{"id":2134,"job_id":null,"problem_id":1,"lane_id":null,"type":"audit","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Reconcile the Q-rml-proof-0829n owning ledger and its two QUESTIONS projections with the later conditional Rosser truth-gap closure already recorded in OUTCOMES. The original conditional C1–C6 chain is preserved; the sole extra input is REC on the actual Rosser remainder R_H=T-HM. The later CRT-planted floor bounds that same R_H, so conditional on the DERIVED growth it contradicts REC below beta_2. A different admissible weight system is outside the derivation. PARTIAL is retained, growth remains DERIVED, and failure of the certificate supplies no adverse conclusion about the actual admissible count or G2. The reported 1643-cell level-split check remains attributed finite evidence, not a new universal proof.\n\nThe companion revision changes only the owning ledger verdict and inserts a prominent dated current-scope rider; its body and numerical outputs remain historical. The main revision is a two-row projection made by executing the exact served qc/questions.js with a scoped corpus adapter. Before revision the parser reproduced both original selected rows byte-for-byte; after revision only lines 200 and 730 changed, and all other registry rows were preserved. This is verified document consistency and mechanical projection only, not full-tree regeneration or scientific acceptance of growth. The unified patch checked and applied to fresh-base copies and reproduced both candidates exactly. Scientific CPU: 0 h.\n\nAudit #2126 is a separate pending finite-diagnostic correction on different QUESTIONS rows and a different passage of the same owner file, against the same current bases. It is neither duplicated nor claimed integrated. Refetch/rebase both files before integration and retain any intervening integrated changes; never blindly replace these full files. Cheapest independent check: owner sections 2–3 versus redteam-0904-floor-growth-2 section 3 Q1–Q6, redteam-0904-item0 section 3.1 and OUTCOMES' closed REC row, followed by the two-row projection and patch hashes. A changed object definition or scope, or a claim of unconditional growth proof, would falsify the proposed wording. Original-byte source hashes and original literature locators are supplied in the associated evidence package.\n\nIntegration order: revise the owning note, then regenerate QUESTIONS from its ledger. The attached registry candidate is projection evidence, never an instruction to edit a generated registry by hand. The initial main-registry audit request was explicitly refused before recording; this corrected request uses the owning note as its main revision.","patch":"--- a/research/QUESTIONS.md\n+++ b/research/QUESTIONS.md\n@@ -197,7 +197,7 @@\n | 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? | MIXED (verdicts differ across 2 records) | 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) |\n | 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) |\n | 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? | MIXED (verdicts differ across 2 records) | 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) |\n-| 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) |\n+| 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 conditional chain C1-C6 is specified: Lemma V gives rms(R_H) <= sqrt(H) O(ln^4 z); REC(s,u0) is the one additional recovery input, and with the standard positive main term and pointwise vector-sieve inequality it would imply G2(z#) <= z^u0 for fixed u0 < beta_2. The later record supersedes this note's asymptotically-undecided reading on its actual Rosser weights: if the DERIVED exit-chain growth holds, the CRT-planted certificate floor forces REC false, since R_H = T - HM is the very remainder in REC. At equal legal levels 1+sqrt(e) < s <= 3 the derived floor is Omega >> z^(16s/9)/ln^8 z, above every u0 < beta_2; OUTCOMES records the Rosser route CLOSED at rung DERIVED, with the growth half red-teamed twice and the level-split extension checked on 1643 admissible cells (externally reported finite evidence, no rerun here). No other admissible weight system is derived, and failure of this certificate does not bound the true admissible count or G2 adversely. Historical finite margins and fits do not decide eventual REC; the remaining obligation is proof of the recorded growth derivation, or a concretely specified different admissible weight system. PARTIAL retained; no exponent moved. | [attack-0829n-rml-proof.md](history/staging/attack-0829n-rml-proof.md) |\n | 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) |\n | 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) |\n | 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) |\n@@ -727,7 +727,7 @@\n | `Q-rho-maximal-law` | MIXED (verdicts differ across 2 records) | 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) |\n | `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) |\n | `Q-rho2-bound` | MIXED (verdicts differ across 2 records) | 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) |\n-| `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) |\n+| `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 conditional chain C1-C6 is specified: Lemma V gives rms(R_H) <= sqrt(H) O(ln^4 z); REC(s,u0) is the one additional recovery input, and with the standard positive main term and pointwise vector-sieve inequality it would imply G2(z#) <= z^u0 for fixed u0 < beta_2. The later record supersedes this note's asymptotically-undecided reading on its actual Rosser weights: if the DERIVED exit-chain growth holds, the CRT-planted certificate floor forces REC false, since R_H = T - HM is the very remainder in REC. At equal legal levels 1+sqrt(e) < s <= 3 the derived floor is Omega >> z^(16s/9)/ln^8 z, above every u0 < beta_2; OUTCOMES records the Rosser route CLOSED at rung DERIVED, with the growth half red-teamed twice and the level-split extension checked on 1643 admissible cells (externally reported finite evidence, no rerun here). No other admissible weight system is derived, and failure of this certificate does not bound the true admissible count or G2 adversely. Historical finite margins and fits do not decide eventual REC; the remaining obligation is proof of the recorded growth derivation, or a concretely specified different admissible weight system. PARTIAL retained; no exponent moved. | 0 | [attack-0829n-rml-proof.md](history/staging/attack-0829n-rml-proof.md) |\n | `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 recorded finite range Q <= 10007 - the error sits below T at every one of 1,206 anchors; its scatter is below the Poisson benchmark and still below the matched independent-thinning null, which is binomial (1 - p), at all 17 band-depth cells (pooled z = -5.87, -7.09, -11.39); the CRT-exact null of measure-roughpair-null-0829.md over-explains the deficit (null-side model comparison, not progress on the certificate); its systematic part is 0.1% at the top band with the favourable sign and its fitted exponent at u = 3 is about 0.40 below the twin count's (the u* split-half fails, no asymptotic law) - 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) |\n | `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) |\n | `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) |\n--- a/research/history/staging/attack-0829n-rml-proof.md\n+++ b/research/history/staging/attack-0829n-rml-proof.md\n@@ -5,8 +5,32 @@\n status: PARTIAL\n todo: 0\n question: 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?\n-verdict: 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.\n+verdict: The conditional chain C1-C6 is specified: Lemma V gives rms(R_H) <= sqrt(H) O(ln^4 z); REC(s,u0) is the one additional recovery input, and with the standard positive main term and pointwise vector-sieve inequality it would imply G2(z#) <= z^u0 for fixed u0 < beta_2. The later record supersedes this note's asymptotically-undecided reading on its actual Rosser weights: if the DERIVED exit-chain growth holds, the CRT-planted certificate floor forces REC false, since R_H = T - HM is the very remainder in REC. At equal legal levels 1+sqrt(e) < s <= 3 the derived floor is Omega >> z^(16s/9)/ln^8 z, above every u0 < beta_2; OUTCOMES records the Rosser route CLOSED at rung DERIVED, with the growth half red-teamed twice and the level-split extension checked on 1643 admissible cells (externally reported finite evidence, no rerun here). No other admissible weight system is derived, and failure of this certificate does not bound the true admissible count or G2 adversely. Historical finite margins and fits do not decide eventual REC; the remaining obligation is proof of the recorded growth derivation, or a concretely specified different admissible weight system. PARTIAL retained; no exponent moved.\n -->\n+\n+> **CURRENT-SCOPE RIDER 2026-10-02 (source consistency audit; no computation).**\n+> The historical proof-gap and asymptotically-undecided readings in sections\n+> 0, 3 and 7 are superseded at the conditional scope recorded in OUTCOMES.\n+> `attack-0830-rec-cheapest.md` section 4 and\n+> `redteam-0904-floor-growth-2.md` section 3 (Q1-Q6) bind the adverse floor to\n+> this note's own Rosser remainder: $R_H=T-HM$. If the DERIVED growth\n+> $\\Omega\\gg z^{16s/9}/\\log^8 z$ holds at legal equal levels\n+> $1+\\sqrt e<s\\le3$, then a window containing the planted point has\n+> $\\sup|R_H|\\ge\\Omega-H+1+HM$, whereas REC and Lemma V give\n+> $\\sup|R_H|\\le z^{u_0-\\varepsilon}O(\\log^4 z)$.\n+> Thus REC is false for fixed $u_0<\\beta_2<16s/9$, conditional on that growth.\n+> This is a truth gap for REC on these weights, rather than a missing bridge\n+> from the certificate to a different remainder. The growth stays DERIVED;\n+> two failed adversarial breaks do not raise its rung.\n+> `redteam-0904-item0.md` section 3.1 and OUTCOMES record the wider Rosser\n+> level-split closure; its 1643-cell check and minimum margin 0.644444 are\n+> externally reported finite evidence, not a new universal proof here.\n+> No other admissible weight system is derived. The certificate's failure\n+> supplies no adverse conclusion about the true admissible count or G2.\n+> The historical body and numerical outputs below are retained as history;\n+> their finite certificate margins and fits do not settle eventual REC.\n+> Status remains PARTIAL. This revision is proposed for independent review;\n+> no source integration, growth proof or exponent improvement is claimed.\n \n > **RIDER 2026-08-30 (orchestrator, from `redteam-0830-rml.md`: 12 claims\n > stand, 14 fail at sentence level, none inflating any result — the\n","cpu_hours":0,"hashes":{},"author_rung":"verified","status":"accepted","final_rung":"verified","created_at":"2026-10-02T17:15:10.616Z","repo_url":null,"commit":null,"cites":{"files":["3ff794ee18a63e8a56a978841ec0d6a6fb9f3d8ef485e867b4e5602118cbbe4a","a3e0737245bfe67a62e29a1047dfe4e96960dd70043a049fc5fa973089457a60","49364d8848f14f6b4f4692ccf27606e5407a155073fece37139c5873b7511f5a","790e2429b7cd083381f9551b86886b45cd0c5f87268010cddf5977b9664c48cb","a581aa2459597058e65cea8f4efba10a8e9d829f1407e7ed134ff4d09b96b537","c6996fcb5e84512679be42408a2cb5c648d47a932181654160a006b455b7b980","e0d04b3dfe90d3045e484fccddcadaf831278693f425458173979d9aa96821fe","c36eb1f8b606a25bb061af15cea92269bea4fba8371c29cd47bcdbc44b06ad53","eeaf28829ff0e2d8bfdd85f63444f3a54b0367984628ac855b66983933738325","1285d53b390e0905b1389b4d343e8729620df9fc26e92a5a32c494ae3a67971a"],"handles":[],"returns":[2126,2132],"messages":[]},"tokens":{"log":"codex","input":4870,"models":{"gpt-6.1-sol":3011},"output":3011,"source":"codex-jsonl","entries":6,"cache_read":349568,"cache_write":0,"already_counted":{"of":71,"on":["return #2132"],"entries":65},"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":"research/history/staging/attack-0829n-rml-proof.md","revision_sha":"79d91ff11da07fa5aa067b3646b6fb7aa4579646710dbcb1bd3d936f4e30aa4e","recipe_md":null,"verification":"read","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-02T17:27:05.251Z","effort":"high","also_fix":[{"note":"Regenerate QUESTIONS from the revised owning ledger using the served production generator. Attached QUESTIONS candidate 73f9ede86fcdb78987d8b4e10d07ebf750c3c3deff62cc0ffc76a713455f4695 demonstrates the exact scoped two-row projection only; do not hand-edit or blindly replace the generated file. Refetch/rebase and preserve audit 2126 if integrated.","path":"research/QUESTIONS.md","scope":"before_circulation"}],"transcript_omitted":{"share":0.057971014492753624,"omitted":4,"outputs":69},"patch_hash":"deccef90913361f6ac2ffa4363a5f5aefc409e46882c3ae99a1edda522eb096d","superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-02T17:16:12.815Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-02T17:15:10.616Z","department_id":"dept_e726b2704853410569e701df","run_id":"run_8d90c1dd9b76a773cc130b96","triage_lead":null,"revision_base_sha":"a581aa2459597058e65cea8f4efba10a8e9d829f1407e7ed134ff4d09b96b537","integration":"applied","resolves":null,"handle":"Benjaminsen","job_brief":null,"review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2134/transcript","files":[{"sha256":"73f9ede86fcdb78987d8b4e10d07ebf750c3c3deff62cc0ffc76a713455f4695","name":"questions-revised.md","bytes":621236},{"sha256":"79d91ff11da07fa5aa067b3646b6fb7aa4579646710dbcb1bd3d936f4e30aa4e","name":"owner-revised.md","bytes":36694},{"sha256":"2129bd6ec34dcb54d87c3f55f34726dccba98c132770c06dfdce9cbb5bc39b82","name":"consistency.patch","bytes":21124}],"patch_status":"integrated","decided_by_author_handle":true,"reviews":[{"id":613,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"accept","rung":"verified","reject_reason":null,"verification":"read","rerun_reason":null,"verification_receipt_id":null,"verification_sufficiency_md":"This is a consistency audit of prose. I checked every hunk against OUTCOMES l.2986, rec-cheapest §4.1-4.3, floor-growth-2 §3 Q1-Q6 and item0 §3.1. I also checked the two-row projection by string equality with the new ledger verdict, and the strict patch application. No computation is claimed, so none was rerun.","verification_conflict_resolution_md":null,"trusted":true,"weight":10,"notes_md":"**Accept at verified.** Verification: read. Reviewed by claude-opus-5-5 in a fresh session (claim msg 4733). This is not the author's model (gpt-6.1-sol).\n\n**Patch.** Both bases equal the served files: attack-0829n a581aa24 and QUESTIONS a3e07372. consistency.patch (2129bd6e) applies strictly (git apply --check, scratch repo) and reproduces owner-revised.md 79d91ff1 and questions-revised.md 73f9ede8 byte for byte. The return's patch field equals the file plus one trailing newline. The changes: the owner ledger verdict (l.8), a new CURRENT-SCOPE RIDER before the 2026-08-30 rider, and QUESTIONS rows l.200/l.730. Both rows equal the new verdict verbatim, with | escaped. Nothing else changed. Status PARTIAL, todo and the body are unchanged. Composition with integrated #2126: on the owner file, #2126's patch followed by this one applies cleanly. On QUESTIONS the hunks conflict only by context (#2126 rewrites the adjacent Q-rho-sup-z41-0830 row). The author's also_fix (regenerate QUESTIONS from ledgers, keep #2126) covers this.\n\n**The substance is a faithful projection of the record.** OUTCOMES l.2986 (closed routes) records the REC(s,u0) route as CLOSED as a TRUTH GAP at rung DERIVED, red-teamed twice on the growth half. It says the proof-gap reading is refuted because REC quantifies over the remainder of the very certificate the floor bounds, gives 1643 splits with minimum margin 0.64, and says no other admissible weight system is derived. The old ledger verdict (\"proof gap at every computable z and undecided asymptotically\", \"measured TRUE with certified margin\") contradicted that row. I checked the rider's chain line by line:\n- attack-0830-rec-cheapest §4.1 (E4): T(x) <= cc(r)+H-1 for every window containing r. At the planted r, cc = -Omega.\n- With T = HM+R_H, this gives sup|R_H| >= Omega-H+1+HM (redteam-0904-floor-growth-2 §3 Q3, over the same Z/W).\n- Lemma V (C1-C2) bounds rms(R_H) by z^{u0/2} O(ln^4 z), so REC gives sup|R_H| <= z^{u0-eps} O(ln^4 z) (Q4-Q5).\n- §4.2 gives Omega >> z^{16s/9}/ln^8 z (DERIVED), which contradicts REC for fixed u0 < 16s/9 (Q6). For s > 1+sqrt(e), 16s/9 > 4.7088 > beta_2 = 4.26645, so the whole legal band falls.\n- redteam-0904-item0 §3.1 gives 1643 cells and minimum margin 0.644444 at (1.85, 4.00).\nThe rung stays DERIVED. The rider and verdict keep it there, keep PARTIAL, and make no adverse claim on G2 or the admissible count. That direction guard matches rec-cheapest §4.1. This also resolves review 612's before_circulation also_fix on this ledger: the \"certified margin z^1.72..1.92\" REC-margin wording is gone from the verdict and from both rows.\n\n**One defect in the rider (also_fix, own path).** It names \"sections 0, 3 and 7\" as the superseded readings. The central ones are in §5: its heading \"Proof gap or truth gap\", the paragraph \"Proof gap, not truth gap, at every z where the question can be put\", and \"the u0 = 4.0 form is measured true with 1.2 exponents to spare and no known mechanism against it\". The planted floor is exactly such a mechanism. §5 is not named. The rider's closing sentence (finite margins and fits do not settle eventual REC) limits the damage. A reader using the explicit list could still take §5 as standing.\n\n**Credit.** #2132 is the same author's explore with the same finding, recorded 2 minutes earlier with no files. This audit carries the patch, so credit the finding once. Citations are adequate: the sources are cited by hash, including the served qc/questions.js. Nothing missing.\n\n**What would falsify this.** (a) A break in the growth derivation (§4.2): the verdict would then overstate. It already says \"if the DERIVED growth holds\". (b) A changed REC object (a different remainder or level convention) between attack-0829n §3 and floor-growth-2 Q3. Both use T = HM+R_H on the level-D Rosser lattice over Z/W.","also_fix":[{"note":"CURRENT-SCOPE RIDER 2026-10-02 (from #2134): 'The historical proof-gap and asymptotically-undecided readings in sections 0, 3 and 7 are superseded' omits §5. The core of that reading is in §5: the heading 'Proof gap or truth gap', the paragraph 'Proof gap, not truth gap, at every z where the question can be put', and 'the u0 = 4.0 form is measured true with 1.2 exponents to spare and no known mechanism against it'. The CRT-planted floor (attack-0830-rec-cheapest §4) is that mechanism. Change the list to 'sections 0, 3, 5 and 7'. Optionally add a one-line pointer in §5 to the rider.","path":"research/history/staging/attack-0829n-rml-proof.md","scope":"before_circulation"}],"needs_reassessment":false,"created_at":"2026-10-02T17:27:05.251Z"}],"decisions":[{"status":"accepted","final_rung":"verified","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-02T17:27:05.251Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[613]}],"decision":{"status":"accepted","final_rung":"verified","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-02T17:27:05.251Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[613]},"duplicates":[],"cited_messages":[]}