# Applied: wave 2, partition D — the entry path *(Eight files: `README.md`, `research/README.md`, `research/GLOSSARY.md`, `TODO.md`, `research/THE-DIALS.md`, `research/THE-LENS.md`, `research/ZONE-POSTULATE.md`, `research/FOLD-PROFILE.md`. Nothing outside those eight was edited, created or deleted, except the three staging files this partition was asked to write. Nothing was committed and nothing was pushed.)* ## qc.js, before and after | check | before | after | my partition's share | |---|---|---|---| | refs | 7 | 5 | **1** (`THE-DIALS.md`:121, and it is a framework bug — see Handoffs) | | quotes | 1 | 1 | **0** | | crosslinks | 0 | 0 | **0** | | scripts | 2 | 2 | **0** | | transfers | 12 | 13 | **2**, both benign and both word-diffed below | | **total** | **22** | **21** | | Other partitions were live in the same tree throughout, so the deltas are not all mine. What is mine: refs lost the two `dead-section` hits only because partition A fixed `origin-excess.md` §6c; my own files contributed no refs finding before or after except the one below. Transfers rose by one net, and the composition changed under partitions A and B; the two pairs with an endpoint in my files are analysed at the end of this file. ## File by file ### `README.md` — the repo's front door - **New §"Where to start"** before the Map, naming the one reading path in three numbered steps. This is the canonical statement; every other entry document now points at it rather than naming its own first read. (`qc-arch.md` (a), rec 6.) - **Map, first row.** "`research/GLOSSARY.md` — Read this first" RETIRED; the router is the first row. 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`, every one of which was absent — including the document TODO calls "THE PROGRAMME'S FOCUS". - **Map, `beta2-note.md` row.** "with the matching lower bound" → the two bounds named, with "not matching; the band between them is the whole problem". It contradicted §Status eleven lines below. (`qc-status.md` B-4.) - **§Status gained a scope line** naming what it owns and what it does not. - **The "Proven:" list, rewritten.** Classical spine marked inline (Holt and Rudd Thm 2.3, Pritchard 1982, Euclid IX.20, Schemmel 1869 / A059861 / Smith 1857); **Zone Equivalence removed from the list**, with one sentence saying why and where the content lives (`ZONE-POSTULATE.md` §2) — Chris's ruling. (`qc-status.md` C-1, C-3.) - **"nine more" → eight proven results**, and the Fused-Window Calm Lemma is out of the list. The replacement sentence states all four calibrations, **including the refutation of the uniform-in-q form, which had never reached any summary**, and points at `research/anchored-calm.md`. (`qc-status.md` B-2, `qc-compound.md` CC-1.) - **"ensemble bounds" → "ensemble bound (at @11, singular — @13 and @17 are not run)"**, and the X-limitation Theorem gained its "from x = 13 up" floor. (`qc-CAMPAIGN.md` Decision 2, `qc-status.md` B-3.) - **§Status, β.** "the whole conjecture is the positivity of β" → sufficiency, one-way, with the weakest sufficient statement named. (`qc-compound.md` CC-2.) ### `research/README.md` — rebuilt as the router Rewritten end to end. It now holds: a scope line saying it holds no mathematics; the three-step reading path, identical to `README.md`'s; a **question-to-file table** with fifteen rows; a **file table with a live/spent/register/submission status column** covering every `research/*.md`; the naming convention in one paragraph with the three known family-head exceptions and an explicit "no renames"; the house rule and the `history/` warning, both kept because they were correct; the vocabulary-drift paragraph, kept **because `qc-history.md` U3 makes GLOSSARY's adoption dates depend on it**; and the six-script measurement table **with the script filenames added**, which is what makes "script 05" resolvable and was the reason five scripts read as orphans. **The displaced prose is not deleted.** It is preserved in full in `research/history/staging/changelog-add-D-readme-prose.md`, with a table naming the current owner of each displaced section, for the parent to file into `research/history/`. Two campaign notes are attached to it rather than to the body: that spine items 1-3 are classical and item 5 is a framing device, and that the attack-4 bullet's two numbers come from the column `attack-04-fourier-budget.js`'s own banner invalidated (`qc-papers2.md` P-1). **The stale 18% Fourier figure is gone from the body.** It lived at `research/README.md`:120, inside the ten-attacks section the rebuild removed, and a grep of all eight of my files for "18%" now returns nothing. It survives only in the displaced-prose file, where it is explicitly marked as a retraction: `attack-04-fourier-budget.js`'s column is "NOT a valid certificate", `natal-cap-02-fourier-budget.js` reverses the conclusion (at x = 11 even an oracle fails, cap 117.3 against N = 90), and the real near-miss is 15% at x = 7 and moot. (Partition C's handoff; `qc-papers2.md` P-1.) I did **not** take up `qc-arch.md`'s open question A1 (whether the proven-spine prose could be kept). `qc-CAMPAIGN.md` records Chris approving the router with the prose moved to history, and that ruling governs. ### `research/GLOSSARY.md` - **Header.** "read THE-LENS.md first" RETIRED, replaced by a declared scope: a lookup document, not a first read, owning no route's status, with pointers to the four documents that own what it kept drifting into. - **Lemma V, JOB 1.** Replaced with `qc-status.md` A-1's text: NEEDED NOT PROVEN, and explicitly **not the operative assumption at the measured working point**, where s/u ≈ 1.2 sits outside the range s ≤ u it is stated in. A **new entry coins and defines the Gaussian Maximal Law for the interval sawtooth**, which `qc-papers2.md` P-3 found appears in no paper file at all. The Gap Reformulation entry's "which is why Lemma V is item 0" repointed to the exponent road. - **Hyperuniformity, JOB 7 / Q1.1.** The three spliced objects separated: the comb ladder, the full process's scaling law with its own u = 2 drift 0.251 → 0.321, and 0.611 marked as the comb's **hypothesis** with the 10:1 odds, the demoted 0.44 and the 0.295-0.343 lever arm. - **Unification Law** gained "(MEASURED to ~1%, Hardy-Littlewood-conditional; ω(u) is Buchstab's survival function)". (`qc-status.md` C-5, B-1.) - **The skeleton** split into three named objects at three calibrations, and "@11 through @23" → **six levels, @11 through @29**. - **The anchored calm / Fused window** now name their sub-claims, record that the calm is a phenomenon and never a claim, state that there is no "Fused-Window Calm Lemma", and point at `research/anchored-calm.md`. - **β and Assumption A**: identity → sufficiency, plus the rule that "Assumption A" is never written without a form. **X-channel**: "@13 on" → "from x = 13 up". - **Anchored-layer heading**: campaign narrative dropped, adoption date kept. - **Three new entries from partition A's handoff**: the Origin Excess Lemma with its one hypothesis and its three companions, pointing at `maier-matrix.md` §4a as the canonical enumeration rather than restating it; the two-class discrepancy with its ×3 ceiling; and the driving term, with the lemma PROVEN and the route REFUTED held apart. ### `TODO.md` - **Header** gained the reading path, so TODO no longer names a different first read from `README.md`. - **Item 000b LEFT the file, CLOSED by inspection**, per the charter. Its premise is false for all three authors; the k^{2+ε} result is Vaughan 1977, with Iwaniec 1971 Thm 2 at the primorial, both inexplicit. Closure recorded in the changelog staging file, and the consequence applied at the two other sites I own. (`qc-refs.md` W7.) - **G₂(41#) repriced and PROMOTED out of Parked to item 1b.** ~6 h by the streaming leg (519 s × 35 = 5.05 h, 5.6 h with the 41/37 deletion-state factor), with the 37 h named as the lattice-walk cost. Written as a pre-registered test against the Poisson law's 476-633 window, with the first move being the memory profile at 2.2e11 slots rather than the launch. Matches partition A's G2-STATE wording and U-FRAME §7's already-applied repricing. - **Item 6**: "the @13 gate is MET" → "the @13 **PRECISION** gate is MET; the @13 bound itself does not exist", and the Remaining list now names the @13 bound with its expected value alongside the @17 rerun, closing with "exactly one beyond-Chebyshev bound exists today, at @11". - **Item 0b**: "0.58 ln p" → "**0.58 to 0.95 ln p**", both ends named with their ρ, plus the sentence that ρ is measured non-monotone so neither end may be presented as favoured. (`qc-numbers.md` Q5.1 as amended.) - **Item 0c**: "U-FRAME §10" → "§5a Step 2" after partition B's restructure, and the two dropped hypotheses restored ("40 of 40 over five folds and m ≤ 8", "no straddling window ever beats a single-copy one"). - **Item 4** renamed to the Skeleton Equidistribution Conjecture. - **Moratorium item (iii)** now names both objects on the exponent road. Nothing else was pruned. I checked every remaining item against the reports for "closed but still live" and found none; `qc-status.md` class (e) came back empty and `qc-shepherd.md` independently found the forward-only charter being kept. ### `research/THE-DIALS.md` - **Scope line** added. - **Dial 7, JOB 5, and it recovers work.** The flat "inert … Do not spend effort here" replaced by the survey's actual split verdict: inert on the two target legs it names (weak Assumption A, the Buchstab transfer at bounded u) and live on the machinery (Siegel-Walfisz at fixed modulus and depth, Bombieri- Vinogradov on the full wheel in the tail regime, one item provable now and elementarily), with the closing sentence that a triage reading the dial as flatly inert kills TODO item 11. §3's summary row rewritten to match. - **§3 dial-2 row** gained "(bracket 1.3-1.9, floor 1)"; the caveat had been 99 lines away in the file's most quotable line. (`qc-numbers.md` Q2.1.) - **§6** loose end replaced by the W7 closure, wording aligned with partition A's G2-STATE §9 and carrying "the constant is the whole question". - **§0** reworded from the adjudication to the conclusion. (`qc-history.md`.) ### `research/THE-LENS.md` - **Scope line** added, stating that §5's triage rule is the corpus's canonical statement of it. §5 keeps its number, per partition A's handoff. - **§4 table**: the u-frame row **decomposed into two**, because the file said CLOSED about the object the router calls the live route. The multiplier form is closed; the copy-theorem form is open and is TODO 0c. Lead-in and follow-on sentences adjusted to match. **This was a live contradiction between two documents I own and is not in any report.** - §3's date stamp dropped, Chris's attribution kept; "still" dropped at :123. (`qc-history.md` U3.) - The adjacent-kill run now names L, matching `ATTACKS3.md`. ### `research/ZONE-POSTULATE.md` - **Scope line and a "Where this stands" block** after the title, in G2-STATE §0's shape. The 10¹¹ verification, the single most useful sentence in the file for a fresh reader, sat at line 90. No content moved. (`qc-arch.md` rec 3, C4.) - **§6 route A, JOB 1**: the Lemma V qualifier applied as written in A-1. - **§6** loose end → the W7 closure, aligned with G2-STATE. - **§7**: the triage rule repointed from `OBSERVATIONS.md` to `THE-LENS.md` §5, which owns it and says so. (`qc-arch.md` rec 1, (d) D2.) ### `research/FOLD-PROFILE.md` — JOB 8 **§8 created, "The natal cohort: dispersion, and the lineage identity"**, in the empty slot before §9 Survival, with zero inbound references to break. I re-ran all three scripts rather than transcribing the session record, and **that caught a number.** The session record's "99.94% of twin primes born at level ≤ 13" is the figure for 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 run also explains a second apparent discrepancy: the census counts 440,311 pairs, not the familiar 440,312, because it starts at (5,7) and (3,5) sits below the comb. Reproduced numbers now in the body: all 7,952,175 slots of T₂₃ classify with ratios 1.000000 at every level; the natal share of D_new falls to 4.50e−9 by fold 31; the dispersion bound of 2 is never exceeded on the ladder p = 7…31; the cohort's half-lives are q = 59, 23, 31, 89, 43, 67, 89, 149; the rarity × quality identity reads EXACT at all seven levels. §8 also carries the **two reasons the natal creation engine is CLOSED** — the lemma's reach expires at u ~ x/ln x, far above β₂, and the cohort is asymptotically empty — so the session's closure verdict now has a citable basis in a working document. Also: the header's script enumeration "01..04" → "01..16" with a pointer to §10; §10 gained the three scripts with their custody lines; §12c's unnamed lemma named the **Head Monotonicity Lemma**, which three other documents already cite by name. ## The reading path, as implemented **One path, stated once in `README.md` §"Where to start", and pointed at from everywhere else.** 1. `README.md` §Status — the central object, the proven bound, the gap, and that nothing has moved it. 2. `research/G2-STATE.md` §0 — what is hard here, before any derivation. 3. `research/README.md` — the router: which file answers which question. Then read for the question, not in file order. Enforcement: `README.md` states it; `research/README.md` repeats the three steps and then routes; `GLOSSARY.md` says it is not a first read and points at the router; `TODO.md` says do not start here and names all three steps. The old three-hop chain README → GLOSSARY → THE-LENS, which cost ~540 lines and never reached G2-STATE, is gone. ## What I left, and why - **`qc-arch.md` rec 9, moving GLOSSARY's 48-line pane block to `THE-DIALS.md` §0.** NOT DONE, deliberately, and I recommend it stay not done. `research/a3-07-pane-overlap.js`:728 cites GLOSSARY for a pane number from inside a pasted output block that the script exemption forbids editing. Moving the numbers out would strand a pointer that cannot be repaired. The altitude cost is real but the scope lines now warn the reader instead. - **`ZONE-POSTULATE.md`:150's pointer to `two-class-lower-bounds.md` §10.** Untouched. `qc-history.md` records partition E moving that content into §5, and `qc-arch.md` rec 17 requires one combined reference sweep at the very end. Left for that sweep. - **`GLOSSARY.md`'s long status-bearing entries** (Seam, Overlap credit, G₂). Each was checked against `qc-numbers.md`; all carry their caveats and none is stale. The altitude complaint is real and the scope line addresses it; cutting them would lose content nothing else holds. - **Every number** in all eight files, unless a report supplied a verified replacement. The three replacements applied are the G₂(41#) price, the 0.58 → 0.58-0.95 range, and @23 → @29 on the skeleton ladder. The one number I corrected on my own evidence is the 99.94/99.93 split, and I re-ran the script to do it. ## Handoffs to other partitions 1. **`THE-DIALS.md`:121's `attack-06b` is a FRAMEWORK BUG, not a defect in my file, and the brief and `qc-CAMPAIGN.md` are both wrong about it.** `research/attack-06b-difference-map.js` **exists**, and the line cites it by its full correct filename. The cause: `qc/checks.js`'s `SHORT_RE` accepts an optional trailing letter, `(\d{1,2})[a-z]?`, while `qc/corpus.js`'s `resolveRef` does not, `^(fold-profile|attack|a3|localized)-(\d+)$`. So any reference to a script with a lettered ordinal false-positives, and there is no prose fix. **Owner: partition G (`qc/`). One-line patch:** in `resolveRef`, make the pattern `^(fold-profile|attack|a3|localized)-(\d+)([a-z]?)$` and test `^${m[1]}-0*${Number(m[2])}${m[3]}-`. Verified this resolves `attack-06b` to the file. **Until it lands, `qc.js --strict` cannot go clean.** 2. **`research/G2-STATE.md` is the seventh of the seven summary documents and is the only one without a declared scope line.** I gave the other six theirs. It is also step 2 of the reading path, so its §0 must keep both its number and its role as the first thing after `README.md` §Status. Owner: partition A. 3. **`research/ATTACKS2.md`:24 — the Unification Law's ω(u) is Buchstab's and is unattributed there** (`qc-status.md` C-4). I applied the calibration and the attribution in GLOSSARY; ATTACKS2 is partition G's. 4. **`paper/PAPERS.md`:18 lists Zone Equivalence among "the spine theorems"** (`qc-status.md` C-3, third site). Removed from README and never in the router; the paper site is partition C's. 5. **`paper/moire-primes.md`:39's "the matching lower bound"** — the second of the two sites in B-4. Partition C. 6. **`research/OBSERVATIONS.md`'s 33-line triage statement** should shrink to two sentences plus a pointer to `THE-LENS.md` §5, now that ZONE-POSTULATE's citation is repointed. Partition G. `maier-matrix.md`:428, :579 and `G2-STATE.md`:473 are the other three citations to repoint. 7. **The router's file table must be re-checked at campaign close.** Two new documents appeared while I was working, `research/anchored-calm.md` (F) and `research/certificate-engine.md`, and both are now in the table. Any file created after this message is missing from it. A `ls research/*.md` diff against the table is a thirty-second check and is the only thing that keeps the router honest. 8. **`research/SCRIPTS.md` needs regenerating** after this wave; `fold-profile-09/10/11` now have a prose home and the index should say so. `node research/gen-scripts-index.js`. Owner: whoever closes the campaign. ## Unresolved - **Transfers pair `TODO.md`:98-115 vs `U-FRAME.md`:260-261 (j=0.05 c=0.90).** Word-diffed: nothing is dropped, and TODO's copy is now *better* than before — it gained "over five folds and m ≤ 8" and the no-straddling clause, which it previously lacked. The pair fires because a short theorem statement quoted in full is necessarily contained. It appeared when partition B moved the copy theorem into §5a Step 2. Recommend accepting it as a true restatement under Chris's rule; deleting the statement from TODO would leave item 0c naming an object the reader cannot see. - **Transfers pair `G2-STATE.md`:546-555 vs `ZONE-POSTULATE.md`:263-273 (j=0.60 c=0.81).** This is the W7 closure, and it is deliberate: the coordinator asked me to match partition A's wording. Word-diffed, nothing dropped either way. Same pair, at the same two documents, was in the wave-1 baseline at j=0.50. If one copy must go, the ZONE-POSTULATE one is the one that must stay, because that is where route A's price is quoted. - **The X-limitation Theorem's scope: RESOLVED mid-pass, and the resolution went against the reports.** I first applied "from x = 13 up" as three documents state it. Partition C then opened `natal-cap-31-calm-vs-kill.js`, whose reading 3 marks the theorem proven **per level** from L2 plus the *enumerated* max VR, at @11, @13 and @17, with **no level-uniform bound on VRmax**. All three of my sites — `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. **`qc-status.md` B-3's HIGH confidence is downgraded**, and the reason is worth keeping: three summaries agreeing on a scope is not evidence about a proof when all three descend from the same home. `qc-compound.md` CC-11 predicted exactly this and was right. - **`research/anchored-calm.md` landed from partition F while I was working**, and its opening wording matches what I wrote into `README.md` and `GLOSSARY.md` independently ("names a phenomenon, never a claim"; "There is no Fused-Window Calm Lemma"). Checked, consistent, no action. - **Em dashes, and it is a scope question for Chris.** `paper/writing-style-math.md` bans them and says it governs "the primeoire papers, **notes**, and any prose that behaves like mathematics", but every one of my eight files used them densely before I touched it, including as `GLOSSARY.md`'s term-definition separator. I matched each host document rather than stripping only my own sentences, which would have made the files internally inconsistent. `TODO.md` item 12 scopes the mechanical sweep to `paper/moire-primes.md` alone. **Decide whether the ban reaches `research/`**; if it does, that is one mechanical pass across the corpus, not a partition job. - **`qc-status.md` D-1 says the Natal Dispersion Lemma should also get a one-line GLOSSARY entry.** Not done: the lemma is a fold-profile result whose statement needs its cohort definition, and GLOSSARY's altitude problem is the thing this partition was fixing. §8 is one pointer away via the router's question table. Flagging it as a judgement call rather than an omission.