearing DERIVATION is REFUTED — "\|B - 1\| >= c forces sigma(q) < u_c - 1" fails at @23 on 21134 (q, K) pairs for the engine's model B at c = 0.1 and on 33875 high-count pairs for the measured B at c = 0.01, because the step bounds every u in a weighted average by the largest one and treats the denominator as e^-gamma, so the "level-free" clause of buchstab-deep section 4 and REFUTED row 97's "\|B - 1\| >= 0.01 forces sigma < 1.798" must be re-graded from DERIVED to MEASURED-at-@23 (where the conclusion survives: the worst sigma is 2.159, still far below beta2 = 4.26645); row 97's "the best sigma any level has" is separately WEAKENED, since @29's head sigma is 5.5785 with width 1.5325 and @97's is 17.1422 with width 1.0000; comb-tail derives its main-term factor from prod (1 - 1/q_i) and measures it against prod (1 - 1/(q_i - 1)), which is what natal-cap-28 line 283 computes against its own line 20 and against certificate-engine.md section 1, a 0.9% difference at @23 that moves nothing certified; comb-tail also misquotes its own cited source as F1 in [1.5, 4] where that source says [1.5, 3] and says there is no bound at all at s < 1; four smaller slips are listed and none opens or closes a route. | 8, A | [redteam-0830-engine.md](history/staging/redteam-0830-engine.md) |
| `Q-redteam-0830-fekete` | ANSWERED | Do the load-bearing claims of attack-0829n-hsubpow-K.md (the sign lemma, the K -> beta_bound map, the zone, the TODO.md base-16 correction) and measure-0830-delta-reader.md (the six pre-registered readers, their kill gates, the joint fit's calibration, the RB circularity argument) survive independent re-derivation, and are the two live-doc corrections they caused the right sentences? | Every number in both notes reproduces on independently written code (all 14 cells of the beta_bound / K_min table, all 48 cells of the reader-calibration table, all 24 figures of the real-control table, the margins, the sups, the 5.607 correction, the 10-of-81 count), and the sign lemma is re-proven as stated for continuous exact laws. Two claims are WEAKENED and one live-doc sentence needs a qualifier: the sign lemma's constant 1.0597 loses 43% of its value if the base floor moves from 2 to 3 and its whole shape fails for the stepped law that a primorial ladder must present, where beta re-enters the sup and a delta = 0 law already needs K = 1.37 at beta = 2, inside the trap; and TODO.md 1d's "the sign of delta is unreadable for G2 at reach 79 by any instrument tried" is wrong on the letter, since reader RB passed all four pre-registered criteria and read delta_hat = +0.80 +- 0.09, the note voiding it post-hoc on a circularity the pre-registration flagged but did not make a kill criterion; the honest sentence adds "non-circular". No claim in either note is refuted. | 1d | [redteam-0830-fekete.md](history/staging/redteam-0830-fekete.md) |
| `Q-redteam-0830-floor-growth` | ANSWERED | Does the DERIVED growth half of attack-0830-rec-cheapest.md sec.4.2 (Omega >> z^{16s/9}/ln^8 z from four-prime Rosser exit chains) survive an adversarial re-derivation on independent code, does it really make REC(s, u0) false for every u0 < 16s/9, and does the blind slope test of blind-0830-omega-floor.md test the LAW or the CONSTRUCTION? | No break found in six attacks, so the growth half SURVIVES this pass and stays DERIVED (one failed break is not a proof, and the whole thing still rests on the exact half E1-E3 that this pass did not grade); but four claims are corrected - the threshold 16s/9 needs the unstated hypothesis s <= 3 (above it the four-prime LP maximum is 2(2s+2)/3, then 8, both below 16s/9, though the corollary that every legal u0 < beta_2 fails survives at every admissible s because 2 x LP-max > beta_2 for all s > 9beta_2/16 = 2.3999), the 2s - o(1) limit needs 3^k <= ln D / ln 8 so only k = 2 is available at every z below 1.1e9, A_i is >= not ~ the dyadic count, and the certified ratio does NOT rise monotonically (0.0118, 0.0128, 0.0101, 0.0057, 0.0051, 0.0093, 0.0336, 0.0801, 0.1658, 0.3545 on my own recount, which reproduces all ten S4b rows digit for digit); the blind test is ruled a test of the CONSTRUCTION's count and not of the law, since it cannot see E1-E3 or the CRT step; on the ruling Chris asked for, the floor does make the RML route a truth gap asymptotically and conditionally on E1-E4, and changes nothing computable, the literal construction first passing H = z^{u0} at z ~ 5.6e31 on the constant 2.93e-4 measured here; no exponent moved. | 0 | [redteam-0830-floor-growth.md](history/staging/redteam-0830-floor-growth.md) |
| `Q-redteam-0830-floor-sign` | ANSWERED | Does the EXACT half of attack-0830-rec-cheapest.md sec.4 (E1-E4, the sign facts, the window bound T <= cc(r) + H - 1, the exact Omega, and sec.(d)/(e)'s calibration sentences) survive an adversarial re-derivation on independent code, and does it by itself constrain REC at any u0 without the growth law? | The mathematics STANDS as PROVEN and is stronger in two places than the note claims, but it constrains REC at NO u0 by itself: E3's identity is pure algebra and holds at every position (0 mismatches in 20.5M positions, both s), E2 holds at every divisor n > 1 under three disjoint routes at every s >= 1 and FAILS at s = 0.8, locating a hypothesis D >= z the note omits, E4 has 0 violations at every x over four complete periods with the wrap, and Omega is reproduced by an independent enumeration at all 26 tabled values and EXTENDED to z = 101 (285, 441, 684, 990, 1155 at z = 79, 83, 89, 97, 101), confirming blind-0830's exact 684 and 1155; three sentences are wrong -- E1's "every pair with gcd \| 2 is realised" (exactly half are; the missing half is all those with 2 dividing one side), the ledger's and sec.0's "251 against z^{u0} = 1.05e6" (1.05e6 is HM, z^{u0} = 7.19e7, so the gap is understated 68.3x), and sec.4.4's reason for lam+(P(z)) = 0 (0.24 exceeds 1/8; the figure that closes the slab is 0.1199 at z = 89, under 1/8 by 4 percent) -- and sup\|rho~\| >= (Omega - M)/2 is loose: sup\|R_1\| = Omega + M exactly. Every exactly known log_z Omega is under 2 while REC needs it above u0 > 2, so the exact half touches REC at no u0 and every adverse consequence in the note still rests entirely on the growth half. No exponent moves. | 0 | [redteam-0830-floor-sign.md](history/staging/redteam-0830-floor-sign.md) |
| `Q-redteam-0830-imports` | ANSWERED | Do the six lighter notes of 2026-08-30 (varE-identification, smooth-aps, rec-killrun, skeleton-door, at43-bigint, coherence) survive an adversarial pass on independent code and at the source pages, and which of their load-bearing claims are wrong? | No note is refuted whole and no exponent moves. Every decisive measurement reproduces on code sharing nothing with the producers: the varE mixed remainder and its 0.844 / 0.826 share below 2L and 94.4 / 98.7 percent unbalanced share at x = 13, 17; the Buchstab deviations and all three crossing levels log10 z* = 33.53, 68.80, 33.62; the skeleton door's 9.2 / -0.9 percent, G30_agg 0.1113 / 0.1011 and the 0.0102 cap at @13, @17, by a path that also verifies cap-36 Theorem A; the @43 parity exactness on all 26,157,448 scour classes with 0 above 2^54 and a constructed @47 counterexample; and the five recon-0828 verdict counts summing to 75, which REFUTES rec-killrun's brief-error clause and confirms the orchestrator's rider. Seven claims WEAKEN. The load-bearing one is smooth-aps's "the weight is unmet in print": Harper's J. London Math. Soc. 112 (2025) e70293 proves a Barban-Davenport-Halberstam asymptotic for an ARBITRARY sequence on exactly that dyadic all-classes object, and his own footnote says the missing max over x' can be incorporated, so the NEAREST citation changes even though the step still does not close (the 2025 range is sqrt(2x) < Q <= x and its Theorem 2 route bars sieved sets by name). Also: Henriot Corollary 2 applies, but to the ERRATUM's statement and under two hypotheses the note leaves unstated (eps < alpha/600, not "every eps"; F at prime powers); varE section 4's display (*) carries an unfilled placeholder and is vacuous by a factor L/d; the skeleton door's "would tighten" is wrong in sign at @17, where the closable block is negative and removing it RAISES G30_agg to 0.1020; Halasz-Montgomery is not applicable for the reason given (it is an abstract inner-product inequality); FGKT's heuristic quote is on p. 4, not p. 3; and the "~13x had no source" is a corpus miss, the retired G2-walk figure at CHANGELOG.md:5716. Not TPC-strength; nothing here opens a route. | 9, 0, D, 1 | [redteam-0830-imports.md](history/staging/redteam-0830-imports.md) |
| `Q-redteam-0830-records` | ANSWERED | Do attack-0829n-parity-dstar.md (CLOSED, HELD) and attack-0830-record-mechanism.md (PARTIAL, HELD) survive an adversarial pass on independent code, does REFUTED row 95 stand as worded, and is TODO Z5's new title supported? | Both notes' measurements reproduce on independent code and neither headline is refuted: D* is confirmed EXACTLY, by a BigInt rational simplex written here, at 299 of 376 anchors with 0 contradictions (the other 77 exceed the exact solver's size cap), the old range's 172-figure gate is re-derived exactly at all 43 anchors with 0 disagreements, and an independent 30-wheel sieve to 1e11 reproduces note (b)'s seven decade gap counts, CV^2 and far-tail slopes to every printed digit, with the counts also matching the published pi_2(10^k). Four sentences are wrong or over-stated and are replaced here: REFUTED row 95, note (a)'s ledger, its section 6 and TODO Z5 all attribute the null's 0.025 agreement to the WIDTH law when 0.025 is the ln Q slope difference (the width-slope difference on the same 84 matched anchors is 0.031); note (a) section 3's "the threshold sits in a gap of at least 0.25 at every anchor" is scoped in its own producer to the true arm and the null arm's exact gap is 0.1212; P6's HIT rests entirely on the decade-2 collapse that section 5 discounts as a sampler artefact when it discounts kill clause (a); and note (b)'s "d b_z = 1.0806 +- 0.0014" carries only the Monte Carlo pairing error, while moving the far-tail slope by 0.02 (against a spread of 0.0174 across six fit windows on the same decade and 0.1196 across decades) moves d b_z from 0.9888 to 1.1720, and continuing the law at slope 1 above the last resolved point still gives 0.7752. REFUTED row 95's CLOSED verdict stands on kill clause (b), which is better powered than the note presents it (paired s.e. 0.0401 against a 0.15 band), and the row needs two clauses reworded; TODO Z5's title is supported for "measured and not derived", and the resolved part of the law carries 72 per cent of the residual on its own with the extrapolation carrying the rest. | Z2, Z5 | [redteam-0830-records.md](history/staging/redteam-0830-records.md) |
| `Q-redteam-0830-rml` | ANSWERED | Do the three HELD notes of 2026-08-29 night and 2026-08-30 on the RML chain survive an adversarial pass — the six-arrow chain and the term-count cap lemma of attack-0829n-rml-proof.md, the same-object ruling and the applied replacement sentences of verify-0830-usup-convention.md, and the reflection identity, custody, pilot bounds and sealed forecast of measure-0830-rho-sup-z41.md? | The three load-bearing PROVEN claims survive independent re-derivation — the CAP lemma (every step, sine sum at worst ratio 0.585568, the constant 6, 0 per-modulus violations at z = 13, 17), the reflection identity rho~(W-3-y) = -rho~(y) (proved here and its two hypotheses verified at z = 13..37, residual <= 1.7e-10 at every position of z = 13, 17, 19), and the same-object ruling (an independent lattice reproduces the repository's term multiset exactly at z = 13..37 and its {Vabs > 0} set equals LSE's records at all ten levels); five of the seven cited exact sups and three of the five walked sup\|R_H3\| reproduce to <= 5.0e-7, and every figure of the sealed z = 41 forecast reproduces from the seven cited sups alone. Fourteen claims do not survive, none of them reopening a route. The load-bearing one is RML sec.2's ms_m/ask column: it measures the PROVEN mean-square BOUND sqrt(B H), not the <R_H^2>^{1/2} that REC names, the two differing by 36.53x to 200.45x on the tabled rows because <R_H^2> saturates in H while B H does not, so sec.5's ordering (ask below the Gaussian factor at u0 = 3.0 and 3.5) is an artifact and reverses at every row against the true mean square. "gauss -> 0" (sec.5) and "sup/rms <= sqrt(2 lnW) O(1) = z^{o(1)}" (sec.3) are the same error twice, against the note's own sec.0: sqrt(2 ln W) = z^{1/2+o(1)}, measured gauss 0.7905 at z = 19 falling to 0.5645 at z = 1e7, limit 1/2. "the recovery exponent is log_z(2 sup\|rho~\|/rms): about 0.99-1.29" quotes the truth column, which is log_z(2 sup\|rho~\|) alone; the quantity named measures 0.5628 to 0.6712. "REC would be moot rather than false" should read false. "u_cap -> 2s + o(1)" and "n ~ z^{2s}/polylog" are asserted where only "<=" is proven and the data cannot decide: u_cap is 4.2652 at z = 47, crosses beta_2 only at z = 53, reaches 4.4891 at z = 79, and passes u_triv from z = 53. "seven points spanning less than one octave" is 1.509 octaves, still uncorrected in three places including the ledger verdict. verify-0830's applied "polynomially many from z = 223 on" is true at every z >= 13, and its z = 331 crossover silently sets A = 1 (A fitted to LSE's own Ssat moves it to 337). No exponent moves, no route opens or closes, and no ledger verdict changes. | 0 | [redteam-0830-rml.md](history/staging/redteam-0830-rml.md) |
| `Q-redteam-0830-slack` | ANSWERED | Do attack-0830-head-remainder.md, attack-0830-tail-derivation.md and verify-0830-record-defects.md survive an adversarial re-derivation on independent code, and do the five riders the verification put on live notes stand as written? | Arithmetically they survive: every figure of the three notes that this pass could recompute reproduced to the printed digit on code written from the definitions, 0 assertion failures over 58 assertion call sites (most inside per-level loops), including every figure of the verification's three claims and the half-decade Delta_HL it quoted rather than recomputed. Four sentences do not survive. (1) verify-0830-record-defects.md:316, a replacement queued for head-residual-hl3.md sec.0, says the pooled value sits "0.038 to 0.052 below the sub-window mean at all three decades"; measured, the two lower decades run to 0.076 and 0.066, and the same note's own falsifier row says 0.038 to 0.076, so the wrong half is the one queued to land. (2) verify-0830-record-defects.md:379's un-measured "+0.005" residual inside the eighths is +0.0004 measured at sixteenths, so the de-pooled top-decade value is converged and the caution can be dropped. (3) the ruling that the class null is "the matched figure" for the tail is matched on residue class only: p'^2 is coprime to every q <= p', and the ensemble's rough-class offset is E_rc - R = 5.6714 -> 7.5357 over x = 7..29 against the class null's 5.6000 -> 6.0336, giving t/(R_shell + 7.5357) = 1.0123 against t/classNull = 1.0157. (4) attack-0830-head-remainder.md sec.3's top row is not gap-scale matched: E[g] 244.0 against 235.9, y_match capped at 19997, and on the note's own six ensemble points Delta_ens ~ E[g]^-0.312, so meas/ens reads 0.9640 not 0.9539 and the headline "0.954 to 0.995" reads 0.964 to 0.995. Three levels the notes recorded as out of reach are run here: the X2 group at x = 23, the tile identities and conditionals at x = 29, and the ensemble ladder at y = 29 (pipe/ens 0.9535, 40 s, against the head note's "about fifteen minutes"). No route opens or closes and nothing here touches Z2. | Z4, 9 | [redteam-0830-slack.md](history/staging/redteam-0830-slack.md) |
| `Q-redteam-0830-zone` | ANSWERED | Do attack-0829n-X-upper.md, blind-0830-quadpoint-31607.md and blind-0830-quadpoint-c1c2.md survive an adversarial re-derivation and an independent re-implementation of their producers, and at what rung does the corpus carry each of their headline claims? | They survive on the numbers and mostly on the wording. On independent code every band sum, tier ratio, sealed forecast, band statistic and z of all three notes reproduces to the printed digit (X-upper 7.82 to 10.13 and the flat 378100.0; the fourth decade's 76 rows at 64 HIT and 12 MISS with the same twelve MISSes; the fifth decade's class A at both bands), and three attacks failed to break them (the paired-se attack on the D rows, a search for a fitted constant in C1, and gap-selection at the band edges). Four defects stand: the X-upper note's "s_max 1.81 to 1.96" is wrong in its own arrow convention, which means B3 to B8, since s_max peaks at B4 and reads 1.85 at B8; the c1c2 note's OLD R2 row at B14 is a boundary call that my 1-in-8 subsample scores the other way; the c1c2 note's custody line "three tails, one code-sha256" is a tautology of tailfmt.js and is not evidence of a seal; and the unscored y* check carries a Jensen bias of about +0.44 in y, which is the whole size of the C2 gap it is read as corroborating. Nothing here moves 4.2665 to 2, no rung rises, and all three notes stay HELD. | Z2 | [redteam-0830-zone.md](history/staging/redteam-0830-zone.md) |
| `Q-redteam-0904-argmax` | ANSWERED | Does measure-0904-argmax.md survive an adversarial re-derivation of its positions, its congruence null, its residue chi-square and its own pre-registration scoring? | Every positional number in the note reproduces exactly on an independent fold-replication engine at x = 11..31, including the argmax lists, m(x), the top-K sizes and components, the per-prime pair counts, the tail counts and the F6 drops, so the note's data survive. What does not survive is three things and the largest is the null: two random TWIN SLOTS are congruent modulo W/p with probability (p-3)/(D-1), not 1/M, so the note's "10^6 to 10^8 times the uniform null" is inflated by 6.9 to 29.1 at these levels and should read 10^4 to 10^6, and the statistic is not a random variable at all but a deterministic function of each window (translate lemma, proven here and checked against every argmax pair count), which makes a null ratio a category error rather than a small correction; the note's own "58 to 82 per cent are translates of another" reports K - components when its wording needs K - isolated, which is 83 to 98 per cent; and the custody table in §2 quotes a code-sha256 (3019147f...) that the producer does not carry (d53a3fd1...), while §2's body and §5(5) still describe a widths annotation the rider says was already deleted. The scoring is faithful in verdict and wrong in arithmetic: F3 and F7 are scored at four levels, not five, so F7's falsifier fired at three scored levels and F3's tally is 2 of 4; the brief's "three of eight" does not exist on disk, both the ledger and §0 say four, and four is right. The exponent is untouched and nothing here is a route. | none | [redteam-0904-argmax.md](history/staging/redteam-0904-argmax.md) |
| `Q-redteam-0904-floor-growth-2` | ANSWERED | Does the growth half of the adverse pointwise floor (Omega >> z^{16s/9}/ln^8 z from four-prime Rosser exit chains) survive a SECOND adversarial pass, and does a floor on the certificate at a CRT-planted window make REC(s,u0) false (a truth gap) or only unprovable by that certificate (a proof gap)? | SURVIVES, at the same rung and no higher: four new attacks and two unasked ones found no break, so the growth half stays DERIVED and red-teamed twice, which is two failed breaks on a derivation and not a proof; the proof-gap reading is REFUTED because REC is a statement about R_H, the remainder of the very certificate the floor bounds below, and the chain has no step where a certificate value must become a true remainder, so it is a truth gap for REC as the corpus states it; five corrections are owed to the record -- the REFUTED row is UNSCOPED and should read "on the Rosser vector-sieve lattice at equal levels" since only the Rosser instance is derived, the "falsity beyond z ~ 5.6e31" is an s = 2.698721 figure quoted without its s and the fitted crossing at the corpus's own measured family s = 3.0 is z ~ 10^15.3, the analytic p* window (4D^{1/27}, D^{1/9}/4) is neither necessary nor sufficient at reachable levels so the exact onset is 4.42e5 at s = 3.0 rather than the quoted 1.055e6, the four-prime construction has NO exit prime below z once s >= 7 so the first pass's "8 beyond s = 5" holds only on [5,7), and the first pass's escape-(a) density 1/W understates the planted class by the factor W/(n1n2) though the escape still fails by an exponential; the LP maximum 8s/9 is confirmed as an exact vertex and the corollary crossing reproduces 9beta2/16 to 4.4e-16, the pre-registered slope band held at a new s (top step 4.9025 at s = 3.0 against a model 4.8990), and no exponent moved. | 0 | [redteam-0904-floor-growth-2.md](history/staging/redteam-0904-floor-growth-2.md) |
| `Q-redteam-0904-item0` | ANSWERED | Do the two HELD notes of 2026-09-04 on item 0, the second adversarial pass on the adverse floor's growth half and the L7 one-class-to-two-class transfer, survive an independent adversarial pass, and do the live-layer changes they propose survive verbatim? | Both notes SURVIVE at their own rungs and neither moves an exponent, but SIX of their proposed live-layer changes need rewording and two of their supporting derivations are wrong; every load-bearing number reproduces on independent code (18 of 18 A1A2 cells digit for digit, the LP maximum 8s/9 at 0 deviations of 16 with residual 4.441e-16, the crossing 2.399878284834 against 9beta2/16 at 1.097e-13, the fitted C = 1.1206e-4 and the s = 3.0 crossing 10^15.30, the onsets 4.390e5 / 1.111e6 / 1.860e6, ln(n1n2) = 7.4993e7, and the L7 CRT counts EQUAL at x = 7, 11, 13), so the truth-gap reading of REC is CONFIRMED and the growth half stays DERIVED and red-teamed twice, not proven; what does not survive is the scoping, the exit-window and the price wording: the proposed clause "at equal levels D1 = D2 = z^s" is NARROWER than the derivation supports, since over 1643 admissible upper-and-lower level splits the floor beats the decoupled window at every cell by at least 0.644444, so no level split escapes and the sibling rider "asymmetric levels give 8s1/9 + 8s2/9 with s1 + s2 pinned" is REFUTED as written (it holds only while both s_i <= 3); the record's z ~ 5.6e31 is u0-specific as well as s-specific (10^31.68 at u0 = 4.2165 against 10^35.36 at u0 = beta2, same s), so replacing it with a beta2-convention 10^15.30 mixes two conventions; the onset correction is right numerically and wrong in wording, since at the record's own s = 2.698721 the exact onset is 1.875e6, LATER than the quoted analytic 1.055e6, not earlier; the escape-(a) correction is right in substance but its "(A1A2)^2 / (2 n1n2)" is a LOWER bound on the split's contribution, and the two-sided version through lambda+(n) <= 2^omega(n) reads 10^{-3.004323e+7} against B ~ 10^{10.1}, still no contradiction; and on the L7 side the union-bound argument and the CRT count are CONFIRMED while the coupled vector-sieve price 2(1 + sqrt e) = 5.297442541400 is the FORCED-equal-level constant, the corpus's live figure being K_BF = 5.158064680330, reproduced here to twelve digits at (a, b) = (2.229949, 2.928115), and the sieve-on-holes is the vector sieve only after the Ford-Halberstam substitution step that sift-limit-attack.md 7b(1b) already owns; the "no third mechanism excluded" line is honest but incomplete, since weighted sieves with Chen switching are already priced and closed at sift-limit-attack.md 4.2; scope of death gains one row, L7's mechanism 2, which the growth note's own section 10 calls untouched while its sibling calls it dead; no exponent moved. | 0 | [redteam-0904-item0.md](history/staging/redteam-0904-item0.md) |
| `Q-redteam-0904-r0-extension` | ANSWERED | Do the seven load-bearing claims of derive-0904-r0-extension.md survive an adversarial re-derivation against Tao's own text, and do its proposed live-layer changes survive? | Six of seven survive at their stated rung and one is refuted: Proposition A, the scope slip, row e'' and the equivariance transfer are CONFIRMED (the slip is strengthened, since Tao's own Example 2 is the target note's missing one-coordinate witness), Propositions B and D are WEAKENED (B's stated mechanism proves too much and its proposed insertion drops the qualifier that saves it; D's "same trigger" is near-definitional and its causal reading of the exponent band does not hold), and the claim that no corpus artifact certifies the window-count variance at width p'^2 is REFUTED by research/06-variance-theorem.js, which computes exactly that, brute-force verified at two levels; separately, EXEMPT throughout means "Claim 1's H5 fails", which is not the parity statement wall-note Face 1 is priced against, and the note's proposed live-layer text carries no H6 conditional. | Z2 | [redteam-0904-r0-extension.md](history/staging/redteam-0904-r0-extension.md) |
| `Q-redteam-0904-sifting-limit` | ANSWERED | Do recon-0904-sifting-limit-floor.md's five claims survive adversarial re-derivation at the page, and in particular is the 4.26645 cap a method artefact at rung MEASURED? | Four of five claims survive with corrections and the headline does not. Claim d is REFUTED as stated on four grounds, each sufficient: the level-D LP fixes one omega-profile out of a class Ford defines by a ONE-SIDED inequality, and inside the classical (Omega_2(kappa,L)) budget a legal profile at x = 13 gives a calibrated reading of 5.0113, above beta_2 = 4.26645, which fires the target note's own pre-registered refutation of its floor; the calibration is a 1.72 multiplicative correction fitted at one point and it misses the second proven point beta(1/2) = 1 by 66 to 82 per cent, two and a half times the 28.7 per cent effect the headline rests on; the pooled 3.3152 averages four statistics of which only s* is the definitional analogue of beta, and that route reads 3.4678 here and 3.9487 at x = 43 in the corpus's own data, still climbing at +0.4297 per ln x with the fitted line reaching 4.26645 at x = 104; and 3.3152 is 22.2961 per cent below 4.26645 rather than the 18 per cent the note prints. Claim a is CONFIRMED with a second source off the OCR channel (Ford 2023 p. 37, "Some authors, e.g. Selberg, refer to 1/beta(kappa) as the sieve limit"), one page correction owed (Halberstam is p. 117, not p. 116). Claim b is CONFIRMED and strengthened: Brady's class is stated on his p. 10 and IS the axiom-only interval class Face 4 needs, his v_R table is reproduced here, and the identity v_{2d+2} = v_{2d+1} his proof asserts is confirmed at d = 0, 1, 2, so 1.819592 rests on proved facts alone. Claim c is CONFIRMED but demoted: beta(2) >= beta(1) = 2 is two lines from Ford's own one-sided (Omega) plus his own beta(1) >= 2, so the padding construction is correct and unnecessary. Of the eight proposed live-layer changes, two survive verbatim, five need rewording and one is refuted; the new SEARCH-CONVENTIONS row adds exactly three clearing phrases and changes nothing for any existing absence claim. | 0 | [redteam-0904-sifting-limit.md](history/staging/redteam-0904-sifting-limit.md) |
| `Q-redteam-at37-score` | ANSWERED | Does the @37 scoring record survive an adversarial pass on its prereg re-score, its independence claim, its interpretation table and the cofactor extrapolation? | The empty-survivor scoring holds - every registered figure reproduces from the committed prereg text and the embedded census block, and the four skipped reference-level gates were run here and all pass - with two findings against the held report, neither touching the verdict: the one-level-drop figure is 8.2x rather than 4x, which strengthens the reversal claim, and the cofactor-one surplus sentence oversells. | none | [redteam-at37-score.md](history/staging/redteam-at37-score.md) |
| `Q-redteam-zonegap-foundation` | ANSWERED | Do natal-onset-01, zonegap-01 and zonegap-prior-art, the three artifacts the Z2 pivot builds on, survive an adversarial pass? | The foundation HOLDS: all four natal-onset claims CONFIRMED, zonegap-01 confirmed at every reachable point by independent code using a different sieve and a different max-gap algorithm, and the prior-art spot checks all confirmed at page image; two prose defects found, both WEAKENED and neither refuted. | none | [redteam-zonegap-foundation.md](history/staging/redteam-zonegap-foundation.md) |
| `Q-refuted-audit-0829-1` | ANSWERED | Do the closures recorded in REFUTED.md rows 1 to 17 survive re-derivation against the object definitions, the producers' embedded output and the corpus corrections through 2026-08-29? | Ten of the seventeen rows stand as written and seven are SOUND-NARROWER on wording that claims more than the record carries; no row is WEAKENED or UNSOUND, no route reopens, and the sharpest defect is row 16 crediting a published lemma whose own hypothesis excludes this corpus's operative range. | none | [refuted-audit-0829-1.md](history/staging/refuted-audit-0829-1.md) |
| `Q-refuted-audit-0829-2` | ANSWERED | Do the closures recorded in REFUTED.md rows 17 to 34 survive re-derivation against the object definitions, the producers' embedded output, the 2026-08-29 corrections, and their own quantifiers? | All eighteen closures stand and none reopens; nine rows are SOUND and nine are SOUND-NARROWER, the worst being row 53's "the search is finished", which its own record contradicts in two places, and the others splitting into three classes: a mechanism clause that covers half its route (rows 47, 58), a universal quantifier wider than the sweep behind it (rows 49, 59), and a measured number carried without its calibration or its unit (rows 43, 46, 60). | none | [refuted-audit-0829-2.md](history/staging/refuted-audit-0829-2.md) |
| `Q-refuted-audit-0829-3` | ANSWERED | Do the closure arguments behind REFUTED.md rows 34 to 51 (the greedy oracle through the bounded-differences family) hold when re-derived against the object definitions, the producers' embedded OUTPUT blocks, and the corpus corrections landed through 2026-08-29? | The band holds: 13 of 18 rows SOUND and 5 SOUND-NARROWER, no WEAKENED and no UNSOUND, so no route reopens; the worst finding is a factual inversion in the anchored-delta row, which asserts that delta exceeds the forced scale at 2 of 7 levels when the record's own table has \|delta\| < F at 7 of 7, and the same wording has already propagated into a second note. | none | [refuted-audit-0829-3.md](history/staging/refuted-audit-0829-3.md) |
| `Q-refuted-audit-0829-4` | ANSWERED | Do the closures recorded in REFUTED.md rows 51 to 67 hold when the record is opened and the closing mechanism re-derived against today's corrected corpus? | All seventeen closures stand: 8 SOUND and 9 SOUND-NARROWER, zero WEAKENED and zero UNSOUND, no route reopens; the narrowings are wording that claims more than the record carries, worst of them row 67, whose closing clause quotes a section its own record headed POST HOC and carrying no verdict after the pre-registered primary went VOID on its matched control. | none | [refuted-audit-0829-4.md](history/staging/refuted-audit-0829-4.md) |
| `Q-refuted-index` | SUPERSEDED | Where do recorded citations to the closed-route index resolve? | The current closed-route records are in OUTCOMES.md. This file is only a compatibility pointer for citations in recorded script output; it contains no separate outcome register. | none | [REFUTED.md](REFUTED.md) |
| `Q-registry-glossary` | ANSWERED | What does each word of the programme mean, one term per object? | The vocabulary registry; adopted terms with dates, the anchored layer, and the calibrated entries (Var/E, hyperuniformity, the freshness dimension count) as corrected on 2026-08-28. | none | [GLOSSARY.md](GLOSSARY.md) |
| `Q-registry-outcomes` | ANSWERED | What has each research approach established, where has it failed or stopped, and what evidence or changed input permits reuse or a further attempt? | One outcome register organized by research question and approach. Each record preserves its calibration, established result, limitation or failed step, evidence and reuse or revisit conditions. The closed-route table is part of this register. Git owns revision and authorship history; an open estimate is not a refuted claim. | none | [OUTCOMES.md](OUTCOMES.md) |
| `Q-registry-research-readme` | ANSWERED | Which file in research/ answers which question, and in what order should a reader open them? | Router only: state lives in ../README.md section Status and G2-STATE.md section 0, the target in ZONE-POSTULATE.md, the queue in ../TODO.md; this file holds no mathematics and no summary of the programme. | none | [README.md](README.md) |
| `Q-research-execution` | ANSWERED | How should agents use the integrated returns, avoid repeated work and select the next bounded research obligation? | The second dispatch from 1285d47 closed at 46fa948 and was independently reviewed on 2026-09-09. A/A2/B/C/D/E and V/W returns are present and integrated at their owning scopes. A2's corrected Type I estimate is accepted; D's fourth residual cut is retained and its remaining moment saving corrected to 7/200. C's low nonzero modes and E's aggregate scope are corrected. No new assignment is started by this integration; next obligations are candidates, not running work. Twin-prime infinitude and every sufficient signed margin remain OPEN. | C | [RESEARCH-EXECUTION.md](RESEARCH-EXECUTION.md) |
| `Q-research-handoff` | ANSWERED | What must an incoming research agent understand, verify and return before its work can advance the current twin-prime argument? | Current handoff after the 2026-09-09 independent review of the dispatch ending at 46fa948. The full residual has four simultaneous complement conditions after D's regional estimate. A's centered truncation and A2's repaired low Type I estimate give the alternative S=C2*x+B+O_A(x/log^A x). B and all sufficient signed margins remain OPEN. The C3 absolute bound, family identities and scoped C/E failures retain their owning hypotheses. Execution is owned by RESEARCH-EXECUTION.md. | C | [RESEARCH-HANDOFF.md](RESEARCH-HANDOFF.md) |
| `Q-research-round-validation` | ANSWERED | Which submitted results from lanes A, A2, B, C, D, E, V and W survive direct review, and what can be integrated or used to choose the next attempt? | Reviewed incoming commits 07ab47f through 46fa948 on 2026-09-09. A's truncation and A2's repaired low Type I estimate are accepted with bookkeeping corrections. B's ordinary-BV family identity survives; its uniform Dickman constant and complement condition are repaired. C's norm obstruction survives on all smooth inputs, but low nonzero Fourier modes are also 1-bounded. D's block estimate and fourth residual cut survive; its next moment saving is 7/200, not 17/200. E's rough-product distribution and aggregate constant 4 are accepted at the stated Wu uniformity reading; rational certificates close the two displayed tests for every fixed u>4. W remains OCR-only at the original 1974 theorem page. All sufficient twin-prime margins remain OPEN. | C | [research-round-validation.md](research-round-validation.md) |
| `Q-residual-coverage` | ANSWERED | What portion of the full residual is controlled with uniform margins, and can the exceptional first branch improve that coverage rather than just a regional corner? | The first-branch and prime-free moments remove the exceptional norm condition. Full rectangles are controlled when delta+nu<19/25 or 5delta+2nu<123/50. Uniform twists justify exact coupled cuts: every fixed de<=x^theta with theta<19/25, and d^5*e^2<=x^lambda with lambda<123/50, as well as their union, have arbitrary fixed logarithmic savings. A concrete remaining endpoint sum has de>floor(x^(3/4)) and d^5*e^2>floor(x^(49/20)). Its twin margin is OPEN. The right zero-frequency budget, after an extra Cauchy inequality, limits the uniform product range; the left cross moment limits the other edge. Finite checks validate identities and masks, not asymptotic rates. | C | [residual-coverage.md](residual-coverage.md) |
| `Q-review-0905` | ANSWERED | Does the present programme justify its latest stopping decision, and what is the next useful campaign toward infinitely many twin primes? | The computational checks pass and the DHR application survives this reading, but several summaries overstate the obstruction or misstate an implication. Recommend repairing those claims, retaining the fold framework, and testing it against Chen on long intervals before attempting a specifically stated parity-sensitive estimate. No proof of twin primes or improvement of an exponent is supplied. | none | [review-0905.md](history/staging/review-0905.md) |
| `Q-review-request-0906` | ANSWERED | Which claims of the arithmetic campaign should an independent reviewer check, in what order, against which records, and what must the review return? | Completed review specification at the bounded scope recorded in handoff-review-0906.md and reports 20 and 21, with the subsequent round reviewed in round-review-0906.md. The dependency list records questions at dispatch, not current unfinished assignments. Imported proofs retain their review limits and the twin margin remains OPEN. Current assignments are in RESEARCH-EXECUTION.md. | C | [REVIEW-REQUEST.md](REVIEW-REQUEST.md) |
| `Q-review-request-0907` | ANSWERED | Which claims of the 2026-09-07 session should an independent math agent check, in what order, against which records, and what must the review return? | Reviewed 2026-09-08 by an outside reader (history/reviews-0907/10): ranked claims 1 (conditional on the unread 1974 page), 2, 4, 5, 6 verified within stated scope; claim 3 verified with its quoted tolerances corrected (max deviation 1.8e-4, not 1e-4 or 1e-5); the Corollary 1 slip sharpened (fails for every representative other than 1, and mis-signs even then); ASSUMED items 4 and 6 discharged, 2 partially, 1, 3, 5 not. Twin-prime infinitude and every sufficient signed margin remain OPEN. Ranked below: the §6.2 demotion in the two-class manuscript (a change to a proof's dependency), the D_y identity reading (a change to what a census can show), the Erdős #687 attribution, and the two measurement artifacts. Twin-prime infinitude and every sufficient signed margin remain OPEN. | Z0 | [review-request-0907.md](review-request-0907.md) |
| `Q-rho-maximal-law` | PARTIAL | What is the rho maximal law, what is its weakest sufficient form against the crossing, and where does it sit against print? | The pricing lemma turns any RML(alpha) with alpha < beta_2 = 4.26645 into G2(z#) << z^alpha ln^2 z, every step proven except the law itself; the sufficiency curve lambda_max falls from 2.31949 at z = 13 to 1.78446 at z = 47, the weakest measured point, and whether it ever reaches zero is model-dependent and undecided, so nothing here is an unconditional exponent. | 0 | [rho-exact-z31-01.md](history/staging/rho-exact-z31-01.md), [rho-maximal-law.md](history/staging/rho-maximal-law.md) |
| `Q-rho-sup-z41-0830` | PARTIAL | What is the exact sup over all positions of the centred sawtooth remainder at z = 41 (period 7.42e12), and of R_H at H = z^3 and z^4, and what does the eighth exact point do to the truth's slope and to the u0 = 3 form of REC(s, u0)? | Not run in full; the exact z = 41 point prices at 4.8 to 5.4 h on this machine from measured per-position costs (naive 69.8, table 23.5, table-plus-windows 36.6 ns per worker; fleet 4.52 ns of wall at z = 41), above the 3.5 h rule, so what exists is a new engine (a PROVEN reflection that halves the walk, a P(29) periodic table worth 2.9x, per-block exact re-seeding) reproducing every cited exact sup at z = 13..37 digit for digit, sup\|R_H\| at H = z^3 walked for the first time at z = 19..37 (F3 = 26.4 to 35.9, the factor 2 was 1.5 to 2.2x loose), a sealed pre-registration (forecast sup 60.07, band [47.25, 76.37], kill needs sup\|R_H3\| >= 1807.417), one pilot twelfth giving lower bounds sup\|rho~\|(41) >= 70.651250 and sup\|R_H3\| >= 64.416936, and an eleven-segment plan for the box; no bound-and-prune exists on three routes; nothing asymptotic can move whatever the point turns out to be. | 0 | [measure-0830-rho-sup-z41.md](history/staging/measure-0830-rho-sup-z41.md) |
| `Q-rho2-bound` | ANSWERED | Is there an analytic upper bound on <rho^2>(z) from its proven closed form, and does it matter for RML? | Already proven 2026-08-21 (attack-rhoms-01); the constant is now named, 170.88 z^{2s} ln^8 z; Chebyshev off any second moment diverges from RML (the true C_L = ms = 1 floor clears at z = 41 and 43 and misses by 2.155x at z = 47), so it is an ingredient, not a route. | 0 | [attack-rhoms-01.md](history/staging/attack-rhoms-01.md), [rho2-analytic-bound.md](history/staging/rho2-analytic-bound.md) |
| `Q-rml-proof-0829n` | PARTIAL | Starting from Lemma V's PROVEN mean-square bound, what is the exact chain of implications to a two-class exponent below beta_2 = 4.26645, which single arrow is open, and does it close? | The chain from the proven mean square to an exponent below beta_2 has exactly one open arrow, the mean-square-to-sup recovery REC(s,u0): sup_x \|R_H(x)\| <= z^{u0/2 - eps} rms(R_H) at H = z^{u0} for one fixed u0 in (2, beta_2); every attempt here dies at a named place (term-by-term accounting is capped at 2s + o(1), the trivial-level exponent; position-union pays e^{theta(z)/q}; window smoothing and the P(y) lever move polylog only; the smooth-profile form is closed on hypothesis and priced above beta_2), the arrow is measured TRUE with certified margin z^1.72 to z^1.92 at u0 = 4 over z = 19..37 and the truth's slope 2.766 +/- 0.212 sits 5.8 se under u0 = 4 on seven points under one octave, so the failure is a proof gap at every computable z and undecided asymptotically; no exponent moved. | 0 | [attack-0829n-rml-proof.md](history/staging/attack-0829n-rml-proof.md) |
| `Q-roughpair-error` | PARTIAL | How big is the empirical error of the rough-pair census, and is Z2 dead on the numbers? | Not dead on the numbers - the error sits below T at every one of 1,206 anchors, its scatter is sub-Poisson, its systematic part is 0.1% at the top band with the favourable sign and its exponent is 0.40 below the twin count's - but the same run moves the wall off the error term onto the depth, where the slack at the crossing is 1.056 and falling and the main term alone is 5.6 times the twin count at the sifting limit. | Z2 | [attack-roughpair-error.md](history/staging/attack-roughpair-error.md) |
| `Q-roughpair-null` | ANSWERED | Does the independent-thinning null named in attack-roughpair-error.md's defects list return chi2/df = 1, and is the measured sub-Poisson dispersion of the rough-pair census error real or a normalisation artefact? | MEASURED, null-side, label (i), no bearing on the certificate: the independent-thinning null is binomial and returns 1 - p (0.8164 to 0.9808), not 1, so attack-roughpair-error.md's "below 1 everywhere: sub-Poisson" is WEAKENED and the registered F1 fires at u = 5; the deficit against the mean-matched null survives at pooled z = -5.87, -7.09, -11.39; and a CRT-exact null that only makes each prime's kill count exact in the window predicts 0.33 to 0.56, which the measured value EXCEEDS by 1.26 to 1.40, so D8 is interval-level in form, elementary in content, and not wall-relevant. | Z2 | [measure-roughpair-null-0829.md](history/staging/measure-roughpair-null-0829.md) |
| `Q-round-review-0906` | ANSWERED | Which conclusions of the completed agent round survive review, and which corrections change the next research specification? | The fixed-band lift and continuous moving-window estimate survive the checked source interface. Interval stability additionally gives a dyadic scale-average logarithmic saving, so the blanket scale exclusion was too strong. The rate and missing prime-cofactor terms with s>1 or s'>1 still prevent a twin margin. Proper-prime-power branches already have a negligible bound on the fixed corner. The driver computes integer parity, not the CRT gcd partition; its total coefficient identities survive. Diagonal lower-bound, reachability and six-cut bookkeeping overclaims are corrected. No region, exact residual cut or twin lower bound changes. | C | [round-review-0906.md](round-review-0906.md) |
| `Q-row11-closure` | CLOSED | Can the (1 - 1/e) greedy-coverage certificate of IMPORT-MAP row 11 ever fire? | No, and now on a producer rather than on prose: the map's paragraph-only pre-pricing reproduces exactly at all six figures it states and extends to the full ladder x = 5..79 with the certificate silent at every level under every constant that could be used, and the step from a density to an algorithm is proved in one line. | none | [row11-closure.md](history/staging/row11-closure.md) |
| `Q-row11-closure-prereg` | OPEN | Does IMPORT-MAP row 11's (1 - 1/e) certificate reproduce, and does its test ever fire? | Pre-registration only, hand-written and committed before its producer existed: the claim being reproduced, what the producer must return, the pass criteria and the disclosed leaks are all fixed here, with the killing arithmetic still living only in prose. | none | [row11-closure-prereg.md](history/staging/row11-closure-prereg.md) |
| `Q-row12-lonely-runner` | CLOSED | Does the lonely runner conjecture, or the Birkhoff and bounded-remainder branch, transfer to the Zone Postulate or to G2? | CLOSED WITH MECHANISM on two independent grounds, either sufficient: the general two-class problem is settled at the trivial bound, and the obstruction Tao names is our own configuration; the Birkhoff branch is subsumed and strictly worse from x = 13, and the row's payoff is a wall address rather than the published anchor the map priced. | none | [row12-recon.md](history/staging/row12-recon.md) |
| `Q-row7-talagrand` | CLOSED | Does Talagrand's concentration on product spaces (IMPORT-MAP row 7) bound anything the corpus needs? | CLOSED WITH MECHANISM: the structural fit is better than the map wrote, since Theorem 8 needs no dependence structure and the shared-draw mechanism that closed rows 3, 4 and 10 does not close this one, but the per-coordinate effect c exceeds the largest tolerable value by a factor that DIVERGES (174x at @11 to 70,576x at @23), and the target hole is on the wrong side of the ensemble/anchor divide, so even a perfect bound would be inert. | none | [row7-recon.md](history/staging/row7-recon.md) |
| `Q-scanstat-t37` | ANSWERED | What does the seventh exact level T37 do to the linear-in-ln D rule for H, and to the sqrt(m) refutation? | The sealed prediction H*5(T37) = 0.381254, band [0.369866, 0.392641], misses the measured 0.356548 +/- 0.0068 by 3.63 of its own s.e., so per the seal the linear form was a coincidence of a short ladder; the exponent series still rises but is concave in ln D, and G2(37#) is certified exhaustively over 217,929,355,875 slots. | none | [scanstat-t37.md](history/staging/scanstat-t37.md) |
| `Q-scanstat-t37-prereg` | OPEN | What is the moving-sum exponent H at T_37, predicted before any producer for the pass existed? | Pre-registration only, sealed and committed alone: the prediction band, the criterion, the weak secondaries, the custody gates the producer must pass before reporting and the compute plan are fixed, and T_31 is explicitly excluded as another pre-registration's verdict. | none | [scanstat-t37-prereg.md](history/staging/scanstat-t37-prereg.md) |
| `Q-scanstat2` | ANSWERED | Does the scan-statistic exponent law survive a sixth exact level, and is the tail factor the extremal index? | Both follow-ups come back negative: T_31 missed the pre-registered exponent rule from outside its own 95 per cent band, so the linear-in-ln D law describes five points and is not a law, and the tail factor is not the extremal index, its correction pointing the wrong way at seven of nine tested places; the sixth level confirms the kill on sqrt(m) harder, at H = 0.3460 +/- 0.0068 against 0.5. | none | [scanstat2.md](history/staging/scanstat2.md) |
| `Q-scanstat2-prereg` | CLOSED | Does the linear-in-ln D exponent rule predict H(T31), and is the tail factor the extremal index? | Sealed and committed alone before any producer for the pass was written; scored in scanstat2.md, where both follow-ups come back negative: T31 missed the pre-registered band from outside, so the linear law describes five points and is not a law, and the tail factor is not the extremal index, with the correction pointing the wrong way at seven of nine. | none | [scanstat2-prereg.md](history/staging/scanstat2-prereg.md) |
| `Q-search-conventions` | ANSWERED | In whose vocabulary do these objects live, and which prior-art searches have already been run in the owning convention? | The owning conventions are tabulated by object and the searches already run are listed so they are not repeated; the rule stands that a clean negative in our own wording proves nothing, and section 5 keeps what is still uncovered separate from what is covered. | none | [SEARCH-CONVENTIONS.md](SEARCH-CONVENTIONS.md) |
| `Q-self-contradiction` | ANSWERED | Which documents in the corpus contradict themselves? | Twenty findings, two rated HIGH because they change what somebody does: theta-ladder.md's retracted crossing still asserted unmarked in three further sections, and G2-STATE.md's confirmed G2(41#) = 546 against three sections still carrying twelve terms; eight more change a number somebody quotes. | none | [audit-self-contradiction.md](history/staging/audit-self-contradiction.md) |
| `Q-session-0828` | ANSWERED | What did the 2026-08-28 wave establish? | 21 agents, zero routes, four TODO items closed or answered, one HELD headline (Var/E = 0.45546, heuristic). | none | [session-0828-summary.md](history/staging/session-0828-summary.md) |
| `Q-session-0829` | ANSWERED | What did the 2026-08-29 session (the Z/G object reads, the measurement wave, the red teams, the refuted-claims audit) establish, and what does it leave open? | Nothing moved an exponent or opened a route; the map moved: a Z2-STATE draft exists, both objects carry labelled legal-open-sets, the Gap Reformulation's discarded origin is proven not needed for the implication and measured worth one unit of exponent against a deficit of 2.2665, all 67 REFUTED rows re-derived with none reopening and 27 clauses corrected, and about forty live-layer and HELD-note defects were applied after verification. | none | [session-0829-summary.md](history/staging/session-0829-summary.md) |
| `Q-session-0830-summary` | ANSWERED | What did the 2026-08-30 overnight campaign (rolling waves of up to ten agents on the queue rewritten after the 08-29 evening wave) change, and what is still open? | Neither exponent moved; twenty-one staging notes landed, all HELD; four routes closed (the skeleton door, the K*-product and fold-composition doubling bridges, the deep-ladder Buchstab transfer), TODO item 4 deleted and items D and 8 parked, the RML route carries an adverse derived floor whose growth law survived one sealed blind test and awaits a red team only Chris can call, Z2's fifth decade rejected the exact-Mertens main term for the omega-form crossing at 13 to 24 se, three record defects were verified on independent code and applied as riders, and a coherence pass corrected 27 lags in the live layer. | none | [session-0830-summary.md](history/staging/session-0830-summary.md) |
| `Q-session-0904-summary` | ANSWERED | What did the 2026-09-04 wave (four Opus attacks on wall-facing questions, one orchestrator note, four Opus red teams, all verdicts applied) change, and what is still open? | Neither exponent moved; item 0's growth half survived a second adversarial pass so the route is a truth gap at rung derived-and-red-teamed-twice; Face 4's "no lower bound on the kappa = 2 sifting limit is known" was a convention failure and published floors at or below 2 are now cited, while the recon's headline that the cap is a method artefact was refuted by its red team; killer 2's coordinate is measured for the first time (argmax mirror-invariant, zero congruence pairs from x = 23, forced) after the multiplicity half turned out to be on the ladder already; no piece of R0 is both legal and parity-exempt with content; L7 is not a transfer; about thirty live-layer sentences corrected across seven files. | none | [session-0904-summary.md](history/staging/session-0904-summary.md) |
| `Q-shadow-amplitude` | MIXED (shadow-amplitude-prereg.md: OPEN; shadow-amplitude.md: PARTIAL) | Where does the kill shadow's drift amplitude come from, and does the record's counting floor explain it? | The finite-y correction is an identity with no free parameter and both measurement routes agree 10 of 10, but the record's own counting floor is four to six times too small and its candidate explanation is the wrong half, so the label stays PARTIALLY EXPLAINED. | 5 (retired) | [shadow-amplitude-prereg.md](history/staging/shadow-amplitude-prereg.md), [shadow-amplitude.md](history/staging/shadow-amplitude.md) |
| `Q-shadow-buchstab` | ANSWERED | Is the kill shadow the band-averaged pair-Buchstab integral? | SURVIVES WITH CORRECTIONS, and under the record's own pre-registration the verdict is SHAPE-ONLY rather than DERIVED, since y ~ 1000 misses D1 at 1.49x tolerance; the drift's amplitude is off by about 2.6x, the coefficient has the closed form 2 - 1/ln 2 = 0.5573049591 that the record missed, and anchored-windows section 5 reproduces 32 of 32 from an instrument sharing no code. | none | [shadow-buchstab.md](history/staging/shadow-buchstab.md) |
| `Q-shadow-prereg` | ANSWERED | Is the kill shadow's 0.85 the band-average of the Unification-Law survival curve over the post-crystallization window? | Scored in shadow-buchstab.md: SHAPE-ONLY under the original y >= 997 rule; D3 passes in the reported ten clusters but D1 fails near y = 1000 at 1.49 times the 0.011 tolerance. Later finite-y normalisation and counting-floor corrections do not promote this verdict. The pair-Buchstab identification remains conjectural; the pre-registration body is preserved. | 5 (retired) | [shadow-prereg.md](history/staging/shadow-prereg.md) |
| `Q-sharp-corner-transition` | ANSWERED | What is the energy of the complete sharp corner coefficient, and can the smoothed estimate be transferred through a negligible L2 transition? | DERIVED using named analytic inputs: for each fixed 0<eta<1/400 the full sharp squared norms and absolute shifted product are O_eta(x log^2 x). For every sufficiently small fixed eta>0 both sharp squared norms and sharp-minus-smoothed squared norms are Theta_eta(x log^2 x) on the actual dyadic intervals. Thus an O_eta(x log x) sharp squared norm or negligible L2 transition fails in that range. Signed transition correlations and the global complement remain OPEN. No region, exact residual cut or twin margin changes. | C | [sharp-corner-transition.md](sharp-corner-transition.md) |
| `Q-sharp-sieve-range` | CLOSED | Do the sharp sieve functions (Jurkat-Richert, DHR) make the two empty certificate-engine theorems non-empty at run levels? | NO at finite level: DH Thm 9.1 carries no written constant and the crude fundamental lemma is strictly better; as limit statements kappa=1 is first non-empty @37 (a 19.8-wide bracket; @53 is the first narrow one, 1.656) and kappa=2 @23. | 8 | [thm-sharp-sieve-range.md](history/staging/thm-sharp-sieve-range.md) |
| `Q-shifted-prime-decomposition` | ANSWERED | Does decomposing Lambda(dk-2) give a provable saving on any part of the actual shifted-prime sum, and what exact arithmetic remains outside the imported hypotheses? | Both second Type I terms are O_H(x/log^H x) by classical Mobius BV. The residual is an explicit weighted sum over dk-ev=2, equivalently an average of two-linear-form Mobius correlations with growing coefficients and possibly one-point intervals. Its required one-sided improvement is OPEN. No twin lower bound or novelty is claimed. | C | [shifted-prime-decomposition.md](shifted-prime-decomposition.md) |
| `Q-shifted-prime-mobius-sums` | ANSWERED | At reachable x, do the shifted-prime Mobius and Liouville sums, the cleanest instance of the parity input the twin reduction lacks, show any size or sign structure that a random-sign model does not, and how loose is the trivial bound on M(x) used for the centered tolerance? | MEASURED to x=2^38 (10.9e9 primes). All four sums sit at random-sign size: \|U\|/control rms at most 2.8 at any j, slopes 0.28 to 0.65 against the control's 0.43 to 0.47 with per-draw spread 0.19 to 0.30; the pre-registered structure falsifier did not fire. M(x)/x is at most 8.8e-5 in magnitude for j>=29 against the trivial bound 0.374, so the -4x/25 tolerance in moving-cutoff-parity is loose by four orders at these scales; a proof still needs a bound on M, which is the same parity object. The squarefree density of p+2 among primes is 0.747911 at 2^38 against 2*Artin = 0.7479116. pi(2^j) matches OEIS A007053 at every j. Nothing here bears on the asymptotic conjecture. | C | [shifted-prime-mobius-sums.md](shifted-prime-mobius-sums.md) |
| `Q-sift-limit-discards` | PARTIAL | Where does the dimension-2 sieve discard our structure, and can any of it re-enter to beat beta2 = 4.2665? | Every asset checked against the five discard points has no known consumer and no entry point, and EH and GRH change nothing here; Lemma V's mean-square form is PROVED and hands back a sup bound, the strata are self-similar and it still does not close, L has no combination law of its own, and the 529 covering route is closed rather than unfinished. | none | [sift-limit-attack.md](sift-limit-attack.md) |
| `Q-sigma31-calibration` | ANSWERED | Is the sigma behind the @31 X-channel detection calibrated at @31 itself? | Calibrated at its own level for the first time: seven known-truth control draws give sigma_true/sigma_reported = 1.127 at the point, 95 percent bracket [0.745, 2.293] (pooled with the earlier draws, [0.772, 1.664]), which restates the detection at z = -2.06 under the point calibration and closes both T2.b findings; the detection weakens rather than dies. | none | [attack-sigma31-01.md](history/staging/attack-sigma31-01.md) |
| `Q-signed-divisor-grouping` | ANSWERED | Can grouping different fibers while retaining their Mobius signs control an explicit part of R, and what signed error remains after that grouping? | For every fixed H>0 the actual remainder restricted to de<=x^(7/10) is O_H(x/log^H x), although each sign's mass there is at least c*x*log(x) eventually. This follows from a written classical-input derivation, with finite algebra and archived-factor checks. The remaining de>x^(7/10) contribution reduces to an explicit weighted CRT endpoint discrepancy whose required one-sided improvement is OPEN. | C | [signed-divisor-grouping.md](signed-divisor-grouping.md) |
| `Q-signed-moment` | PARTIAL | Is there an argument for the block that does not pay sqrt(M) at the first Cauchy inequality or that extracts cancellation from the R=0 class, and what are its budgets at the corner a=b=1 and at the target box (delta,nu)=(8/25,9/20)? | The true diagonal has an upper bound x^(1+o(1)) on the transition band, not a uniform nonzero lower bound. Lemma A controls only u1=u2,h1=h2; unequal proportional R=0 pairs remain outside it. Lemma B and the now-priced joint Cauchy arrangement add no region. The former general Holder floor is valid only under additional coefficient assumptions, not for arbitrary sparse coefficients. Conditional off-diagonal budgets and the random-matrix ceiling remain conditional and heuristic. No necessity of using both signs, full-corner estimate or sufficient twin margin is established. | C | [signed-moment.md](signed-moment.md) |
| `Q-single-alignment` | CLOSED | Does the head's single-alignment fold recursion for M(x, x^3) give a proven-shaped handle on the per-fold multiplier that the max-over-alignments recursion lacked? | The answer splits: the multiplier IS different in shape, measured - exactly 1 at 225 of 240 folds from x = 53, total spend 1.09 nats against a tile-shaped ladder's 7.12, measured M(1613) = 2220 against a tile-shaped 3.7e5 - but the route to a growth law through the recursion closes anyway, because the growth is initiated by the window's expansion into fresh ground, a boundary term that is the localized gap problem re-posed and that no fold reaches. | 0d (retired) | [localized-single-alignment.md](localized-single-alignment.md) |
| `Q-singleton-fiber-audit` | ANSWERED | Can the one-point fibers of the coupled remainder be discarded or controlled in absolute value at scale x, and what do the actual weights and archived intervals show? | The grouped coefficient is zero whenever either integer is prime. Each sign's ungrouped singleton mass is at least c*x*log(x) eventually for an absolute c>0, by a written derivation from named classical inputs. Finite full-interval and archived-prefix checks validate the partition. The signed singleton and longer-fiber contributions remain OPEN; no twin lower bound or novelty is claimed. | C | [singleton-fiber-audit.md](singleton-fiber-audit.md) |
| `Q-skeleton-bound` | PARTIAL | Does the aggregate 30-skeleton bound hold, and can it be certified at every level? | Certified as an exact BigInt inequality at six levels @11 through @29, margins 0.287 to 0.406, with the Skeleton Collapse Theorem proven for all x and all q and an exact exception criterion; the all-x form is open and its blocking term is prime-equidistribution of window residues rather than branch algebra. | none | [natal-cap-30-skeleton-bound.md](natal-cap-30-skeleton-bound.md) |
| `Q-skeleton-decide-0830` | ANSWERED | Should TODO item 4, "Skeleton Equidistribution: restate or demote", be restated around the modulus-W mass or demoted off the board, and what exactly is banked either way? | DEMOTE. Over every scour prime the branches on which the door is a fixed-modulus question carry 9.2, -0.9, 0.2 and 0.5 percent of the skeleton at @13, @17, @19, @23 (the -10.8 and 5.5 percent on record were 9 and 2 percent subsamples), so the door as named removes at most 0.0102 from a G30_agg whose open part is 0.094 to 0.126; on the open side the phase never wraps and no equidistribution statement remains, only the inequality; nothing on the live board consumes G30_agg < 1/2; no first move exists that is not already ANSWERED. Banked regardless: the Skeleton Collapse Theorem (PROVEN, all x, all q) and G30_agg < 1/2 CERTIFIED at six levels @11..@29. | 4 (retired) | [decide-0830-skeleton-door.md](history/staging/decide-0830-skeleton-door.md) |
| `Q-skeleton-door` | ANSWERED | Is the Skeleton Equidistribution Conjecture the blocker on the anchored calm? | It is not the blocker as far as the door can be seen: Theorem A (Trapezoid Cancellation) is proven for all x, q and branches, @29 is certified as an exact integer inequality at G30_agg = 0.1176 with margin 0.3824 over 7,863 scour primes, and the decay-law shortcut is REFUTED, the six levels being flat within their own spread with every fit made strictly worse by adding @29. | 4 (retired) | [natal-cap-36-skeleton-door.md](natal-cap-36-skeleton-door.md) |
| `Q-small-divisor-kernel` | ANSWERED | Does reciprocity separate the j<=x^(1/20) kernel of grouped-divisor-moment (21) at delta=8/25, nu=9/20, and do the Duke-Friedlander-Iwaniec / Bettin-Chandee and Kuznetsov interfaces then supply the required saving? | The separation is exact and cheap: reciprocity splits index by index, the correction phase has sup norm and total variation O(A/(MN))=O(1/x) at this box, and Mellin separation of the endpoint weight costs x^epsilon with L1 mass min(1,Ax/(MN)), so the whole block reduces to a pure trilinear Kloosterman fraction with unimodular twists. The interfaces then fail by explicit amounts: Bettin-Chandee Theorem 1 gives block exponent 129/125, above the required 1 by 4/125 and above the classical 103/100; DFI (1.1) gives 1267/1200; every box Bettin-Chandee controls is already controlled, verified on 19005 rational boxes; the audit's spectral diagnostic factor is trivial for all common divisors up to x^(19/50). Closing this box inside the same interface needs the (M+N) exponent below 27/140 or the (AMN) exponent below 9/28. Target (21) and the global twin margin remain OPEN; nothing is added to the controlled region. | C | [small-divisor-kernel.md](small-divisor-kernel.md) |
| `Q-smooth-sieve-literature` | PARTIAL | Which nearby published results should be imported instead of rediscovered, and do their methods give a more focused next question for the complete global remainder? | Existing sources supply the finite-difference mechanism, one-point concentration and quadratic profile optimization; shifted divisor-sum estimates admit fixed shift two under their own support and smoothness conditions. A derived application of corrected Henriot bounds gives small-prime mass O_sigma(delta^sigma x)+O_epsilon(x^(39/40+epsilon)), uniformly in delta for fixed 0<sigma<1. This permits approximation by bounded-factor configurations at fixed delta, but their joint signed estimate, usable constants and the twin margin remain open. Fixed delta alone cannot absorb a shrinking logarithmic margin. The unrestricted ordered-prime formula in GKM Lemma 10.5 is refuted without the symmetry used in its proof and subsequent application. | C | [smooth-sieve-literature.md](smooth-sieve-literature.md) |
| `Q-smoothness-front` | PARTIAL | Do the Vaaler coefficients, a completion or decomposition step, or the Kowalski-Michel-Sawin branch clear the fixed-smooth-profile hypothesis? | Three verdicts, one route surviving as arithmetic and none as an instrument: the Vaaler coefficients clear Pascadi's condition maximally but buy nothing, because the binding dyadic block is h about 1 where Y_N about N is vacuous; what moves the frontier instead is Theorem A's admissible range (1.5), a hypothesis nobody had read. | none | [smoothness-front.md](history/staging/smoothness-front.md) |
| `Q-sparse-dispersion` | ANSWERED | Can the opposite dispersion orientation control the left nonsquarefree sector beyond the previous sparse-norm boundary, and what signed second moment remains at the resulting boundary? | A paired second-moment bound controls the left B/right Q sector with all harmonics, including distinct-prime zero numerators. Combined with the existing left-prime dispersion and sparse bounds for other sectors, it controls d~x^0.275, e~x^0.541 at product scale x^0.816. The product-exponent supremum of the stated sufficient inequalities is 1368/1675. The remaining tight budgets are BB and the left-prime cross moment; neither a uniform product cutoff nor a twin lower bound follows. | C | [sparse-dispersion.md](sparse-dispersion.md) |
| `Q-special-levels-recon` | CLOSED | What level and modulus engineering does the literature own, and does any of it compose with the natal frame at primorial levels? | None of it composes: the literature's level engineering is entirely on the deviation side, every construction surveyed certifies that something deviates and none certifies smallness or regularity of a max-type object at its engineered level, so the i.o. licence to pick levels adds nothing to what is already imported. | none | [special-levels-recon.md](history/staging/special-levels-recon.md) |
| `Q-sqrt-cancellation` | CLOSED | Can the 35 per cent of square-root cancellation be bought from the literature that owns the sum? | Not reached, and the best in print is one sixth of the way: the sum is a trilinear form with Kloosterman fractions, Duke-Friedlander-Iwaniec 1997 evaluates at gamma = 1.009638 (worse than trivial) and Bettin-Chandee 2015 at 0.970624 against the needed 0.824975, and feeding Bettin-Chandee into the vector sieve returns exponent 5.090707, worse than the 4.266450 already held. | none | [attack-sqrt-cancellation.md](history/staging/attack-sqrt-cancellation.md) |
| `Q-stretch-structure` | ANSWERED | What is the stretch S_q = [q^2, q'^2) as an object, where does the Stretch Postulate sit against the Zone Postulate, and does the square anchor's QR structure buy any density advantage? | The implication chain and the QR kill law re-derive independently arrow by arrow; the anchor's structure is real, deterministic and redistribution-only (exactly two killed offset classes at every prime anchor checked), so there is structure and no advantage, and SP sits strictly above the strong Zone Postulate. | Z3 (retired) | [stretch-01.md](history/staging/stretch-01.md) |
| `Q-structural-literature-audit` | ANSWERED | Which established mathematical structures match the current endpoint remainder, and which concrete next estimate is justified by a broad literature audit? | Exact gcd/lcm normalization identifies dispersion coefficients, classifies equal frequencies and cancels the common-factor Mobius sign on the squarefree sector. The reviewed spectral, bilinear, trace-function, graph and correlation theorems do not directly close the residual. In the natural level diagnostic the structured spectral improvement disappears for common factors at most x^0.27. The grouped-divisor follow-up derives the proposed full moment using classical completion and controls the benchmark; its next small-common-divisor kernel and the global twin margin remain OPEN. | C | [structural-literature-audit.md](structural-literature-audit.md) |
| `Q-structured-dispersion-estimate` | PARTIAL | Can the actual coefficient structure of b_u=A_right(gu), preserved through one further factorization, improve the small-common-divisor cross term at (delta,nu)=(8/25,9/20) beyond the arbitrary-coefficient moment, and what does it buy regionally? | Derived 2026-09-08; read by the handler (research-round-validation section 10) and independently by reader V3, both verifying Lemma H and (D1) within stated scope, with grouped-divisor-moment (7) and the required separate-coefficient upstream block shape rechecked on 2026-09-09; one correction applied (the regional cut is a fourth simultaneous condition of W_dagger, not a substitute for the third). Writing u=eq and applying Cauchy over (m,q) instead of over m keeps every pair of the moment inside a common prime-power factor, so the completed modulus grows by q while the pair count is that of e; one elementary harmonic gcd lemma prices the fixed factor. The block bound (D1) saves x^(min(sigma,alpha)/4) on the cross term and costs x^(sigma/2), x^sigma on the zero and period terms. At the target box the worst sector exponent falls from 41/40 to 407/400 and the box is not controlled. (D1) controls the strip delta<71/100, delta+3nu<327/200 outside the existing region (245 of 36481 grid boxes); section 6 adds the concrete cut d<=floor(x^(141/200)), de^3<=floor(x^(1631/1000)), de>floor(x^(77/100)) as a fourth simultaneous condition of W_dagger through the Perron machinery, changing only the summation domain of E_dagger. The target box (407/400), the corner, the uniform product threshold 19/25, the sign of E_dagger and the global twin margin are unchanged; the margin remains OPEN. | C | [structured-dispersion-estimate.md](structured-dispersion-estimate.md) |
| `Q-supported-coefficient-dickman` | ANSWERED | Can the whole supported coefficient be priced using existing literature before enumerating its factor cells, and does the resulting separate-sign sieve estimate supply a positive twin margin? | DERIVED from classical inputs: at delta=1/100 the harmonic limit is H_delta=D(25/12)-1+E_delta with 0<=E_delta<=24/22!, hence -1<H_delta<-2/3. The elementary separate-sign lower-bound constant is less than -80/9 and cannot supply positivity after adding only the main term. This is an INSUFFICIENT BOUND, not a negative upper bound on the regional residual. Existing integration and Dickman machinery is prior art; literature novelty of this application is unestablished. The joint prime-partner/complement estimate and twin infinitude remain OPEN. | C | [supported-coefficient-dickman.md](supported-coefficient-dickman.md) |
| `Q-switching-negative-mass` | ANSWERED | Can existing switching and rough-number estimates price an actual opposed-sign factor family, and can a bound on the negative part alone close the current twin consumer? | DERIVED from classical inputs: liminf Nhat/(C2*x) is at least kappa=(10*log(3)-36/5)*I>3/2, where I is the explicit ordered two-factor integral below. A three-prime left input and rough composite right input suffice; prime partners are subtracted using an upper sieve. The witness survives every fixed delta<1/50 and every averaging profile with the same plateaus. Consequently the negative-only consumer is false, and liminf Phat/(C2*x)>1/2. The signed twin margin remains OPEN; literature novelty is unestablished. | C | [switching-negative-mass.md](switching-negative-mass.md) |
| `Q-tail-deficit-model` | ANSWERED | Does the exact compound-geometric thinning of the previous level's own gap histogram, with the qualifying-gap constraint g = 0, +/-2 (mod q) carried through the ladder, predict the tile's tail-deficit factor G2/(mbar ln D) at zero parameters, and does that make object-models-read-0829's D5 residue-level classification constructive rather than inferred? | NO. The zero-parameter CRT-constrained thinning predicts a tail HEAVIER than the tile's at every level, delta_M2 = 0.6461, 0.6746, 0.7021 against a measured 0.4577, 0.4463, 0.4791, so the pre-registered "classification was wrong" arm fires and D5 returns to OPEN with C3's constructive route REFUTED; the constraint is informative but small, carrying 4.0 to 10.0 percent of ln(null/truth) at the far tail, or 7.7 to 14.4 percent read against a rate-matched control, against the grain's ORDER at 39.4 to 54.6 percent at the deepest abscissa each level resolves; at shallow abscissae the ordering reverses (B 8.7 against C 4.8 at x = 23, u = 4), which the exact operator on a shuffled true grain confirms without any model (maximum 276, 354, 426 against the true 204, 258, 348), and the order effect is now localised (sections 7 and 9): a first-order Markov word from the true adjacent-pair statistics carries 32.3, 34.2 and 60.8 percent of ln(shuffled/truth) at the deepest abscissa of the three folds, and a SECOND-order word from the true adjacent-triple statistics carries 97.3, 97.9 and 102.6 percent there, r = 0.972, 1.061 and 1.000 on draw-mean maxima over 40, 20 and 10 draws, so the folded tile's tail is MEASURED to be a function of the previous grain's three-consecutive-gap statistics and of essentially nothing longer-range; that surrogate is seeded on the true previous grain at one fold, is not iterated, predicts no delta and does not revive C3, and the 348.0 sd 0.0 at 29->31 rests on ten draws. | 0 | [measure-tail-deficit-0829.md](history/staging/measure-tail-deficit-0829.md) |
| `Q-tail-derivation-0830` | PARTIAL | Does the tail's measured law c = 0.7522 ln^2(p'^2) and its surplus derive, and which part of the coefficient is the tile's own (no prime input) against which part needs Hardy-Littlewood? | PARTIAL, kill clause fired on the coefficient: the ensemble object (the same functional averaged over all p# translates) derives exactly, E_all = R + 5/2 and E_odd = R + 3 with R = Sum g^2/2W, computed exact at x = 7..29 with every conditional the rough-origin candidate needs, and its Mertens constant e^{2gamma}/(8 C2) = 0.6007 is 1/(2 C2) times rho(2) = e^{2gamma}/4 by construction; every route from there to the anchored 0.7574 passes through rho(2)'s limit (the sharp form of Assumption A, algebraically equivalent to HL) and through the zone's gap shape CV^2 -> 1 (an HL statement), so the anchored coefficient is HL in disguise and nothing beyond HL is derived; the tile's own (1 + CV^2)/2 is 0.6306 -> 0.7532 over x = 7..29 and not settled; the record's 0.7522 = HL x 0.9644 x 1.0298 is two non-HL-sized factors cancelling at this height; the rough-origin candidate has an exact ensemble counterpart E_rc/E_cls = 1.0050 -> 1.0523, right sign, wrong size and trend against the anchored 1.0157, not identified; one number derives that the record measured: the class-null offset E_cls - R = 5.600 -> 6.034 exact against the record's 6.05, replacing both the prereg's 0.5 and the note's 7.5; and the corpus's "R + 1/2" is the other convention, under the tail's own the constants are 5/2 and 3. | Z4 | [attack-0830-tail-derivation.md](history/staging/attack-0830-tail-derivation.md) |
| `Q-tail-maximal` | CLOSED | Is a tail-only maximal inequality a smaller ask than the full one, as attack-AB-bounded section 4.4 supposed? | No: the split is exact but is a reparametrisation rather than a localisation, the tail is maximal and saturates the Gaussian law, a fixed cut buys nothing asymptotically, and the tail is not a smaller ask but the whole ask. | none | [attack-tail-maximal.md](history/staging/attack-tail-maximal.md) |
| `Q-tailcount-transport` | ANSWERED | Does the Tail-Count Transport survive an independent adversarial re-derivation? | The inequality, the certificates and the NO-CHAIN verdict all STAND on an implementation written from the operator definition, with a seventh fold added exact (31: 348 = 348); three corrections follow, the stated equivalence is false at fold 29, zero loss is exactness-by-relaxation rather than a tail fact, and the measured spends are 1, 1, 2, (1 or 2), 3, 2. | none | [verify-tailcount-transport.md](history/staging/verify-tailcount-transport.md) |
| `Q-tau-repricing` | CLOSED | Does the tau(m) re-pricing of the x-free bound stand? | The separability claim is true and re-derived four ways, but the re-pricing substitutes one quantity for a different one: summed over the modulus set the tau(m) bound IS the divisor-pair count up to the vector sieve's fixed factor 3, and used as a bound it is 4 to 5x weaker than the exact quantity in the Fourier basis and 23 to 44x weaker in the divisor-pair basis. | none | [attack-tau-repricing.md](history/staging/attack-tau-repricing.md) |
| `Q-the-dials` | ANSWERED | Which variables can this programme actually push, and which is Chris missing? | The square frontier constrains certification from roughness alone, not every arithmetic method. The current campaign uses long intervals, a classical Chen benchmark and an OPEN signed estimate; uniform maximum-gap control is a sufficient secondary target. Finite slopes do not determine an asymptotic exponent. | none | [THE-DIALS.md](THE-DIALS.md) |
| `Q-the-lens` | ANSWERED | Why is the tile the right object, and what does the lens buy? | Completeness is PROVEN and elementary (every twin prime above p is a twin slot of T_p) and the recursion is exact; nothing here is claimed as new mathematics, and the triage rule of section 5 states what the lens does not buy. | none | [THE-LENS.md](THE-LENS.md) |
| `Q-theta-ladder` | CLOSED | Does the all-positions exponent theta turn over below 2, converge to exactly 2, or settle above 2? | The answer is above 2 with an amendment, and the route is retired regardless: theta does not turn over (it dips and comes back, need/z^2 = 0.3550 to 0.6119 at z = 13..31 and rising from 31), convergence to exactly 2 is not supported (e = 1 rejected at 95% in all four fits), point estimates run 2.37 to 2.99 without settling, and OUTCOMES.md records the certificate route as RETIRED because the sharp maximal law it needs is itself TPC-implying. | 0 | [theta-ladder.md](theta-ladder.md) |
| `Q-theta-last-gap` | CLOSED | Can the last 0.209 of theta_total be recovered by sharper absolute-value accounting? | No: theta_total stays 1 and the obstruction now carries an exponent, the absolute-value ceiling is c*H^theta_total with c > 0 rather than H*polylog, so the shortfall is a power H^0.212 and the entire budget any constant could ever buy is O(lnln H / ln H) against a break-even of 1.208983. | none | [attack-theta-last-gap.md](history/staging/attack-theta-last-gap.md) |
| `Q-theta-selfconsistent` | ANSWERED | What does the exact-supremum theta ladder give when re-run self-consistently in H? | All five published self-consistent values reproduce exactly from two independent implementations; z = 31 is now measured at nP = 588, nP/z^2 = 0.6119, so the published 1.1776 is overstated by 1.93x, continuing the pattern, and at z = 47 a prefix walk finds the certificate failing at H = 1.0412 z^2, so the self-consistent unconditional requirement leaves the zone budget by z = 47. | none | [theta-selfconsistent.md](history/staging/theta-selfconsistent.md) |
| `Q-transition-energy-review` | ANSWERED | Does the sharp-energy chain in sharp-corner-transition.md survive an adversarial check, and do the upper norm, the small-fixed-eta lower norm and the failed negligible transition each stand at their stated scope? | All ten assigned rows survive at their stated scope; no counterexample or decisive contradiction was found. The upper norm, the small-fixed-eta lower norm and the refuted negligible L2 transition each stand separately. Two repairs are citation-level only: the integer Barban-Vehov input is Graham 1978 quoted by Chen An, and the note should record why the k=Q constant is absolute. The de la Breteche-Dress-Tenenbaum PDF was refetched and its SHA-256 matches the pinned hash; its (1.5) and Theorem 1.1 supply exactly the imported (3) and (4). eta_0 remains positive and unextracted, and the signed sums, E_out and the twin margin remain OPEN. | C | [transition-energy-review.md](transition-energy-review.md) |
| `Q-transition-energy-review-spec` | ANSWERED | What independent checks are required before the sharp-energy and non-negligible-transition conclusions can guide the next signed research attempt? | Bounded review assignment with explicit source, algebra, interval, error and quantifier checks; per-claim verdicts and dependency consequences are required. The assignment is specified, not executed. | C | [transition-energy-review-spec.md](transition-energy-review-spec.md) |
| `Q-transition-joint-budget` | PARTIAL | Can the mixed and smoothed terms be handled jointly with the transition pair, and what complete inequality would make such an estimate useful for the twin consumer? | The exact split, cutoff-average identities and separate upper budgets survive. Averaging cutoff norms after triangle and Cauchy is saturated for sufficiently small fixed eta, but signed cutoff arguments and joint cancellation are not closed. R_00 need not be estimated separately under every grouping. The short-window constraint is corrected with a bounded majorant and a safely reduced lower constant. No consumer input or signed improvement is supplied; E_out and the sufficient twin margin remain OPEN. | C | [transition-joint-budget.md](transition-joint-budget.md) |
| `Q-transition-joint-budget-spec` | ANSWERED | Can the mixed and smoothed terms be handled jointly with the transition pair, and what complete inequality would make such an estimate useful for the twin consumer? | Bounded assignment to audit the exact four-term decomposition, price a concrete joint treatment, and return a sufficient one-sided or common-scale inequality with all open terms explicit. The decomposition and existing norm budgets are inputs, not new findings. | C | [transition-joint-budget-spec.md](transition-joint-budget-spec.md) |
| `Q-transition-research-execution` | ANSWERED | How should the core research handler execute and integrate the three bounded transition assignments while retaining the central signed estimate? | Prepared execution contract with a fixed mathematical baseline, three independently assignable specs, handler-owned signed research, dependency checks, shared-file ownership, reporting requirements and stopping rules. Execution is complete; the corrected results are in transition-round-review.md and transition-round-audit.md. The specification itself supplies no arithmetic estimate. | C | [TRANSITION-RESEARCH-EXECUTION.md](TRANSITION-RESEARCH-EXECUTION.md) |
| `Q-transition-round-audit` | ANSWERED | Which conclusions of the completed transition round survive direct review, which require correction, and what research decisions remain justified? | The sharp upper norms and sufficiently-small-fixed-eta lower norms survive. The integration contained substantive errors: an omitted lower cutoff, an incorrect Mellin formula for the transition, a conflation of singleton divisor fibers with long cofactor fibers, an unpriced source representation and overbroad closures of joint or cutoff arguments. Owning notes and current records are corrected. No signed improvement or sufficient twin margin is established; the corrected cofactor and joint-correlation interfaces remain open. | C | [transition-round-audit.md](transition-round-audit.md) |
| `Q-transition-round-review` | ANSWERED | What survives the executed transition round after direct review, and what combined estimate is still missing? | The energy chain survives at its original scope; the integration's missing cutoff, Mellin representation, fiber identification, normalization and general closure claims are corrected. The exact cofactor and joint-cutoff formulations remain useful. No signed estimate, controlled region, exact cut or sufficient twin margin changed. Only the stated norm-only procedure and the arbitrary-factor fixed-shift relaxation are refuted at their specified scopes. | C | [transition-round-review.md](transition-round-review.md) |
| `Q-transition-signed-estimate` | PARTIAL | Can the signed transition kernel (E1) be estimated beyond its absolute norm budget, and if not, what exact input does the consumer need? | No signed improvement. Derived: the proper-prime-power part of R_11 is O(x^(39/40+epsilon)); the prime part is an exact beta-weighted sum over pairs of linear forms of two-point Mobius correlations with coefficients up to x^(6/25+2eta) and x^(1/20+2eta); the Cauchy budget is at most 2B*eta*x*log^2(x)(1+o(1)) and the fiber triangle budget 4*eta^4*x*log^4(x)(1+o(1)), so every existing inequality loses one of the two signs. The cutoff-difference identity converts T at pn into a sharp-window coefficient times log(p)/L plus two boundary windows; the entropy-decrement route then needs bounded coefficients, a short-interval one-point input for T and a log-weighted consumer, none available. The required one-sided input is stated exactly in section 5. The twin margin remains OPEN. | C | [transition-signed-estimate.md](transition-signed-estimate.md) |
| `Q-transition-source-match` | ANSWERED | Do the inspected divisor-correlation, shifted-convolution and averaged-Chowla statements directly supply a usable estimate for the exact transition kernel? | No direct supplier was established among the inspected statements. The cofactor exchange and Theta identity are exact, but their scalar coefficient mass is not a full bounded-class representation for T. The transition Mellin kernel requires a sharp subtraction with a 1/s tail. Fixed-divisor singleton fibers differ from potentially long cofactor fibers. The fixed-shift arbitrary-factor relaxation is refuted; broader signed and cutoff methods remain open. | C | [transition-source-match.md](transition-source-match.md) |
| `Q-transition-source-match-spec` | ANSWERED | What bounded source investigation could supply a usable signed estimate for the transition kernel, and how must its hypotheses and losses be priced? | Specification for up to three detailed source-interface assessments, including coefficient representation, scale quantifiers, normalization, separation errors and exact downstream payoff. No new theorem match or literature-absence result is claimed. | C | [transition-source-match-spec.md](transition-source-match-spec.md) |
| `Q-twin-reduction` | ANSWERED | What has the arithmetic campaign of 2026-09-05 and 2026-09-06 actually established about the twin sum, at what calibration, what exactly remains, and what would suffice? | Consolidates the checked regional reduction S=C2*x+E_dagger+O_H(x/log^H x), its sufficient unbounded-scale margins, coefficient definitions and source dependencies. Later complete smooth and centered formulations are owned by RESEARCH-HANDOFF.md and their linked derivations. No new arithmetic estimate is supplied. Imported theorem proofs retain their stated review limits; every sufficient twin margin remains OPEN. | C | [TWIN-REDUCTION.md](TWIN-REDUCTION.md) |
| `Q-two-class-lower-bound` | PARTIAL | What does the two-class LOWER bound on G2 say, and does it conflict with attack E's measured law? | The finite range cannot decide and it is not close: with both constants set to 1 the transferred bound and attack E's measured law do not cross until x = 10^7327 while the exact ladder stops at 79, so neither result refutes the other and no computation ever will. | none | [attack-lower-bound.md](history/staging/attack-lower-bound.md) |
| `Q-two-class-lower-bounds` | PARTIAL | How large can G2(x#) be FORCED to be? | The best PROVEN lower bound costs nothing, the Kalmynin-Konyagin substitution is carried out here (DERIVED, independently checked, not refereed), and the certificate ladder is MEASURED with an oracle test whose load-bearing caveat is stated on its own; against the target x'^2 and the proven x^(4.2665+eps) upper bound the question stays open. | none | [two-class-lower-bounds.md](two-class-lower-bounds.md) |
| `Q-two-moire` | ANSWERED | Do the Grain and the Scour, generated by disjoint prime alphabets, force twins to be infinite? | The provable content is exact CRT factorization: over the JOINT period the miss count is guaranteed positive, so aggregate alignment is arithmetically impossible, but that is an aggregate statement over a period vastly wider than the zone and does not reach TPC; the nearest unclaimed theorem is a two-class Jacobsthal upper bound at ANY exponent, and exponent < 2 would prove TPC outright. | none | [two-moire-argument.md](two-moire-argument.md) |
| `Q-u-frame` | PARTIAL | Does restating the Zone Postulate as one inequality in u, stepping on odd numbers rather than on primes, buy anything against the wall? | It buys form and closes off a class of dead ends, but no difficulty and no slack: the requirement ln c(p) <= 2 ln p/p is exactly what the per-prime analysis already gave and the measured ladders run at about the full rate, so this is a change of coordinates rather than of terrain. | none | [U-FRAME.md](U-FRAME.md) |
| `Q-u2-engine-depth` | ANSWERED | Is the certificate engine's operative depth heading to u = 2, and does that make TODO item 8's payout form TPC-strength? | It is not: the measured operative depth runs u = 4.191 at @17 down to 3.557 at @97 and is still falling, so the brief's conditional does not fire and item 8 is shown neither TPC-strength nor safe; a WALL-ADDRESS in the weakest sense, every figure SCRATCHPAD-GRADE. | 8 | [u2-engine-depth.md](history/staging/u2-engine-depth.md) |
| `Q-unreached-sources` | ANSWERED | What is actually in the three sources SEARCH-CONVENTIONS section 5 lists as unreached? | The 2009 SeqFan thread on A144311 does not exist, now a read negative over 19,964 archived messages with zero hits; Paseman's n is the number of distinct prime factors and at that reading his shape is asymptotically weaker than our x^{4.2665}; MathSciNet stays paywalled and unswept. | none | [audit-unreached-sources.md](history/staging/audit-unreached-sources.md) |
| `Q-usup-convention-0830` | ANSWERED | Are lemmaV-sup-extension.md's u_sup and u_sat and attack-0829n-rml-proof.md sec.4.1's CAP(z) statements about the same object (level D = z^s at s = 3.0, same moduli, weights and normalisation), so that the sec.4.1 correction in passing applies, or does a level-convention mismatch void it? | SAME object, VERIFIED at the code: both notes build the lattice through buildTerms(z, z^3), the modulus sets and Vabs(e) agree to 6.9e-18 at z = 13..23 and the count convention matches at all ten levels, the cited Ssat and u_sat reproduce on the RML lattice to every printed digit at z = 13..19 and the full-level alternative does not (19.544 against 19.602 at z = 13, 45.827 against 50.314 at z = 17); so the PROVEN cap Ssat <= CAP <= z^{2s+o(1)} applies and refutes lemmaV-sup-extension.md's asymptotic prose at lines 485-486 and 508-516 (2^pi(z) moduli, a C^pi(z) theorem as the reachable end), while sec.4.1's attribution sentence overreaches by calling that note's "reading" a shape it lists as one of two indistinguishable fits and flags as its likeliest error; neither ledger verdict line changes. | 0 | [verify-0830-usup-convention.md](history/staging/verify-0830-usup-convention.md) |
| `Q-var41` | OPEN | What does the stable law predict for Var(41), and what can the tenth Var/E point pin? | Pre-registration only, sealed and committed alone before any Var(41) engine exists: it freezes the prediction, a band taken from the law's own residuals at z <= 37, the derived z(41) prediction, and the honest statement that one more point cannot separate a limit from a drift. | 2, 9 | [var41-prereg.md](history/staging/var41-prereg.md) |
| `Q-varE-identification-0830` | PARTIAL | Can either open step behind lim Var/E = 0.45546 (the identification delta*(X - X_dec) -> 0, or the theta = 2 mean-coefficient replacement) be proven, and if not, which single inequality does not close? | Neither closes, and the two named steps are one statement (Conjecture 1 of variance-note sec.10; the model half is PROVEN in varE-limit-theorem.md). The remainder is re-split exactly at five levels: the corpus's X2 column doubles the positive half of one shift pattern (X2c = 2.66 against the group sum 0.09 at x = 19, PROVEN by rebuild), so its Xmix is overstated 2.3x; the true mixed remainder is MEASURED at -0.49 ln y and 82 % of it sits BELOW 2L, in the two-branch type, in the unbalanced range min(d,e) <= L^(2/5) (99.7 % of that cell at x = 19), outside the range of every bilinear Kloosterman-fraction bound; the divisor-distribution estimate the record names (n > 2L only) is therefore not the whole open step. Henriot's Corollary 2 (read at the page, erratum read) applies as stated and cuts the moduli to n <= L ln^(2+o(1)) y, PROVEN given that theorem; the one inequality left is the uniform o(1) equidistribution of y-friable squarefree integers in progressions to moduli up to y^(4/5), NOT SEARCHED at the page. The limit 0.45546 stays HEURISTIC. Not TPC-strength. | 9 | [attack-0830-varE-identification.md](history/staging/attack-0830-varE-identification.md) |
| `Q-varE-limit` | PARTIAL | Does lim Var/E on the diagonal window exist, and what is it? | The theta=2 mean-coefficient step is neither proven nor refuted: the replacement error is exactly a sum over shifts of W(h) - V(h), it splits into a c=0 group (needs no decoupling) and CRT-mixed lags (open); measured ratios true/model 1.0098, 1.0039, 1.0014, 1.0013 at x = 13..23 with delta(X - X_dec) ln y falling rather than settling, so the error is O(1/ln y) or better MEASURED on four levels that exclude growth and nothing finer, and the limit 0.45546 stays HEURISTIC with varE-spectral's second step, its own limit theorem, still open. | 9 | [lit-dickman-variance.md](history/staging/lit-dickman-variance.md), [lit-smooth-divisors.md](history/staging/lit-smooth-divisors.md), [varE-asymptotic.md](history/staging/varE-asymptotic.md), [varE-exact-ladder-01.md](history/staging/varE-exact-ladder-01.md), [varE-limit-theorem.md](history/staging/varE-limit-theorem.md), [varE-spectral.md](history/staging/varE-spectral.md), [varE-theta2-proof.md](history/staging/varE-theta2-proof.md), [varE-theta2-step.md](history/staging/varE-theta2-step.md) |
| `Q-vc-prior-art` | ANSWERED | Does arXiv:2208.06442 contain or overlap the VC-dimension = 4 finding of import-vc-nets? | DISJOINT at theorem level; not found there nor in the reachable one-hop neighbourhood; Helmbold-Sloan-Warmuth 1992 Thm 3.1 owed (abstract only). | none | [lit-vc-multiples.md](history/staging/lit-vc-multiples.md) |
| `Q-verify-audit-numbers` | ANSWERED | Is audit-numbers.js circular? | Not circular in the way that would matter most, since it reads no other repo script, but 15 of its 117 checks certify nothing and 17 more are artifact echoes among transcribed constants; the one bug class the charter was written against had nothing in sections A to W to fire against and still has nothing, and one from-scratch re-implementation found a check depending on an unnamed hard-coded phase choice. | none | [verify-the-verifier-numbers.md](history/staging/verify-the-verifier-numbers.md) |
| `Q-verify-cofactor-convolution` | ANSWERED | Does the cofactor-convolution identity at the anchor hold, and does it test the joint law? | RESTATED with corrections: the arithmetic is right, an independent re-derivation reproducing every figure to the digit at all five levels and confirming the asserted closed-form step, but the framing does not survive, since X is pinned by the identity X = M - Nbar + n_0 so the whole comparison collapses to one cell and the joint is measurably not a product elsewhere; the model error is 0.52 per cent, not 0.050. | X | [verify-cofactor-convolution.md](history/staging/verify-cofactor-convolution.md) |
| `Q-verify-monotone-depth` | ANSWERED | Does the Monotone Depth obstruction, which retires dial 4, survive an adversarial re-derivation? | NARROWED: every measurement in the record reproduces, several to the last digit, but the mechanism as named is false as a general law and the corpus already holds a counterexample to it; what survives is an accounting of three channels priced in tenths of a nat against a need of 6.700, 8.191 and 9.637 nats, so dial 4 becomes priced slack with one channel open and unpriced. | 0e (retired) | [verify-monotone-depth.md](history/staging/verify-monotone-depth.md) |
| `Q-verify-record-defects-0830` | ANSWERED | Do the three defect claims of 2026-08-30 (attack-0830-varE-identification.md sec.8 on the doubled X2 column; attack-0830-tail-derivation.md sec.7 on the corpus's "R + 1/2"; attack-0830-head-remainder.md sec.1 on the decade-pooled Delta = 0.6214) reproduce on independent code from the definitions, and which of the corrections they list apply? | Claim 1 CONFIRMED: the corpus delta*X2 column is the positive half of the p \| h-2 pattern doubled, that pattern's mirror is the p \| h+2 pattern (W-(-h) = W+(h) exactly, W-(h) != W-(-h) at 9 to 900,679 shifts), the group sum 2X2 reads -0.5603 .. 0.1846 at x = 7..19 against 5.7147 .. 5.3266, and Xmix is overstated 2.305x at x = 19 (6.9x at x = 7); X, X1 untouched. Claim 2 AMENDED: R + 5/2 and R + 3 are exact for the tail convention (all and odd origins, asserted at x = 7..23) and t/(R + 3) = 1.0228, but head-residual-factor.md:70 is the HEAD's forward convention where R + 1/2 and R + 1 are exact, so that correction does not apply; and p'^2 is 1 mod 6, where the tail constant is 5 (t/(R + 5) = 1.0181), with the class null (1.0157) the matched figure, so 1.0228 is one unmatched convention replacing another. Claim 3 CONFIRMED as an artefact, AMENDED on mechanism and on the half-decade reading: 0.6214 pooled against 0.6592, 0.6705, 0.6736 at 2, 4, 8 sub-windows; the between-slope (Simpson) piece the note derives is half of the pooling term (0.0187 of 0.0378 at halves, 0.0261 of 0.0522 at eighths), the other half is the within slope's own fall with height weighted by Var(g); and re-reading the halves from their eighths puts HL BELOW the measurement at 5 of 6 half-decades by 2.5 to 3.4 percent at the top decade, so "within 1.6 s.e., sign alternating" is itself a pooled statement. | Z4, 9 | [verify-0830-record-defects.md](history/staging/verify-0830-record-defects.md) |
| `Q-verify-the-verifier` | ANSWERED | Does the QC gate's alarm ring when a defect of each real class is present, rather than merely reading green? | Of the 31 blind mutations the existing selftest covers zero: it is a reachability test proving each alarm can ring, never a sensitivity test asking how far a defect must move before the alarm stops, and its fourteen controls are all obvious silences; the ranked blind spots are listed with a proposed fix each, led by out-sha256 being written and never read. | none | [verify-the-verifier-checks.md](history/staging/verify-the-verifier-checks.md) |
| `Q-w1-singular-series` | ANSWERED | What is the endpoint comb W1 in the literature's terms? | W1 is exactly the Hardy-Littlewood singular-series ratio for (0, 2, v, v+2) over the twin series squared, truncated to the folded primes and normalised by a v-independent constant, PROVEN algebraically and VERIFIED as exact BigInt-rational equality, so the fold-factor comb is the twin-twin correlation comb evaluated at v = theta_p. | none | [w1-singular-series.md](history/staging/w1-singular-series.md) |
| `Q-width-repairs` | ANSWERED | Can the five loaded containers found by the width sweeps be guarded without invalidating any embedded figure? | Forward protection only: every repair is a widening or a bound check, storage-only by construction, no corpus figure was retroactively corrupt and none moved, with maxgap-law.js at 0 of 1389 figures unreproduced and attack-foldL-01-census.js byte-for-byte on the same out-sha256. | none | [width-repairs.md](history/staging/width-repairs.md) |
| `Q-width-sweep` | ANSWERED | Which big-level enumeration and census scripts carry a fixed-width container that is safe at every level run and aliases silently above a threshold? | Three instances: two CORRUPT (the one-word residue mask that corrupted the census from x = 37 up, and a Uint16 index into the scour-prime array in the @37 census, both since fixed) and one that threw rather than aliased; every internal identity in the corrupted producer is a COUNT identity and stayed PASS throughout, because the alias corrupts which prime, not how many. | none | [width-sweep-census.md](history/staging/width-sweep-census.md) |
| `Q-width-sweep-attacks` | ANSWERED | Does the attack and analysis script family carry the fixed-width-container defect class that corrupted the @37 census? | No live corruption across 123 scripts, every stored value derived at the level actually invoked and fitting its container; one hazard is serious, attack-x-offset-02-profile.js storing an index into the scour-prime array in a Uint16Array, the identical mechanism in the identical role as the census defect fixed at 605ce83, and it fires at @37. | none | [width-sweep-attacks.md](history/staging/width-sweep-attacks.md) |
| `Q-wrap-identity` | ANSWERED | Can T4 be computed without enumerating quadruples? | Yes: the 4-point wrap identity exists and is verified through @13 against the certified value, turning @17's dead T4 (4.9e16 quadruples) into an 11-minute computation, but at a precision that certifies T4 itself and not yet the quartic bound. | none | [natal-cap-32-wrap-identity.md](natal-cap-32-wrap-identity.md) |
| `Q-wrongdirection-audit` | ANSWERED | Are any of the ten live targets secretly TPC-strength, before the sessions are spent on them? | The audit closes no target: two of the ten come out TPC-strength and three more carry a TPC-strength face under a quantifier they are likely to drift into, which is a labelling result and not a reason to drop them; item 1e is settled only because the answer was already on disk, and one route-blocking number in it is hand arithmetic and unstamped. | 1e (retired) | [attack-wrongdirection-audit.md](history/staging/attack-wrongdirection-audit.md) |
| `Q-xchan-at29-prereg` | OPEN | Does the joint-deficit closed form survive a blind test at @29? | Pre-registration only, committed alone before any producer existed: the statistic, the predictions adopted verbatim from the record, two acceptance bands, the validation gate the instrument must clear before any @29 number is reported, and what each verdict does to TODO item X. | X | [xchan-at29-prereg.md](history/staging/xchan-at29-prereg.md) |
| `Q-xchan-at37-offset` | ANSWERED | Does any registered offset-correction candidate for the ~3.8 law survive at @37? | Sealed and committed alone before any @37 census of any kind existed, fixing the candidates, the sigma model and its projection band, the scoring rule and what each verdict does to item X's offset clause; scored in xchan-at37-score.md, where every registered candidate is killed and the number survives an independent recount. | X | [xchan-at37-offset-prereg.md](history/staging/xchan-at37-offset-prereg.md) |
| `Q-xchan-at37-score` | ANSWERED | What does the @37 census say about the sealed X-channel offset pre-registration? | The census measured 1 - J = 0.020823, below every registered prediction, so scored exactly as registered every one of the seven candidates dies at \|z\| = 104 to 122 and the survivor set is EMPTY, an outcome the sealed prereg has no consequence clause for; the number itself survives an independent recount on a different marking scheme, and the offset question is replaced by a larger one. | X | [xchan-at37-score.md](history/staging/xchan-at37-score.md) |
| `Q-xchannel-at23` | PARTIAL | What is the fifth point of the X-channel statistic, at @23, and does the monotone rise hold? | The fifth point is +0.2658 at @23, the rise holds at five levels and is larger than the four-point trend predicted, and the deficit has migrated into m >= 3, whose share of the X-gap runs 10.5, 23.5 and 81.1 per cent at @17, @19 and @23; the constant itself is not derived here. | X | [xchannel-at23.md](history/staging/xchannel-at23.md) |
| `Q-xchannel-closedform` | PARTIAL | Does the zero-parameter closed form for the joint deficit survive its two blind tests at @29 and @31? | 1 - J = 4S2 is the only one of the three pre-registered laws left standing and it is not exact: a clean hit at @29, z = -0.90, and 4.93 sigma low at @31 where sigma_J falls to 0.000024, with the two rivals dying at 6.35 and 20.81 sigma; both blind levels agree on a stable relative offset of about half a percent, -0.41% and -0.48%, whose absolute residuals match to 2%. | X | [xchan-at29.md](history/staging/xchan-at29.md) |
| `Q-xchannel-offset` | PARTIAL | What produces the ~3.8 law's -0.45% offset, and which candidate correction survives? | The best available description is a finite-level correction of S3's size and sign - 1 - J = 4S2 - S3 scores z = +0.04 at @29 and -0.41 at @31 where the standing law scores -0.43 and -2.32 - but it is POST HOC; two candidate corrections and one shape are refuted on existing data, the sigma behind the @31 detection is calibrated on seven known-truth controls, and the deciding blind test at @37 is pre-registered and committed alone. | X | [item-x-offset.md](history/staging/item-x-offset.md) |
| `Q-xchannel-triples` | ANSWERED | Does the joint deficit deepen or decay as the mixed super-W triple census is extended past @17? | It decays: J = 0.9025, 0.9599, 0.9659 at @17, @19, @23, so the deficit runs 9.7%, 4.0%, 3.4%, both new points land inside the pre-registered DECAYING FASTER THAN FORCED band, and the DEEPENING instinct is refuted by 3.50 sigma between @17 and @19 and a further 1.68 sigma to @23. | X | [xchannel-triples.md](history/staging/xchannel-triples.md) |
| `Q-y2-recompute` | ANSWERED | Does the sixteen-level Y2 ladder reproduce on the corrected instrument, and does Y2/x^2 fall? | The ladder reproduces exactly, sixteen of sixteen from sixteen independent processes, digit for digit against the published 2026-08-18 ladder, and Y2/x^2 falls at 15 of the 15 consecutive steps; this does NOT show that G2(x#)/x^2 falls, since the shortfall Y2/(G2-1) is unmeasured above x = 79. | 1d | [y2-recompute.md](history/staging/y2-recompute.md) |
| `Q-z2-state` | PARTIAL | What is known about Z2, the largest gap between twin openers inside the zone (p, p'^2), and at what calibration? | Draft consolidation only, computes nothing new: the zone statement is an interval statement, the parity obstruction applies to it in full, and no proven statement about Z2 survives past the zone's own width. | none | [z2-state-draft-0829.md](history/staging/z2-state-draft-0829.md) |
| `Q-z3-immune` | CLOSED | Do the square anchor's immune offset classes (stretch-01 §4) carry a survivor surplus beyond the redistribution-only guardrail, do they attract the floor's first survivor, and does restricting the transplanted caps to them lower K*? | No, on all three. The preregistered surplus test is VOID on its own matched control (a 0.6% ratio-of-means bias present with and without the quadratic point); the preregistered placement test HOLDS at Z = +0.49; the design-free class test reads the guardrail's r/(r-2) over 3.4 million twin openers with a largest per-prime deviation of 0.11% and per-prime Z in -0.48..+1.66; and the restricted certificate, while lowering K* at 61% of anchors, has no certificate at all at 93 of 1219 and is beaten head to head by the QR-BLIND restriction that certifies 1219 of 1219. The refinement is closed. | Z3 (retired) | [attack-z3-immune-01.md](history/staging/attack-z3-immune-01.md) |
| `Q-zone-postulate` | OPEN | Is every zone occupied by a twin pair, and what is proven toward it? | OPEN: the weak form is PROVEN equivalent to the twin prime conjecture (both directions, elementary), the zone's supply is MEASURED to grow like p^2/ln^2 p with margin about p and verified by segmented sieve to 1e11, and the obstruction is named; none of the four attack routes closes it. | none | [ZONE-POSTULATE.md](ZONE-POSTULATE.md) |
| `Q-zone-tail` | PARTIAL | What is the tail field of the zone (p, p'^2) - its law against ln^2, its worst case, its share of the R0 width, and is it the frozen-sieve last survivor below p'^2 at the rate the head is the frozen sqrt(p)-level first survivor above p? | The field exists now, 1,225 zones, and nothing in it is derived. The tail is the head's own renewal functional read at height p'^2 rather than p: c_tail = 0.7771 ln^2(p'^2) at [3163,1e4) against the head's 0.6693 ln^2 p on the same zones and the same estimator, both referenced to HL's 0.7574, and the apparent factor of four is the unit ln^2(p'^2) = 4 ln^2 p and nothing else. The band drift does not settle (0.7518, 0.7288, 0.7771; the pre-registered 0.03 step is missed), so this is band composition on two decades and not a measured convergence. The frozen-sieve mirror is 100% at the zone's own level p, but that is the Zone Restriction Lemma restated and not a rate comparable to the head's 96.65%; the non-vacuous mirror is one fold back, where the tail survives at 98.69% with the residual priced exactly (88 extra lpf(n) = p survivors, 18.18% of them biting), and the head's own frozen level sqrt(p) identifies the tail in only 22.86%, refuting this note's own pre-registered [0,5] zones. The renewal surplus t/R = 1.0619 at B4 is NOT RESOLVED, its bootstrap [0.9937, 1.1321] containing 1, and an exhaustive class-matched origin null over 5,962,057 origins gives the same 1.0619; three matched non-square endpoints see no difference at all, sign tests z = 0.14, -0.54, 0.66 with six paired intervals all containing zero, so nothing here is a property of the endpoint being a prime square. R0 is asserted at all 1,225 zones and the shares are 1.82% head, 89.72% Z2, 8.46% tail at B4 with the tail's share FALLING, so filling the tail row moves the decomposition's difficulty nowhere: Z2 was the obstruction before and is more of it after. | Z4 | [zone-tail-01.md](history/staging/zone-tail-01.md) |
| `Q-zone-tail-02` | ANSWERED | On the full zonegap-01 range to 1e11, what is the per-zone tail law in both units, is the renewal surplus t/R real at 27,292 zones, and do the head and the tail of a zone have a joint law? | Resolved DOWN and nothing is derived: zone-tail-01's unresolved t/R = 1.0619 at 782 zones reads 1.0298 on a height-matched comparator at 17,700 zones (bootstrap [1.0156, 1.0443], excluding 1) and 1.0157 against the exactly matched discrete class null (bootstrap [1.0013, 1.0308], clearing 1 by 0.0013), so part of the original figure was the comparator and the pre-registered rule returns MATCH by two parts in ten thousand; c_local = 0.7522 at the top band with bootstrap [0.7410, 0.7630] now CONTAINING HL's 0.7574 and the band drift inside the registered 0.03 per step for the first time but still non-monotone (0.7518, 0.7664, 0.7416, 0.7522), so no convergence is measured; global worst tail/ln^2(p'^2) = 6.840 at p = 15107 with max/mean no longer flat (4.40, 5.36, 8.59, 8.43); Q5 is answered in the negative, head and tail showing no dependence at 27,292 zones (detrended r = -0.0009 against null s.e. 0.0061, permutation p = 0.8920, variance ratio 0.9990, no KS rejection, no chi-square near threshold), so the R0 pieces are a product structure to first and second moments and in the sum's whole law while independence is NOT proven and the simultaneous-extremes regime is untouched; a candidate rough-origin mechanism for the surplus is HEURISTIC and does not fit the head's own excess band by band; the head field's effective sample size is measured at 1,910 distinct a_first among 17,700 top-band zones, so this note's own head interval is priced over draws the field does not hold, a cluster bootstrap over distinct a_first (producer SEC I(a), seed 613009117) measuring the inflation at 4.10 rather than the 3.04 the redundancy alone implies and moving the top-band interval to [0.6848, 0.7692], still inside the registered [0.68, 0.78] (correction originating with redteam-0829-measure-b.md section 1c C15); the scope of that defect is that one interval and not the corpus, since destroyer-census-01.md publishes no bootstrap, head-residual-factor.js bootstraps over gaps, zonegap-01.js has none and zone-tail-01.js bootstraps only tail quantities; ten of ten predictions hit, which is a criticism of the pre-registration; and the R0 shares read 1.40% / 92.80% / 5.81% with the tail's share still falling, so Z2 is more of the obstruction after this pass than before it. | Z4 | [zone-tail-02-0829.md](history/staging/zone-tail-02-0829.md) |
| `Q-zonegap-01-prereg` | SUPERSEDED | What is Z2(p) in the unswept half-decade p in [1e5, 316228)? | Pre-registration only, committed before the X = 1e11 sweep ran: five predictions are sealed on the per-zone distributional structure the published record ladders do NOT determine, with the records excluded from scoring and used as custody instead; the scoring document is the stage-2 embedded output, in zonegap-01.md. | none | [zonegap-01-prereg.md](history/staging/zonegap-01-prereg.md) |
| `Q-zonegap-03-prereg` | OPEN | What is Z2(p) in the unswept decade X in (1e11, 1e12]? | Pre-registration only, sealed before any sweep past X = 1e11 exists: five theorem-grade predictions at sigma = 0 (resting on Z2(p) = env(p) identically, a two-line theorem conditional on the adopted ladder being the true running max) and five blind statistical ones with sigma models and kill rules, scored by the stage-3 embedded output with misses stated first. | none | [zonegap-03-prereg.md](history/staging/zonegap-03-prereg.md) |
| `Q-zonegap-03-score` | ANSWERED | Do the ten predictions sealed in zonegap-03-prereg.md score against the stage-3 sweep at X = 1e12? | All ten sealed rows score HIT and none miss, after a second pass added a band-edge argument to zonegap-01.js and re-ran the decade so the two rows that named an unprinted band could be scored; the four Group T hits are a custody promotion that follows from CUSTODY 1 and 3 passing, one sub-clause of T5 (the full-decade sd) stays unprinted, and the sweep still needs a DERIVED engine because zonegap-01.js's inlined 41-record ladder makes it exit at 1e12. | Z7 | [zonegap-03-score.md](history/staging/zonegap-03-score.md) |
| `Q-zonegap-Z2` | PARTIAL | What is Z2(p), the largest twin-pair gap inside the zone (p, p′^2), measured at every zone to 1e11? | MEASURED to 1e11 over 27,292 zones: every zone holds at least two twin pairs, Z2 is the record envelope wearing zone coordinates, Z2(p) <= G2(p#) is a one-line theorem with equality only to p = 7, and the zone-local margin runs away like p^2/(3.9 ln^3 p); the pre-registration scored 2 of 5. | none | [zonegap-01.md](history/staging/zonegap-01.md) |
| `Q-zonegap-model` | ANSWERED | What is Z2 once decomposed, and does the per-zone field carry anything the record ladder does not? | Z2(p) = env(p) with D(p) identically zero (PROVEN conditional on the adopted ladder, VERIFIED 204 ways), so the per-zone field is the record ladder wearing zone coordinates and the u bimodality is closed; the blind tests for the [1e11, 1e12] decade are sealed and the sweep itself is not run. | none | [zonegap-03-model.md](history/staging/zonegap-03-model.md) |
| `Q-zonegap-prior-art` | ANSWERED | Who owns Z2(p), the maximal twin-prime gap below a quadratic cutoff, in the owning conventions? | Kourbatov (2013) and Kourbatov-Wolf (2019) own maximal twin-prime gaps, with heuristics and records and nothing proven; the zone form (p, p′^2) has five neighbours and no owner, and the per-zone quadratic-cutoff object appears absent on channels calibrated in the same session. | none | [zonegap-prior-art.md](history/staging/zonegap-prior-art.md) |
| `Q-zonegap-reduction` | PARTIAL | What must be proven for Z2, what already is, and what does the proven head machinery give the zone? | The Zone Restriction Lemma is proven and verified at five levels - the in-zone twin slots of T_p ARE the in-zone twin primes, so Z2(p) IS the whole-tile gap object restricted to the head window - the three-slack chain is graded honestly, the transfer inventory is listed item by item, and the deep end is proven an onset desert over 24 levels; section 5 lists what was not reached. | Z (retired) | [zonegap-02-reduction.md](history/staging/zonegap-02-reduction.md) |
| `Q-zonegap-witnesses` | ANSWERED | Do independent second witnesses confirm the twin-gap record table, and does the due OEIS flip-search turn anything up? | Both witnesses AGREE at 82/82 rows with no extension and no conflict and the lesser-to-lesser convention verified rather than assumed; the OEIS check returns one loud hit, the per-zone pair-count sequence being A273257 one index over, while the gap objects stay absent, and one literature item, Korevaar 2012, is still walled and read only by arXiv proxy. | none | [zonegap-witnesses.md](history/staging/zonegap-witnesses.md) |

## 3. Unindexed notes (0): title only, until a block is added

*(Legacy notes written before the ledger existed. A grep for the object still
lands here. Add a block when a note is next touched; `node research/qc.js
ledger-backlog` lists them.)*