## 2026-08-17, wave 2 partition D: the entry path *(Staged entries for `research/history/CHANGELOG.md`, in its house form. Written by the applier of partition D of the consistency campaign; the parent merges them. Sources: `qc-arch.md`, `qc-status.md`, `qc-numbers.md`, `qc-compound.md`, `qc-refs.md`, `qc-history.md`, adjudicated in `qc-CAMPAIGN.md`.)* ### research/README.md **The whole document.** REPURPOSED from a summary into the research directory's router, per Chris's ruling recorded in `qc-CAMPAIGN.md`. As it stood it was an accurate summary of the work as of **2026-08-13** wearing the filename a fresh agent opens first: a grep of it for U-FRAME, G2-STATE, ZONE-POSTULATE, FOLD-PROFILE, THE-DIALS, THE-LENS, natal-cap, anchored-note, 4.2665 and the bare string "4.26" returned zero hits on all ten. It now holds a question-to-file table, a file table with a live/spent/register status column, the naming convention, the house rule and the `history/` warning, and the six-script measurement table with the script filenames added. **The displaced prose is not deleted**: it is preserved in full, with a table saying which document now owns each section, in `research/history/staging/changelog-add-D-readme-prose.md`, for filing beside `CHRONICLE.md`. Forced by `qc-arch.md` recommendations 4, 5 and 20 and diagnosis (a), (b) B1 and (f). **§"The proven spine" items 1, 2, 3, 5.** SUPERSEDED as a list of this repository's results. Items 1 and 3 are Holt and Rudd arXiv:1408.6002 Thm 2.3, item 2 is the classical sieve p² rule (Pritchard 1982), and item 5, Zone Equivalence, is a framing biconditional that `research/PRIOR-ART.md` instructs be presented as a framing device rather than a result. The section moved to history; the attribution now sits at the point of use in `README.md` §Status. Forced by `qc-status.md` C-2 and C-3. **§"The ten attacks", the attack-4 bullet.** Its two numbers — the Fourier budget growing ~2ⁿ and the 18% near-miss at p = 11 — are outputs of the column that `research/attack-04-fourier-budget.js`'s own banner invalidated, and the corrected artifact `natal-cap-02-fourier-budget.js` reverses the conclusion. Recorded in the displaced-prose file rather than carried forward. Forced by `qc-papers2.md` P-1. ### README.md **"Proven: Copying Theorem, Redundancy Lemma, Crystallization, Euclid-in-moiré, Zone Equivalence, …".** SUPERSEDED. The first four are classical and now carry their citations inline; **Zone Equivalence is removed from the list entirely** and the reason is stated — it is an equivalence between our target and TPC, so listing it beside the Copying Theorem invites a reader to count a restatement of the problem as progress. The content stays where it is used, `ZONE-POSTULATE.md` §2. Chris's ruling, via `qc-status.md` C-1 and C-3. **"The natal-cap campaign … added nine more: … the Fused-Window Calm Lemma …".** SUPERSEDED, and this was the campaign's worst scope inflation. Eight proven results, not nine: the anchored calm is a measured phenomenon whose mechanism is proven, whose effect is certified at six levels @11..@29, whose **uniform-in-q form is REFUTED**, whose all-x form is open behind a door reaching about a tenth of the mass, and whose last leg is measured at ≈ 0.94 with no proof mechanism in sight. The refutation had never reached any summary. Pointer added to the new status parent `research/anchored-calm.md`. Forced by `qc-status.md` B-2 and `qc-compound.md` CC-1. **"the first beyond-Chebyshev ensemble bounds" (plural).** RETIRED. Exactly one exists, at @11. @13 is listed as a next step in `natal-cap-21-beyond-chebyshev.md` with an expected value and was never run; @17 never started. Forced by `qc-status.md` B-3 and `qc-CAMPAIGN.md` Decision 2. **"the X-limitation Theorem" (unqualified).** SUPERSEDED, and the correction is larger than the reports first thought. Three documents said "proven from x = 13 upward"; reading 3 of `research/natal-cap-31-calm-vs-kill.js` marks the theorem proven **per level**, from L2 plus the *enumerated* max VR, at @11, @13 and @17 only, and **no level-uniform bound on VRmax exists**. So "from x = 13 upward" is an extrapolation off two measured trends rather than what is proven. `README.md`, `GLOSSARY.md` and `TODO.md` item X now state the per-level scope with the all-x case open and the missing ingredient named. This downgrades `qc-status.md` B-3, which carried HIGH confidence on the wider claim on the strength of three summaries agreeing — and all three descended from the same home, which is the failure mode `qc-compound.md` CC-11 predicted. Forced by the artifact read. **Map row for `paper/beta2-note.md`, "with the matching lower bound".** RETIRED. The bounds are exponent ≈ 4.27 and exponent 1 + o(1); they do not match, and the band between them is the repository's central fact. The row contradicted §Status eleven lines below it. Forced by `qc-status.md` B-4. **§Status, "the whole conjecture is the positivity of the anchored bias β(x)".** SUPERSEDED. What is proven is one-way: liminf β > 0 ⟹ TPC. No converse is proven or claimed, so β's positivity is at least as strong as TPC and may be strictly stronger, and writing it as an identity makes the target look easier than it is. The weakest sufficient statement the corpus owns — one anchored survivor at infinitely many levels — is now named. Forced by `qc-compound.md` CC-2. **Map, and the first-read pointer.** "`research/GLOSSARY.md` — read this first" RETIRED: the glossary is a lookup document and, until this campaign, the file a first-time reader was sent to carried the wrong open problem. The Map gained `ZONE-POSTULATE.md`, `U-FRAME.md`, `THE-DIALS.md`, `THE-LENS.md`, `FOLD-PROFILE.md`, `TODO.md`, `SCRIPTS.md` and `qc/README.md`, all previously absent, and a "Where to start" block naming the one reading path. Forced by `qc-arch.md` (a) and recommendation 6. ### research/GLOSSARY.md **"Lemma V — the one missing ingredient on the exponent road".** SUPERSEDED, and it was the most expensive misdirection in the corpus for a planner. At the measured working point s/u ≈ 1.2, which is outside the range s ≤ u that Lemma V is stated in, so proving Lemma V as stated would not reach the regime the ladder sits in. The operative unproven input is a **Gaussian Maximal Law for the interval sawtooth**, which now has its own glossary entry and its own name; four documents including the home said so already. Forced by `qc-status.md` A-1, `qc-compound.md` CC-7, `qc-papers2.md` P-3. **"Hyperuniformity", the Var/E tail.** SUPERSEDED. The bullet spliced three objects: the comb-restricted ladder 0.152 → 0.396, the full process's scaling law ln(Var/E) ≈ −(0.24u² + 0.13u), and the comb's 0.611 limit hypothesis. Read as one object it contradicted itself, since that law at u = 2 gives 0.290 while the full process only reaches 0.321 by y = 2003. The two ensembles are now stated separately, and 0.611 is marked as the hypothesis it is. Forced by `qc-numbers.md` Q1.1. **"Unification Law — one curve governs …".** Gained the calibration and the attribution it never carried: MEASURED to ~1%, Hardy-Littlewood-conditional, and ω(u) is Buchstab's survival function. Forced by `qc-status.md` C-5 and B-1. **"The skeleton", "certified in exact BigInt at @11 through @23".** SUPERSEDED: six levels, @11 through @29, confirmed by the clean re-run of `natal-cap-36-skeleton-door.js --at29` reproducing G30_agg = 0.1176. The entry now separates three objects that shared one name — the Skeleton Collapse Theorem (PROVEN, all x, all q), the Aggregate 30-Skeleton Bound (CERTIFIED, six levels) and the Skeleton Equidistribution Conjecture (OPEN). Forced by `qc-status.md` F-1 and `qc-compound.md` CC-1, CC-11. **"The anchored calm" and "Fused window".** Both now name the claims underneath them and point at `research/anchored-calm.md`. The rule is recorded in the entry: the anchored calm is a phenomenon, never a claim, and there is no "Fused-Window Calm Lemma". **"Anchored bias β" and "Assumption A".** The bolded sentence "The whole Twin Prime Conjecture is the positivity of this one number" RETIRED, for the reason given under `README.md`. "Assumption A" now carries the rule that it is never written bare: every occurrence names the weak or the sharp form. **Header.** The instruction "read THE-LENS.md first" RETIRED; a declared scope replaces it, saying that the glossary is a lookup document, is not a first read, and owns no route's status. The adoption dates STAY, because `research/README.md` relies on them to tell readers that older files use older vocabulary (`qc-history.md` U3). The campaign narrative in the anchored-layer heading goes. ### TODO.md **Item 000b, "An afternoon with three papers".** LEFT the file per the charter, **CLOSED by inspection of the sources rather than done.** Its premise, that Kanold, Stevens and Paseman each prove one-class exponent-(2+ε) bounds with stated constants, is false for all three: Kanold gives 2^{√k}, Stevens k^{Θ(log k)} and Paseman k^{O(log log k)}, none of them an exponent-2 statement. At the primorial k = π(x) ~ x/log x, so g(x#) < x′² needs Iwaniec's shape and nothing weaker. The k^{2+ε} result is **Vaughan 1977** for general n, with Iwaniec 1971 Thm 2 already covering the primorial case, both with inexplicit constants. So the explicit- constant route does not exist in this literature and route A's second difficulty floor does not collapse. Forced by `qc-refs.md` W7, which read the sources. The consequence is applied in `ZONE-POSTULATE.md` §6 and `THE-DIALS.md` §6, which carried the same loose end. **Parked item "G₂(41#) … about 40× the 37# runtime, roughly 37 hours".** SUPERSEDED and PROMOTED out of Parked to item 1b. The 37-hour figure prices the lattice walk, which scales by tile width (54 min × 41). The streaming leg scales in slots and `U-FRAME.md` §8 records it recovering G₂(37#) = 528 from T₃₁'s 6,226,553,025 slots in 519 s; the slot ladder D_x = ∏_{3≤p≤x}(p−2) gives T₃₇/T₃₁ = exactly 35, so 519 s × 35 = 5.05 h, or 5.6 h carrying the deletion-state factor 41/37. The measured 519 s already folds by 37, so the per-state work is inside it. **A 37-hour commitment is parked; a 6-hour one is a same-day falsifiable test** of the Poisson law's pre-registered 476 to 633 window, and it discriminates whether x = 37's c₂′ = 0.594 is an outlier or a level shift. Forced by `qc-numbers.md` and verified arithmetically in `qc-CAMPAIGN.md` Decision U1. **Item 6, "The @13 gate is MET".** DISAMBIGUATED. What is met is the T₄ *precision* gate; the @13 beyond-Chebyshev bound does not exist and is listed as a next step with an expected value in `natal-cap-21-beyond-chebyshev.md`:141. As written the item read as though the bound were in hand. Forced by `qc-CAMPAIGN.md` Decision 2. **Item 0b, "The gap is a factor 0.58 ln p".** SUPERSEDED: **0.58 to 0.95 ln p** (0.18/0.31 at ρ = 1.5 and 0.18/0.19 at ρ = 2.4). 0.58 is the optimistic end of the corpus's own range, quoted as a point value in eight places. The item also now records that ρ is measured non-monotone, so neither end may be presented as the one the trend favours. Forced by `qc-numbers.md` Q5.1 as amended in `qc-CAMPAIGN.md`. **Item 0c, "U-FRAME §10".** REPOINTED to §5a Step 2, where the exact copy theorem for the whole maxsum family now lives after the U-FRAME restructure, and the dropped hypotheses restored: VERIFIED 40 of 40 **over five folds and m ≤ 8**, and no straddling window ever beats a single-copy one. Forced by `qc-history.md`. **Item 4, "the calm's last analytic step".** RENAMED to the Skeleton Equidistribution Conjecture, the all-x form of the Aggregate 30-Skeleton Bound, since the parent name "the calm" is retired. Numbers unchanged; they were already correct at six levels. **Header.** Gained a pointer to the one reading path, so that TODO no longer names a different first read from `README.md`. ### research/THE-DIALS.md **Dial 7, "`research/bv-import-survey.md` already returned the verdict for us: inert. … Do not spend effort here".** SUPERSEDED, and this is the campaign's one finding that returns work rather than removing it. The survey scopes "inert" narrowly, to weak Assumption A and the Buchstab transfer at bounded u. Elsewhere it says the opposite: §3.2 is titled "Provable by BV: the full-wheel prime-comb equidistribution, tail regime", it calls the full wheel product at depth q_K = T^{o(1)} a BV theorem, marks an item provable now and elementarily, and says Assumption A is a theorem for the P₂-weakened comb with BV proving it. Read literally, dial 7 retired TODO item 11, which is three theorems that need writing up rather than discovering. The dial now carries the split verdict, and the §3 summary row with it. Forced by `qc-status.md` F-2. **§3 summary row for dial 2, "1.57 measured".** Gained the bracket 1.3-1.9 and the floor 1 in the row itself; the caveat was 99 lines away, and this row is the file's most quotable line. Forced by `qc-numbers.md` Q2.1. **§6, "Unchecked: whether an explicit elementary bound (Kanold, Stevens, Paseman) already delivers g(x#) < x′² at the needed constant".** SUPERSEDED: checked, and the answer is no. See the TODO 000b entry above. **§0, "His call on overlap is CORRECT, and it retires an old objection".** REWORDED to state the conclusion rather than the adjudication; the argument is unchanged and entirely current. Forced by `qc-history.md`. ### research/ZONE-POSTULATE.md **§6 route A, "missing the signed cancellation … (Lemma V)".** Now carries the qualifier that at the measured working point s/u ≈ 1.2 sits outside Lemma V's stated range, so the operative unproven input is a Gaussian maximal law for the sawtooth rather than Lemma V itself. Forced by `qc-status.md` A-1. **§6, "Loose end, logged and not chased" (Kanold, Stevens, Paseman).** SUPERSEDED by the closure; see the TODO 000b entry. **§7, "From `research/OBSERVATIONS.md`: if a statement can be phrased in residues …".** REPOINTED to `THE-LENS.md` §5, which owns the triage rule and says so in writing at its line 184. One of four sites citing a sightings notebook for a rule it does not own. Forced by `qc-arch.md` recommendation 1 and (d) D2. **Where this stands.** A three-line status block added after the title, in `G2-STATE.md` §0's shape. The document's single most useful sentence for a fresh reader, the 10¹¹ verification, sat at line 90 behind 89 lines of logical status. No content moved. Forced by `qc-arch.md` recommendation 3 and (c) C4. ### research/THE-LENS.md **§4, the one-number reformulations table, "u-frame | CLOSED, the rate has no slack".** DECOMPOSED into two rows, because the file said CLOSED about an object the router calls the live route. The per-fold multiplier form is closed; the copy-theorem form is open and is the branch's one live entry point, TODO 0c. **§3 heading date, and "Both are still correct reformulations".** The date stamp goes and Chris's attribution stays, per `qc-history.md` U3: dates stay where a reader uses them to date other documents, and go where they only date the idea. "still" dropped for the same reason. ### research/FOLD-PROFILE.md **§8 CREATED, "The natal cohort: dispersion, and the lineage identity".** The **Natal Dispersion Lemma** (PROVEN, one line; VERIFIED, never exceeded) and the **lineage identity** (EXACT at every level) previously existed only in `research/history/SESSION-2026-08-17.md` and in a script comment. Under the rule that `history/` is not read for current understanding, both had no findable status — and the first is load-bearing for the session's verdict that the natal creation engine is CLOSED, so a closed route's justification rested on a lemma with no home. §8 was the empty slot in a numbering that ran 0-7, 9, 11, 12, 10, it sits in the right reading order before §9 Survival, and it gives `fold-profile-09/10/11-*.js` their first prose home. All three scripts were re-run for this section rather than transcribed. Forced by `qc-status.md` D-1 and `qc-arch.md` (d) D1, which corrected the provisional §9 placement. **One number corrected in the transcription.** The session record's "99.94% of twin primes born at level ≤ 13" is the figure for the real twin primes below 10⁸; on the tile the cumulative share is **99.93%**. Both are now stated, with the object each belongs to. The twin count in that run is 440,311 rather than the familiar 440,312 because the census starts at (5,7); (3,5) sits below the comb. **§12c, "*Lemma (PROVEN).* A position r < p² is a twin slot of T_p iff …".** NAMED as the **Head Monotonicity Lemma**. Three other documents refer to it by name while its home left it unnamed. Forced by `qc-status.md` §4. **Header, "`research/fold-profile-01..04-*.js`", and §10 Reproduction.** The enumeration stopped at 04 while the family runs to 16; scripts 09, 10 and 11 are now listed with what they own and what their custody is. Forced by `qc-arch.md` (g) G1.