# qc-scope-T — wave 5, partition T: the surface partition R left unswept Read-only pass over the files R named as its own coverage gap: `research/U-FRAME.md` and its three children (`kappa-not-L.md`, `operator-and-pair-count.md`, `f-decays.md`), `FOLD-PROFILE.md`, `OBSERVATIONS.md`, `ATTACKS.md`, `ATTACKS2.md`, `ATTACKS3.md`, and the ~40 leaf research notes R and P did not open. Hunting the campaign's dominant defect — a result established somewhere with a SCOPE attached, restated elsewhere with the scope dropped — and the class wave 4 proved nothing can catch, the FALSE ABSENCE CLAIM. Nothing here supplies replacement text. Each entry gives the two ends, the home, the nature of the flattening and the evidence. Coverage statement at the end. **Structure.** Part 1 (T-1…T-15) is my own end-to-end read of the entry documents. Parts 2–4 (TA, TB, TC) are three read-only leaf sweeps I ran in parallel, each briefed on the defect class, the settled values, the false-absence class and the no-supplied-answer rule. **Provenance is marked per finding.** Findings I verified myself carry VERIFIED HERE; findings from a delegated sweep carry the artifact each one was settled against, and I have not independently re-derived those. Where a delegated finding contradicts something this campaign already settled, it is marked **CONTRADICTS A SETTLED VALUE** and must be adjudicated before anything is applied. **Nine of the findings across the four sweeps were settled by RUNNING an artifact**, not by reading it. That is the single most productive thing done in this partition and it is the method note at the end. --- ## The four findings a shepherd should read first **TC-1 changes something the campaign believes.** Wave 4's R-2 and this brief both carry "max VR is enumerated at @11, @13 and @17 — three levels". The @19 enumeration exists, ran over all 9,699,690 rotations, and reads **2.293**, which breaks the falling trend 2.78 → 2.35 → 2.14 that three papers and the theorem's conjecture box rest on. It is not a scope drop; it is a fourth data point nobody looked for. **Adjudicate this before anything else in this report.** **T-1, TB-1, TC-2 and TC-3 are four more of the R-1 shape** — a document asserting an artifact does not exist while the artifact sits in the same directory. One of them (T-1) is contradicted by the flagship paper, which already carries the resolved verdict. That is now six confirmed instances of the class in two waves, and none of them was reachable by any instrument the repo has. **TA-1 is the shape that costs the most downstream**: a live instruction to withdraw text that has already been withdrawn. A future agent obeying it may reintroduce the retired text in order to have something to remove. **TA-3 propagates into three documents including two of mine.** The band "flat at 3.2 to 3.7" is 2.93 to 4.20 on the table printed directly above it, and the derived constant 3.5 is the midpoint of a band whose unfavourable end is 4.2. --- # PART 1 — the entry documents (my own read, end to end) ## Ranked | # | severity | where | one line | |---|---|---|---| | T-1 | **HIGH** | `ATTACKS2.md` row 2 + campaign verdict | logs the rich vein as "the one unexplained novelty" while `attack2-rich-vein.js` solves it and `paper/moire-primes.md` §8 already says "the rich vein is solved" | | T-2 | **MED-HIGH** | `ATTACKS3.md` A5 | the superseded sifting limit "about 4.42" where the corpus settled on β₂ = 4.26645 — the fourth copy, and A7 of the same file uses 4.26645 | | T-3 | **MED-HIGH** | `FOLD-PROFILE.md` §12a | prints five of the ten `M/ln Y` values its own fit runs on and labels them "over the upper two thirds"; the five omitted run 21.85 down to 12.14 and the quoted slope 12.2 exceeds every value printed. VERIFIED BY RUNNING THE SCRIPT | | T-4 | **MED-HIGH** | `ATTACKS.md` attack 10 | "the framework's most original **unexplored** formalization target" — `research/anchored-windows.md` is that formalization and `paper/anchored-note.md` is a paper on it | | T-5 | MEDIUM | `U-FRAME.md` §5a step 3, `kappa-not-L.md` | the effective run length is "strictly smaller [than L+1] at three folds"; `a3-10`'s own table gives five, and the count was carried from a five-fold grid to a nine-fold one | | T-6 | MEDIUM | `FOLD-PROFILE.md` §12c | the Staircase Theorem's certified survivors quoted at four levels where the home says six | | T-7 | MEDIUM | `U-FRAME.md` §9 | "Nothing is proven about L" four paragraphs above "§10 Theorem B's **proven** L ≤ 0.18 p", in the file's own calibration section | | T-8 | MEDIUM | `U-FRAME.md` §11 | "31 exact diagonal points" flat, where the child says "about 31" and "the count is not an identifier … machine-dependent and moves between runs" | | T-9 | MEDIUM | `U-FRAME.md` §5a step 7 | carries half of `f-decays.md`'s instruction: home forbids quoting 1.06 **or 1.45**, U-FRAME forbids only 1.06 and then states 1.451 as a definite value | | T-10 | LOW-MED | `U-FRAME.md` §6a | "decays monotonically from n = 6" refuted by its own printed series at the ninth-to-tenth entry, 0.758 → 0.765 | | T-11 | LOW-MED | `FOLD-PROFILE.md` §0 vs §10 | header promises `fold-profile-01..16-*.js`; §10 reproduces 01–11 and says "all eleven"; 13/14/15/16 exist, and one of them carries a self-retraction that lives nowhere else | | T-12 | LOW-MED | `ATTACKS.md` attack 8 | "Every zone (p,p²) … unconditionally" drops the home's stated hypothesis p ≥ 17 | | T-13 | LOW | `OBSERVATIONS.md` §4 | five MEASURED tables with no artifact pointer; `research/lucky-control.js` reproduces every figure exactly. VERIFIED BY RUNNING THE SCRIPT | | T-14 | LOW | `FOLD-PROFILE.md` §9 / §9b / §11 | one √W in three renderings, 14,936 / 14,937 / 14,947, and the fold-budget table's T₁₇ row uses floor+1 where its other five rows use floor | | T-15 | LOW | `kappa-not-L.md` | "all seven" and "all 56 cases" carry no stated fold range anywhere in the corpus | --- ## T-1 (HIGH). The rich vein is solved. The scoreboard still logs it as the campaign's one unexplained novelty, and the flagship already disagrees. **The scoreboard**, `research/ATTACKS2.md`, row 2 status cell: > "✅ DONE (attack2-02-08-tomography.js): 13's depth identical at 4 levels — CRT > identity (independent proof of the Invariance Lemma). Seams = anti-shadow (4× > over-represented in richest windows). **NOVELTY: unexplained rich vein > [1667,1956) mod 2310, non-seam, non-p².**" and the same file's **Campaign verdict (all ten complete, 2026-08-14)**: > "**One unexplained novelty logged: the rich vein at [1667,1956) mod 2310.**" **The artifact**, `research/attack2-rich-vein.js`, whose banner reads "ATTACK 2 FOLLOW-UP — THE RICH VEIN [1667,1956) mod 2310 (2026-08-14)", reading 5: > "**VERDICT: REAL STRUCTURE, KNOWN MECHANISM, NO NEW PHYSICS.** The vein is a > genuine, exactly-repeating enrichment (T11 ceiling region, frozen by CRT at every > level), so it is NOT width-289 sampling luck in the sense of being spurious — but > its 'top-5 twice' billing overstates uniqueness: 58 offsets mod 2310 tie its T11 > count and 120 windows mod 510510 tie the scan max. … Mechanism, fully stated: > 20-of-135 T11 slots in 289 positions (layout luck of the level-11 tile, mirror- > symmetric), propagated exactly by uniform CRT survival, topped by a favorable > mod-13/17 class layout that lets 4 copies per 510510 reach the width-289 T17 > ceiling." **And the flagship already carries the resolved verdict.** `paper/moire-primes.md` §8: > "Three questions this section posed in earlier drafts have since been answered by > the record and moved to results: the grain census law is derived and digit-exact > (`research/grain-census.js`); **the rich vein is solved (a T₁₁ ceiling plateau, > `research/attack2-rich-vein.js`)**; and the Labos d=2/d=4 coincidence is proven…" **Home determination.** `attack2-rich-vein.js` governs; it is the artifact that ran the question, and `paper/moire-primes.md` §8 is the summary that already inherited it. `ATTACKS2.md` is the only document still carrying the pre-follow-up verdict. **Why this is the worst of the fifteen.** It is R-1's exact shape — an absence claim ("unexplained") contradicted by an artifact sitting in the same directory under a name that matches the claim — and it is worse in two respects. First, it is a NOVELTY claim, and three novelty verdicts have already moved in this campaign. Second, it is the closing verdict line of a scoreboard, the sentence a reader takes away as "what this wave left open", and the corpus has one open item there that is not open. **Second, smaller, in the same cell.** Row 2's "Seams = anti-shadow (4× over-represented in richest windows)" is reinterpreted by the same follow-up: "tomography's 'richest windows align with seams' is the SAME phenomenon: the 62 seam-containing max windows are the wrap-runs 2063-2267, i.e. the ceiling-plateau segment that happens to straddle 0 — **seam-richness and the vein are both faces of the T11 ceiling plateau**." The row states the two as separate findings. **Grep validated against a known positive.** `grep -rn "rich-vein"` over `research/*.md paper/*.md README.md TODO.md` returns `paper/moire-primes.md`:605 and `research/SCRIPTS.md`:90, so the pattern reaches both layers and its silence on `ATTACKS2.md` means `ATTACKS2.md` does not cite the follow-up at all. --- ## T-2 (MED-HIGH). A fourth copy of the retired sifting limit, in a file that uses the correct one forty lines later. **`research/ATTACKS3.md`**, A5, closing paragraph: > "What would be needed is a decay hypothesis on runs of large gaps, and A5 names > two sharp reasons it is hard: it is a two-dimensional lower-bound sieve at sifting > parameter 1+o(1) **against a limit of about 4.42**, and **no polynomial moment of > any fixed order can give it** — decay needs exponential moments, that is > quasi-independence." **The same sentence at its home**, `research/kappa-not-L.md` §"The wall, located precisely": > "It is a two-dimensional lower-bound sieve at sifting parameter 1+o(1) **against > the dimension-2 sifting limit β₂ = 4.26645** (`research/dhr-verification.md`, > rigorous, Booker and Browning). And **no polynomial moment of any fixed order can > give it**…" **`ATTACKS3.md` refutes itself in the same document.** A7, some forty lines below: > "the pane (n², (n+2)²) sits at u → 1 and **needs u > 4.26645**, against the zone's > 2." **Home determination.** `research/dhr-verification.md` governs; 4.42 is Ankeny–Onishi and is superseded. Wave 4's partition P retired exactly this value at `a3-05-bound-L.md` and at `kappa-not-L.md`, recording that "the sentence's whole point was the distance to the limit, so the stale value overstated the gap". The same sentence is what stands here, and it overstates the gap by the same amount. **Evidence that this is the same retired value and not an unrelated 4.42.** `grep -rn "4\.42" research/*.md` returns three hits: this one, the historical citation at `dhr-verification.md` §"the book's own comparison against 4.42 (Ankeny–Onishi) and 4.834 (Rosser–Iwaniec)", which is correct and is the known positive for the pattern, and a numeric table cell at `natal-cap-36-skeleton-door.md` (`4.42e−4`), which is unrelated. --- ## T-3 (MED-HIGH). §12a shows the flat half of a fit and calls it the whole. VERIFIED BY RUNNING THE SCRIPT. **The document**, `research/FOLD-PROFILE.md` §12a: > "**MEASURED: M grows logarithmically in the window width.** At T₂₃, **sampling > fourteen cuts across the tile, M/ln Y over the upper two thirds reads** > > 11.36, 11.92, 11.29, 11.09, 10.61 → **M ≈ 12.2 · ln Y at T₂₃**" **The artifact.** `research/fold-profile-08-zone-localized-gap.js` sets `nb = 14` and fits `for (let i = Math.floor(nb / 3); i < nb; i++)`, i.e. cuts 4 through 13 — **ten** values, not five. Run here, its T₂₃ block prints ``` T23: W = 223,092,870, ln W = 19.22, G2 = 204 Y | ln Y | M(x, Y) | M / ln Y 9.59e+2 | 6.87 | 150 | 21.85 3.78e+3 | 8.24 | 150 | 18.21 1.49e+4 | 9.61 | 150 | 15.61 5.90e+4 | 10.98 | 150 | 13.66 2.33e+5 | 12.36 | 150 | 12.14 9.19e+5 | 13.73 | 156 | 11.36 3.63e+6 | 15.10 | 180 | 11.92 1.43e+7 | 16.48 | 186 | 11.29 5.65e+7 | 17.85 | 198 | 11.09 2.23e+8 | 19.22 | 204 | 10.61 slope through the origin, upper two thirds: M ~ 12.16 * ln Y ``` **The nature of the flattening, and it is the campaign's signature shape.** The document prints the last five of the ten and attaches the label of all ten. The five it prints span 10.61 to 11.92; the five it omits span 12.14 to 21.85. The omitted half is the steeply falling transient, which is the evidence *against* the claim being made in that very sentence ("M grows logarithmically in the window width"). **And it is self-checking, which is what makes it worth a reader's time.** The quoted slope 12.2 is **larger than every one of the five values printed**. A reader who tries to reconstruct 12.2 from 11.36, 11.92, 11.29, 11.09, 10.61 cannot — their mean is 11.25 — and will conclude the fit is wrong when in fact the range was dropped. That is R-9's exact shape from wave 4: a correct calculation made uncheckable by the loss of the range it was computed on. **Home determination.** `research/fold-profile-08-zone-localized-gap.js` governs. It labels its own fit window in its own output and the prose narrowed it. **Adjudicate this together with TA-3.** The same underlying constant is quoted at its favourable half twice, in two different shapes: §12a's `M(x, x′²) ~ 3.5·ln³x` here, and `maxgap-law.md` §8's "`M(x,x^2)/ln^3 x` is flat at 3.2 to 3.7" where the true span on its own table is 2.93 to 4.20. `LOCALIZED-GAP.md` §5 carries the second verbatim. **Everything else in §12a reproduces exactly.** The margin table (108/361/3.34/60/**6.02**; 150/529/3.53/72/**7.35**; 204/841/4.12/150/**5.61**) is the script's S3 block digit for digit, "sampling fourteen cuts" matches `nb = 14`, "12.2" matches the printed 12.16, and "the reduction is only 1.4 to 2.1 at these levels" matches the printed 1.36 / 2.08 / 1.80. Only the five-of-ten is wrong. --- ## T-4 (MED-HIGH). The scoreboard calls the anchored-window programme unexplored. It has a note and a paper. **`research/ATTACKS.md`**, attack 10 status cell: > "✅ **DONE.** Three-phase life cycle of the head window measured … The zone sits at > the phase boundary; **anchored windows vs random windows = the framework's most > original unexplored formalization target.** At window S = x'², measured later, the > origin carries 21% LESS than mean density (origin-excess.md)." **The artifact**, `research/anchored-windows.md`, title and opening line: > "# Anchored windows vs random windows > > **Formalization of the attack-10 idea (2026-08-13).** The variance theorem > (script 06) and all Montgomery–Vaughan-style statistics describe a window dropped > at a **uniformly random position** of the pattern mod P_n#. But the window the > Twin Prime Conjecture needs is not random: it is **anchored at the origin** … > **This note makes the distinction precise, proves what is provable**, gives the > head window's life-cycle law and the constant behind its dip, and reports one new > measured object (the kill shadow)." **And downstream of it**: `paper/anchored-note.md`, a research note carrying ten exactly computed levels of β out to W = 3.04·10¹⁴, the Anchored Typicality Measurement, and the Aggregate 30-Skeleton Bound; plus the whole natal-cap campaign, whose entry document is `research/NATAL-CAP-CAMPAIGN.md`. **Nature of the flattening.** This is an absence claim ("unexplored") about a target whose formalization is a file named for the sentence making the claim. The cell was edited after the fact — its last clause cites `origin-excess.md` for a later measurement — so the row was maintained and the word survived the maintenance. **Home determination.** `research/anchored-windows.md` governs on whether the formalization exists. Whether the *target* is still open is a separate question and a real one — `anchored-calm.md` grades the Anchored Typicality Measurement "MEASURED, no proof mechanism in sight" — but "unexplored" is not the word for it. **Needs a determination, not a guess.** The honest replacement depends on whether Chris wants ATTACKS.md kept as a dated 2026-08-13 record (in which case the whole file wants a header saying so) or as a live scoreboard (in which case row 10's status is stale). I will not choose between those. --- ## T-5 (MEDIUM). "Strictly smaller at three folds" is a five-fold count carried onto a nine-fold table. **`research/U-FRAME.md` §5a step 3**, "The upper half is LOOSE": > "Write j\*(m) for the sharp shift … Then 1 + j\*(1) is the EFFECTIVE run length, > the smallest window of old gaps that covers the new record, and it measures > **3, 2, 2, 3, 2, 3, 3, 3, 4 at folds 7 to 37** against **L + 1 = 3, 2, 3, 3, 3, 4, > 3, 5, 5**: never larger, **strictly smaller at three folds**, and at fold 31 it is > 3 where L + 1 = 5." **`research/kappa-not-L.md`**, "And no constant can replace the effective run length either": > "The effective run length of U-FRAME §5a step 3 is the better coordinate, **never > worse than L+1 and strictly better at three folds**…" **The artifact.** `research/a3-10-lower-tightness.js` §6, its own printed table: ``` // fold p | G2new | maxsum_2 | maxsum_3 | L | L+1 | smallest m that works // 7 | 30 | 24 | 30 | 2 | 3 | 3 // 11 | 42 | 42 | 66 | 1 | 2 | 2 // 13 | 66 | 66 | 96 | 2 | 3 | 2 // 17 | 108 | 96 | 138 | 2 | 3 | 3 // 19 | 150 | 150 | 168 | 2 | 3 | 2 // 23 | 204 | 186 | 210 | 3 | 4 | 3 // 29 | 258 | 234 | 300 | 2 | 3 | 3 // 31 | 348 | 330 | 390 | 4 | 5 | 3 (deep31) // 37 | 528 | 408 | 510 | 4 | 5 | 4 (deep37) ``` Comparing the last two columns row by row: fold 13 (2 < 3), fold 19 (2 < 3), fold 23 (3 < 4), fold 31 (3 < 5), fold 37 (4 < 5). **Five folds, not three.** Equality at folds 7, 11, 17 and 29. **Where the "three" came from, and it is the campaign's shape exactly.** The count is correct on a narrower grid and was carried onto a wider one. `a3-04-maxsum-recursion.js` reading 7 measures `j*(1)` on **five folds only** (T11→T13 through T23→T29) and records: > "At m = 1, j\* = 1, 2, 1, 2, 2 against L = 2, 2, 2, 3, 2: **strictly below L at > three of five folds** and never above." That is right: on those five folds it is three. `a3-10` then extended the grid to nine folds and its prose comment kept the old count — > "So the working m runs 3, 2, 2, 3, 2, 3, 3, 3, 4 over folds 7 to 37: always at or > below L+1, **strictly below it at folds 13, 23 and 31**, but NOT constant." — naming three folds explicitly and omitting 19 and 37, both of which its own table shows strictly below. `U-FRAME.md` and `kappa-not-L.md` inherited the prose count, and U-FRAME attached it to the nine-fold scope in the same sentence. **Home determination.** The **table** in `a3-10-lower-tightness.js` §6 governs, per the campaign's own rule that an artifact which computes a number is the authority over a prose count. The narrower `a3-04` reading is correct as written and should not be touched; the scope "three of five folds" is stated there. **Direction.** Conservative for the argument it supports — §5a's verdict is "aim at κ(m), not at L", and five is more evidence for that than three — but it is still a supplied count contradicting a computed table, and this campaign has now had five wrong counts. --- ## T-6 (MEDIUM). The Staircase Theorem's certified ladder quoted at four levels where the home says six. **`research/FOLD-PROFILE.md` §12c**: > "**The Staircase Theorem does certify survivors (≥ 34/110/82/1877 at > @11/13/17/19)** but those are twins in a TILE, not in a zone, and they do not > scale." **The home**, `research/NATAL-CAP-CAMPAIGN.md`, the campaign table, row 8: > "refined ladder proves survivors ≥ **34/110/82/1877** @11/13/17/19, **since > extended to 4841 @23 and 31,327 @29 (six certified levels in all, > `paper/staircase-note.md` Theorem 8)**" **Two other sites carry the extension**, so this is not an isolated reading: `research/certificate-engine.md` — "certifies a floor of **31,327** twin pairs in the 29-tile" — and `paper/wall-note.md` — "at x = 29 the certificate proves at least **31,327** twin pairs exist in [the tile]". **Nature of the flattening.** The four-level form is the pre-extension state. Two certified levels, @23 and @29, are missing, and @29's figure is 31,327 — an order of magnitude above the largest number §12c quotes. The sentence's purpose is to concede that the natal ledger *does* certify something before saying why it does not reach, so the concession is understated by two levels. **Home determination.** `paper/staircase-note.md` Theorem 8 governs, per `NATAL-CAP-CAMPAIGN.md`'s own pointer. `NATAL-CAP-CAMPAIGN.md` carries the count. --- ## T-7 (MEDIUM). U-FRAME's calibration section says nothing is proven about L and then cites the proof. **`research/U-FRAME.md` §9 "Honest status"**, under **Not solid**: > "**Nothing is proven about L.** We have nine integers, 2, 1, 2, 2, 2, 3, 2, 4, 4, > and a heuristic." **The same section, four paragraphs later**, under **The hole, priced**: > "So the branch goes through iff **L ≤ 0.19 to 0.31·p/ln p** on average over the > ladder, against **§10 Theorem B's proven L ≤ 0.18 p**." **And §10 of the same file**, in its own list of what is proven: > "**PROVEN:** the Alternation Lemma … Theorem A, the Run Cost; **Theorem B, the > first unconditional bound on L, L ≤ 0.18 p**; and Theorem C, which carries the > argument to κ(m)." **Home determination.** `research/a3-05-bound-L.md` §5 governs and states Theorem B with its proof; §7 there prices the distance "from Theorem B's **proven 0.18 p**". `research/kappa-not-L.md` carries the same. Every other site in the corpus treats Theorem B as proven; §9's opening clause is the single outlier. **Why it matters more than an under-claim usually would.** §9 is the section titled "Honest status", the one a reader opens precisely to calibrate the branch, and its first three words under "Not solid" are the strongest calibration statement in the file. It is also the wave-4 R-2 shape — a claim refuted inside its own section without the reader leaving the page. **Needs a determination, not a guess.** The sentence may have meant "nothing useful is proven about L", which is defensible (§10's own wall paragraph says Theorem B is structurally capped at the failing branch). That is Chris's call, not mine. --- ## T-8 (MEDIUM). "31 exact diagonal points" is stated flat where the home says the count is not an identifier. **`research/U-FRAME.md` §11**: > "The head engine gives the tail at any level and **31 exact diagonal points**, > carrying a FIT that must not be used past the range it was fitted on." **The home**, `research/operator-and-pair-count.md`, "The tail at any level, and the fit that goes with it": > "Extending the grain-census inclusion-exclusion into a head engine gives count(d)/D > at any level with no tile in memory, agreeing with enumeration to 5e−16, and yields > **about 31 exact diagonal tail points over a range of 20 in x** against the seven > U-FRAME §5a step 7 has from tiles. **The count is not an identifier: the engine > stops on a per-level time budget, so it is machine-dependent and moves between > runs.**" **Nature of the flattening.** Two things go missing: the hedge ("about"), and an explicit warning that the number is not reproducible across machines. U-FRAME then prints it as a bare integer alongside genuinely exact counts in the same sentence ("VERIFIED at every fold to 37", "PROVEN, VERIFIED exactly at six folds"), which is the context in which a reader will read 31 as an exact census. The next agent to re-run the engine and get 29 or 33 will read it as a discrepancy. **Home determination.** `operator-and-pair-count.md` governs; it is the child U-FRAME §11 points at, and it is the only site that states the warning. **Note the child is otherwise exemplary on this axis** and gets an unusual thing right: it separates its own 1.06 from §5a step 7's 1.062 in terms — "That 1.06 is the localized head's rate and has nothing to do with §5a step 7's seven-point slope of 1.062, which the digits otherwise invite a reader to connect" — which is a defence against precisely this defect class written by hand. --- ## T-9 (MEDIUM). U-FRAME inherits half of f-decays' instruction on the slope. **The home**, `research/f-decays.md`, "What is real is that the coefficient is range-dependent": > "The raw halves give 1.695 against 0.906 (t = 2.92), a quadratic term is > significant (t = −2.68), and even comb-corrected the threshold coefficient runs > 1.866 against 1.115 between halves (t = 5.21). **No specification yields a stable > slope, so none of 1.06, 1.45 or anything between should be quoted as "the" slope of > this law.**" **`research/U-FRAME.md` §5a step 7**: > "Regressing ln(1/f) on 2p/m̄ over the seven points gives slope 1.062 and intercept > 1.357 with R² 0.730, **but SE 0.289, so the 95% interval is [0.32, 1.81]**. That > contains 1 … and it equally contains **the 1.451 the 42-point census fit gives**, > which is why the two are not in conflict (`research/f-decays.md`). Two extra points > move this slope to 1.881. **Do not quote 1.06 as a measured exponent.**" **Nature of the flattening, and it is a one-sided prohibition.** The home forbids quoting either end. U-FRAME forbids one end and, in the same paragraph, states the other as a definite measurement ("the 1.451 the 42-point census fit gives"). A reader following the instruction as written drops 1.06 and carries 1.451, which is the outcome the home's sentence exists to prevent. **A second, smaller inheritance gap in the same passage.** U-FRAME says the two readings "are not in conflict" because the intervals overlap. The home says something stronger and different: "**The two are not two measurements. The seven tile points ARE the first seven of these 42, carrying the same f** … there is nothing here for the two to disagree about." Overlapping intervals is the weaker reason and leaves the reader thinking there are two estimates. **Home determination.** `f-decays.md` governs; it is U-FRAME §12's own child and it holds the 42-point census, both regressions and the range-dependence result. Wave 3's partition K established this and U-FRAME took part of it. --- ## T-10 (LOW-MED). "Decays monotonically", against the series printed on the same line. **`research/U-FRAME.md` §6a**: > "**Their 21 terms are free data, and they extend every reading we have.** The > adversarial ratio a(n)/(lnW)² **decays monotonically from n = 6**: 1.411, 1.111, > 0.997, 0.990, 0.882, 0.842, 0.806, 0.804, **0.758, 0.765**, 0.704, 0.689, 0.674, > 0.666, 0.649, 0.604." The ninth entry is 0.758 and the tenth is 0.765. The series is not monotone, and the counterexample is inside the sentence making the claim. **Nature.** Not a dropped scope but the same failure mode as T-3: a document contradicting its own pasted numbers, which no diff can find because there is no near-duplicate to diff against. Sixteen values for n = 6 to 21 is the right count and every other figure in the paragraph checks out, so this is one word. **Home determination.** The series governs. `grep -rn "decays monotonically"` over `research/*.md paper/*.md` returns this site and one unrelated positive (`h2-scoping.md`: "The ratio decays monotonically to 0.50"), which is the known positive confirming the pattern reaches; no other document repeats U-FRAME's claim, so the defect is confined to one line. **Marked as needing a judgement, not a number.** Whether the right description is "decays with one reversal at n = 14" or "decays with the twin-fold staircase of §12 visible" depends on whether that reversal is the same twin-pair mechanism §12 proves for f. It looks like it and I did not check it; that is a real question, not an edit. --- ## T-11 (LOW-MED). The reproduction list stops five scripts short of what the header promises, and the gap holds a self-retraction. **`research/FOLD-PROFILE.md` §0**, the header: > "Calibration marked throughout: PROVEN, VERIFIED by exact computation, MEASURED, > REFUTED. **Code, output and readings in `research/fold-profile-01..16-*.js`**; the > ones this file reads from are listed in §10." **§10 "Reproduction"** lists `fold-profile-01` through `-11` and closes: > "**All eleven run in seconds.**" `ls research/` holds `fold-profile-12-anatomy-survival.js`, `-13-hotspot-sweep.js`, `-14-underdispersion.js`, `-15-variance-law.js` and `-16-is-it-the-tile.js`. **12 is cited elsewhere** (`GLOSSARY.md`, `ATTACKS2.md` row 1, `paper/moire-primes.md`). **13, 14, 15 and 16 are cited by no working document**: `SCRIPTS.md`'s consumer column for those four rows names only `research/history/staging/qc-arch.md` and `research/history/SESSION-2026-08-17.md`. Their results appear nowhere in `research/*.md` or `paper/*.md` — `grep -rniE "sub-binomial|underdispers|variance deficit"` over the working corpus returns only `paper/anchored-note.md`'s "the sub-binomial **house splits**", which is the natal-cap ensemble object and not this one, and two mentions of the tile's gap under-dispersion (`gate-multiplies.md`, `U-FRAME.md` §9) which are a third object again. **And the gap holds a correction that lives only inside a script.** `fold-profile-13-hotspot-sweep.js` carries, in its own printed readings: > "\*\*\* **CORRECTED 2026-08-17.** This reading originally called the deficit 'an > independent sighting of the anchored calm recorded in NATAL-CAP-CAMPAIGN … now > seen in a fourth place and by a fifth method'. That identification was never tested > and is now superseded twice over. fold-profile-14 established the deficit is real > rather than an estimator artifact (synthetic control 0.993-1.014 against real > 0.962, 0.921, 0.838), and **fold-profile-16 established it is NOT a tile > phenomenon**: it survives with the tile normalisation removed entirely, so it is > the ordinary short-interval variance of twin primes, which is classical and > expected. **Nothing here supports joining them.** \*\*\*" **Nature.** Not a scope flattening: an unmet reproduction promise plus four results with no summary above them. It is the mirror image of the false-absence class — a result exists and nothing in the working corpus records it — and it is exactly the coverage gap R named as the highest-value target for the next wave ("no pass in this campaign has compared a script's own reading against the summary that cites it"). **Checked and clear**: the retraction does *not* affect `NATAL-CAP-CAMPAIGN.md`'s "one sighting, not four". That paragraph enumerates its four sightings — house splits (9), CRT overlaps (6), the drift toward 0.793·E, and the anchored strike variance (5, 13) — and fold-profile-13's would have been a fifth, self-withdrawn before it entered. The count of four stands. **Marked as needing Chris's judgement**: whether 13–16's findings belong in `FOLD-PROFILE.md`, in `anchored-calm.md`, or nowhere (16's own verdict is that the result is "classical and expected") is an editorial call. The header/§10 mismatch is not. --- ## T-12 (LOW-MED). The pigeonhole theorem stated for every zone, where the home states a hypothesis and flags it. **`research/ATTACKS.md`**, attack 8: > "✅ **DONE — THEOREM.** **Every zone (p,p²) contains two primes at distance ≤ > 2(1+o(1))·ln p, unconditionally** (crystallization+Chebyshev+pigeonhole); certified > constant already 2.00 at p=1009." **The home**, `paper/moire-primes.md` §7: > "**Theorem (pigeonhole small-gap).** *Let **p ≥ 17** be prime and put K := π(p²) − > π(p). Then the interval (p, p²) contains two primes q < q′ with q′ − q ≤ (p² − > p)/(K − 1), and that bound is (2 + o(1))·ln p as p → ∞.*" and, immediately after the proof: > "**The hypothesis p ≥ 17 is where the Rosser–Schoenfeld input holds in the form > used**, and the o(1) is a statement about the limit rather than about any single p, > which is why the theorem is stated in the finite form first." **Nature.** "Unconditionally" is correct in its own sense — no RH, no Hardy–Littlewood — and is not what is dropped. What is dropped is the range hypothesis the home goes out of its way to name and justify, and the finite/limit distinction the home says is the reason the theorem is stated finitely first. `research/attack-08-pigeonhole-theorem.js` reading 1 has the same unrestricted phrasing, so the scoreboard inherited it from the script rather than from the paper. **Home determination.** `paper/moire-primes.md` §7 governs; it is the only statement of the theorem with a proof attached. --- ## T-13 (LOW). Five MEASURED tables with no artifact pointer, and the artifact reproduces them exactly. **`research/OBSERVATIONS.md` §4**, "The lucky numbers as a falsification control", states **MEASURED to 10⁷** and gives a decade table (lucky(x), π(x), ratio, x/ln x), twin counts, largest gaps and an overlap figure, with **no script named anywhere in the entry** and no artifact pointer in the section. `research/lucky-control.js` exists, has no pasted OUTPUT or READINGS block, and `SCRIPTS.md`'s row for it has an empty consumer column pointing only at `research/history/staging/qc-arch.md` — that is, the corpus's own script index records it as having no consumer, while §4 *is* its consumer. **Run here.** Every figure reproduces: ``` x lucky(x) pi(x) ratio x/ln x 1000 153 168 0.9107 145 10000 1118 1229 0.9097 1086 100000 8772 9592 0.9145 8686 1000000 71918 78498 0.9162 72382 10000000 609237 664579 0.9167 620421 lucky twins: 55,548 prime twins: 58,980 ratio: 0.9418 largest gap below N — lucky: 182, prime: 154 members of both: 62,446 (10.2% of luckies are prime) expected overlap if independent at these densities: 40,489 ``` against the document's 0.911 / 0.910 / 0.915 / 0.916 / 0.917, "55,548 lucky against 58,980 prime, ratio 0.94", "182 lucky, 154 prime", "only 10.2% of luckies are prime, 62,446 shared members against 40,489 expected". No defect in any number. **Nature.** A custody gap rather than a scope flattening: the numbers are right and nothing in the document lets a reader find that out. Reported because §4's whole proposal is to use the luckies as a falsification gate for the corpus's headline measurements, and a gate with no named instrument is the shape that produces false absence claims later. **Checked and NOT a defect.** §4's "This is a cheap falsification gate and **we do not currently have one**" is an absence claim and it **stands**: `lucky-control.js` generates the two sets and compares counts, twins, gaps and overlap, and does not run any corpus measurement (the 0.79 zone share, the window variance, the ±1.1σ Hardy–Littlewood agreement, the grain census, the G₂ growth law) against them. I read the file end to end to establish that. --- ## T-14 (LOW). One √W, three renderings, and one floor convention out of six. For the 23# window, W = 223,092,870, so √W = 14,936.29 and the largest prime below it is 14,929. - `FOLD-PROFILE.md` §9: "Folding every prime up to **√W = 14,937**…" - `FOLD-PROFILE.md` §9's own table, last row: "| **14929** | 2.000 | 895,790 | 0.8926 | **survivors ARE the twin primes** |" - `FOLD-PROFILE.md` §9b, the boxed honest position: "4,361,681 survivors provable at y = 89; **895,790 actually survive to y = 14,947**; and no proof of positivity exists anywhere in between." - `FOLD-PROFILE.md` §11's fold-budget table: "| T₂₃ | 223,092,870 | **14,936** | 1,739 | 14,929 |" **Home determination.** The scripts settle it. `fold-profile-07-impact-window.js` sets `ROOT = Math.floor(Math.sqrt(LIMIT)) + 1` = 14,937 and sifts to `ROOT + 10` = 14,947, which is why 14,947 appears; both `fold-profile-05` and `-07` end their mark lists at **14929**, and `-07`'s run here ends its table at "14929 | 1 | 7,056,385 | 100.00 | 895,790", i.e. every removal is finished by 14,929 and the two folds above it (14,939 and 14,947) remove nothing. So the endpoint is 14,929; 14,936 is √W; 14,937 and 14,947 are the script's `ROOT` and its padded sift ceiling. **Not reported as a defect**: §11's damage-band row "(10,000, **14,947**] | **521**" is a faithful copy of the script's own printed band and should not be touched. The 1,741 folds it implies against §11's own "1,739 damaging folds" is the same padding, correctly so, since the two extra folds do no damage. **A second, separate cell.** §11's fold-budget table gives T₁₇'s √W as **715** where floor(√510510) = **714**; the other five rows (48, 173, 3114, 14936, 80434) are all floors. The damaging-fold count 120 and last damaging fold 709 are right either way. Verified by direct computation, along with T₂₉'s row: π(80434) − π(29) = **7,863** ✓ and the largest prime ≤ 80,434 is **80,429** ✓. --- ## T-15 (LOW). Two verification counts with no stated range. **`research/kappa-not-L.md`**, Theorem A: > "**Attained with equality at every fold with L ≥ 2, all seven.**" **and Theorem C:** > "**Verified in all 56 cases.**" Neither states which folds. Reconstructed: `a3-05-bound-L.js`'s Theorem C block prints seven fold rows (7, 11, 13, 17, 19, 23, 29) × m = 1..8 = **56** ✓, so "56" encodes its own scope. "All seven" only comes out right if the fold set is 7 to **31** — eight folds, of which fold 11 has L = 1 — since L = 2, 1, 2, 2, 2, 3, 2, 4, 4 at folds 7 to 37 puts eight folds at L ≥ 2 if fold 37 is included and seven if it is not. **Home determination.** `research/a3-05-bound-L.md` §"Theorem A" governs and states it identically — "Equality at every fold with L >= 2, all seven of them" — so `kappa-not-L.md` is a faithful copy and the missing scope is at the home. That file is partition P's, so I am recording rather than claiming it. **Marked as needing the artifact.** Whether Theorem A's verification set stops at fold 31 or reaches 37 should be read off `a3-05-bound-L.js`, not inferred. Note that `operator-and-pair-count.md` says "**Alternation confirmed at fold 37**, which is the deepest test the **Alternation Lemma** has" — a different theorem — so fold 37 being absent from Theorem A's set is plausible and is not established here. --- ## Checked and NOT reported Recorded so the next pass does not spend the same time. - **The whole 0.58-to-0.95 axis is clean on this surface.** `U-FRAME.md` §5a step 4, §7 item 1 and §9 all carry "0.58 to 0.95 ln p" with "(0.18/0.31 and 0.18/0.19)"; `a3-03-f-from-census.md` and `a3-09-histogram-operator.md` likewise. No single-ended copy survives in my files. - **The copy theorem's marker.** `U-FRAME.md` §5a step 2, §5a step 3a and §7 item 2 all carry "VERIFIED 40 of 40, over five folds and m ≤ 8", and §5a step 2 carries the unproven clause in terms ("No straddling window ever beats a single-copy one"). Wave 3's D-1 fix held. - **The Poisson law's 476 to 633.** Carried at both ends and with its centre at all three U-FRAME sites (§4, §6a, §7 item 3). Wave 4's 475→476 fix landed. - **`Lgrowth.js`'s stale prohibition.** `U-FRAME.md` §8 now reads "`research/Lgrowth.js` **was corrected on 2026-08-16 and may be quoted**", with the bug and its fix described. Wave 4's P fix landed. - **U-FRAME §8's "the repo holds no script that regenerates them".** This is an absence claim and it is the deliberate output of commit 7e6e49f ("U-FRAME's reproduction promise was hollow: the scratch is gone, say so and file the job"). I checked it against `ls research/`: `verify-ladder.js` and `verify-ladder-big.js` regenerate the *census* ladder (D, seams, survivors) and not §§2/4/5's fold ladders or max-gap forensics, and no other script does. **The claim stands.** - **OBSERVATIONS §1a's "no mention anywhere in `research/` or `paper/` as of 2026-08-15"** for the mirror-centre pair. Grepped `p#/2`, "mirror centre", "cousin slot" and "centre pair" over `research/*.md`, `paper/*.md`, `README.md`, `TODO.md` and `GLOSSARY.md`: `OBSERVATIONS.md` is the only file. The known positive for the pattern is `OBSERVATIONS.md` itself, so the zero is meaningful. **The claim stands.** - **OBSERVATIONS §7's Mertens crossing.** "2·Σ_{7≤q≤U} 1/q … is 0.931 through q = 23 and 1.0002 once 29 joins" — computed directly, 0.93125 and 1.00021. ✓ The capacity table's U = 30 closure and U = 32 failure are consistent with it. - **OBSERVATIONS §§1, 1a, 2, 3, 5, 5a, 6.** Every count and every series I could check reproduces: the distinct-jump column 1, 2, 3, 5, 7, 10; the largest-jump column 2, 4, 6, 10, 14, 22 against A048670; p_next − 1 = 4, 6, 10, 12, 16, 18 at T3..T17; the five β residuals giving four decay-power estimates; the lineage of entry 5's almost-prime table. - **FOLD-PROFILE §2 and §3, checked arithmetically end to end.** The un-tightened K-level bounds 4·3^{π(x)−1} = 9.72e2 / 2.92e3 / 8.75e3 / 2.62e4 ✓; the tight bounds 2·(27.019392·3^{π(x)−7} + ½) = 19.0 / 55.0 / 163.1 / 487.4 ✓; 2·3⁶/27.019392 = 53.96 ✓ (wave 4's P fix landed, no 81.0 survives); "the tight bound crosses below the mean at x = 11" ✓; the six worst-copy fractions 6.3e−1 … 4.4e−5 ✓ against the min/max columns; the "true max deviation" column ✓ against §3's table. - **FOLD-PROFILE §4's "VERIFIED 45 of 45".** Counted: tiles T₇..T₂₃ against primes p > x, p ≤ 43 gives 10+9+8+7+6+5 = **45** ✓, and the stated scope "from T₇ to T₂₃, p ≤ 43" is exactly what produces it. This is the best-scoped count on the surface. - **FOLD-PROFILE §5's Head Lemma table.** All four rows verified by hand: T₁₃|17 the self-strike only (17²−2 = 287 = 7·41 is not a slot); T₁₇|19 only 359 = 19²−2 (21 is not a slot); T₁₉|23 zero (25 and 527 = 17·31 both fail); T₂₃|29 both. ✓ - **FOLD-PROFILE §8's lineage census.** The twin-pair column sums to 440,311 ✓ against the stated total; 0.999327 → "99.93%" ✓; 440,033/440,311 → "99.94%" ✓; m̄(19)/m̄(5) = 25.615/10 = **2.56** ✓. - **`ATTACKS.md` attack 4's prohibition on `attack-04-fourier-budget.js`** is live and correctly maintained at four sites (`NATAL-CAP-CAMPAIGN.md`'s header warning and item 136, `SCRIPTS.md`, `paper/wall-note.md`). Not stale. - **`ATTACKS3.md` A3's Lemma A** states d_min by p mod 3 where `kappa-not-L.md` states it by p mod 6. Equivalent for odd p; not a defect. - **`ATTACKS3.md` A7's "4.267 proven, 1 needed"** matches `THE-DIALS.md`'s own idiom ("4.2665 proven, 1 needed") and reads backwards only if the reader imports the exponent convention. Not a defect. - **`kappa-not-L.md`'s 0.18x against U-FRAME's 0.18 p.** These are two different objects and the home says so: `a3-05-bound-L.md` §7 derives the *ceiling* as G₂/(3p) ≈ 0.18**x** and separately prices "Theorem B's proven 0.18 **p**". Both are right. - **`a3-04-maxsum-recursion.js` reading 7's "three of five folds"** is correct on its own five-fold grid and must not be changed; see T-5. - **U-FRAME §6a's counts.** "VERIFIED at all twelve shared terms" ✓ against the twelve-term G₂ ladder; the two margin series each carry 19 values for n ≥ 3 of 21 terms ✓; the exact-term OEIS search lists all twelve ✓. - **U-FRAME §5a's other counts.** "In four of seven folds the winning stretch contains the old maximum" ✓ against the table's four bolded entries and `a3-10` §6a's merge column; "329 (tile, prime) cells" ✓ = 305+23+1 from `a3-10` §6; "20 of 40 cases" ✓ against `a3-04` reading 7; "the lower bound is exact at 3 of the 9 ladder folds" ✓ (folds 11, 13, 19); "L = 2, 1, 2, 2, 2, 3, 2, 4, 4 at folds 7 to 37" and §8's eight-value "folds 7 to 31" version ✓ consistent. --- # PART 2 — TA, the gap-route leaves Files: `gate-multiplies.md`, `maxgap-law.md`, `theta-ladder.md`, `exponent-control.md`, `h2-scoping.md`, `two-class-lower-bounds.md`, `covering-dive.md`, `discrepancy-two-class.md`. Two engines re-run (`gate-multiplies-02.js`, `two-class-lower-bounds.js`) plus an independent recomputation of c₁ from A048670. ## TA-1 (HIGH). A live instruction to withdraw text that has already been withdrawn. `h2-scoping.md` §8 items 1 and 2 quote two sentences from `exponent-control.md` §8 and say **"Both halves need withdrawing"**. Neither quoted string exists in `exponent-control.md` any more: §8 now reads "**Extending h2 past 21 terms is not available and would not help** … **There is no reachable ladder length at which the exponent becomes readable**", and "Deciding whether Q is bounded … **is capped at the 19 points now available**". `grep -n "highest-value computation available|OEIS computations rather than new theory"` over `exponent-control.md` returns nothing, and the same pattern hits `h2-scoping.md` twice, which is the known positive. `h2-scoping.md`'s own head section already says the withdrawal happened — "`research/exponent-control.md` §8 now carries the same verdict and cites the pricing below" — so §8 contradicts the top of its own document. **HOME:** `exponent-control.md` §8 governs its own bullets and has already carried out both withdrawals. This is the `Lgrowth.js` shape from wave 4: **an instruction a future agent obeys without checking**, and here obeying it means reintroducing retired text in order to withdraw it. ## TA-2 (HIGH). Four spacing ratios that are not the four named folds. `gate-multiplies.md` §4 reading 1: "If NFP3 held as a *fact* the ratio would be flat at `mbar_new/(p-2)`, measured **1.84, 1.53, 1.51, 1.12**", attributed in the same paragraph to "both MEASURED at all four folds (13, 17, 19, 23 by 17, 19, 23, 29)". **`research/gate-multiplies-02.js 29` run here prints** 1.528, 1.507, **1.336**, 1.116 for those four folds. The document **prepends 1.84**, which is the `T₁₁ by 13` fold the paragraph says it is not reporting, and **drops 1.34**, which is `T₁₉ by 23` — one of the two folds the document pastes verbatim two paragraphs above. The list is shifted at the head and holed in the middle. **HOME:** `gate-multiplies-02.js`, whose output the document pastes. ## TA-3 (HIGH). "Flat at 3.2 to 3.7" against 2.93 to 4.20 on the table directly above it — and it reaches three more documents, two of them mine. `maxgap-law.md` §8, under its own pasted table: "`M(x,x^2)/ln^3 x` is **flat at 3.2 to 3.7** over a 47-fold range in `x`", concluding "**the true localized margin is `x^2/(3.5 ln^3 x)`**". Recomputed from the document's own `M(x,x²)` column (x = 211…9973): **3.249, 2.926, 3.099, 3.615, 3.274, 4.202, 3.673**. True span **2.93 to 4.20**, two of seven rows outside the quoted band, one at each end. The band's own script carries the string as a hardcoded `console.log`, not a computed value, so the script repeats it. **Two consequences.** The derived constant 3.5 is the midpoint; since margin = x²/(c·ln³x), the honest worst case on this data is **x²/(4.2 ln³x)**, 20% tighter. And §8 concludes "the measurement above settles it in `LOCALIZED-GAP`'s favour", where `LOCALIZED-GAP.md` §5's band at k = 2 is 2.4 to 3.2 — against the true 2.93–4.20 the agreement is partial, not clean. **It propagates.** `LOCALIZED-GAP.md` §5 quotes "flat at 3.2 to 3.7 over a 47-fold range" verbatim. And **it is the same object as my T-3**: `FOLD-PROFILE.md` §12a's "M(x, x′²) ~ 3.5·ln³x" and its "c measured flat in 1.2 to 1.75" both descend from this constant. **T-3 and TA-3 should be adjudicated together**; they are one measurement quoted at its favourable half in two different ways. **HOME:** the table in `research/maxgap-law.js`. **NEEDS CHRIS'S JUDGEMENT** on whether 3.5 moves. ## TA-4 (MED-HIGH). "All nineteen terms" against seventeen enumerated, and the two dropped are the ones that break flatness. `two-class-lower-bounds.md` §5: the free-choice shortfall "is **flat at about 0.73 across all nineteen terms with no trend** (0.80, 0.54, … 0.74 for `n = 5 .. 21`)" — seventeen values, labelled n = 5..21. `node two-class-lower-bounds.js` §1c run here runs **n = 3..21 = nineteen terms**, and the two omitted head terms are **1.000 and 1.000**. Across all nineteen the mean is **0.755**; the quoted 0.73 is the seventeen-term mean (0.7265). The §5 custody bullet repeats it: "mean about 0.72, no trend over `n = 3 .. 21`" is the n = 5..21 reading wearing the n = 3..21 label. **Why it matters more than a count.** The caveat's whole job is to rebut the objection that the shortfall *decays* with x. The two terms it silently drops are the 1.000s — precisely the early-decay evidence for the objection. ## TA-5 (MED-HIGH). The Ziller–Morack mean loses its range restriction, growing from 9 terms to 21. `gate-multiplies.md` §9: "the measured multiplier is already at that rate, **mean 1.06 of budget over Ziller and Morack's 21 terms** with no downward trend." **HOME, `U-FRAME.md` §4:** "**At p = 41 to 73** it reads 1.39, 0.97, 1.36, 0.75, 1.15, 1.10, 1.18, 1.00, 0.61, **mean 1.06**" — nine values, nine primes, mean 9.51/9 = 1.057. `gate-multiplies.md`'s own §1 and §7 carry the restriction correctly; §9 is the site that drops it. Not conservative: the tail of that nine (1.00, 0.61) is where the reading is lowest. ## TA-6 to TA-8 (MEDIUM) - **`gate-multiplies.md` §4 reading 2**: "The counting bound is loose by **3.5x to 6.7x**" is labelled "MEASURED at all four folds" but 3.5 and 6.7 are the min and max over the **two** folds the document pastes. Over the four the script runs, the extremes reach **7.9x** (`T₁₇ by 19`, m = 32: 63.5 against κ(32) = 8). The same 3.5–6.7 is quoted three more times, in §5 and §6, where it is load-bearing against the Overshoot Budget's factor 1.82. - **`discrepancy-two-class.md` §10** says the two-class rising-zero share falls "**100% → 3.24%**"; its own §2 table starts at **66.67%**, confirmed against the script's pasted output and against 2/3. The error inflates the very contrast §10 is drawing (a 31-fold fall becomes a 21-fold fall once corrected). - **`covering-dive.md` "REALISTIC TARGETS"** (dated 2026-08-14): three of six targets have since been executed inside the repo — target 1 is `paper/beta2-note.md`'s theorem, target 3's G₂ computation is `research/oeis-G2-submission.md`, target 4 is `two-class-lower-bounds.md` §5's certified greedy ladder — and target 3's "extending terms" is directly countermanded by `h2-scoping.md` §7.1, "**Do not attempt exact term 22**". Relatedly, `covering-dive.md` synthesis point 3 still calibrates the two-class upper bound **INFERRED** ("folklore-available but unwritten") against `two-class-lower-bounds.md` §8's **PROVEN**. The literature layer (Q1–Q5) is unaffected; only the forward-looking list is stale. ## TA-9 (MEDIUM). A MEASURED calibration mark with nothing behind it. `theta-ladder.md` §8 reading 13: "**MEASURED.** The upper ladder is **3x to 10x more expensive** than the divisor-pair count suggests at first glance (**§9**)". §9 contains no such statement; its cost model (N²·2.85e−8 s) checks against §2's own measured `secs` column to **±20%** at all five levels (0.76, 1.01, 1.04, 1.17, 1.15). No reading of §2 or §9 produces a 3-to-10 factor. **NEEDS COMPUTE OR CHRIS'S JUDGEMENT**: either stale text from a superseded cost model, or a measurement no longer in the file. It is one of the two reasons reading 13 gives for not extending the ladder. ## TA-10 to TA-16 (LOW-MED and LOW) - `gate-multiplies.md` §4: "`kappa(m)/m` **falls monotonically** … **at every fold**" is false at 2 of 4 folds, visibly in its own paste (`T₂₃ by 29`: 16:0.313 → 24:0.333). Endpoint values check out. - `gate-multiplies.md` §4: "**Four folds**" where `gate-multiplies-02.js` emits seven. Defensible as a curated subset — except that it is exactly the confusion that produced TA-2. - `maxgap-law.md` §2: "**fourteen** exact max gaps" against a **nine**-row paste with no ellipsis. **Here the prose is right and the paste is wrong** (the script loops 7 levels × 2 modes = 14 under `--big`); the fix is to mark the paste abridged, not to change the count. Recorded because the campaign's "the enumeration is the authority" rule gives the wrong answer here. - `maxgap-law.md` §7a: "the **MEASURED c1 = 0.3722**" is the `[11,271]` 54-term mean; the repo-canonical value carried in §2, §3 and `two-class-lower-bounds.md` §6 is **0.3718 over 46 terms, p ∈ [11,229]**. Recomputed from A048670 directly. 0.1% numerically, but §4's own governing rule is "Report `c` with `(x, lnD)` attached or do not report it", and §7a reports it bare under a level (229) it does not belong to. - `two-class-lower-bounds.md` §9: "all **50** exact terms of A048670 … from 0.240 at x = 5 to 0.0145 at x = 229" — both endpoints verified exactly, but [5, 229] is **48** terms. Fifty would start at x = 2, where the ratio is 0.5, which would also break "falls monotonically from 0.240". - `two-class-lower-bounds.md` §3: "This is the strongest lower bound available for G₂ today and **it is not in the repo**." `G2(x#) ≥ g(x#)` now appears in seven files including three paper files. §1 of the same document has the past tense right ("it *was* not being used"). A live false-absence claim about a repo artifact. - `exponent-control.md` §7 item 3, the line other files are instructed to copy, says "**58 terms**, true exponent 1, measured 1.282 ± 0.008"; §1 and §2 say **56** (`p ∈ [5, 271]`). Both land on 1.282 so nothing downstream is numerically wrong, but the mandated quote-line pairs a 56-term fit's value and error with a 58-term label, and `U-FRAME.md` §4 has copied it verbatim. - Four smaller slips in `discrepancy-two-class.md` and `maxgap-law.md`: "×1.177 per fold" is the 7-fold geometric mean where the sentence says "from x = 11" (there ×1.147); "about √3 per fold, which is **exactly** the square-root gap" where the measured rate is 1.634 = 3/1.8356 and √3 = 1.732 is the asymptote; "across **five** folds" against six pasted values (home `FOLD-PROFILE.md` §3 says "at x = 7 to 23", six levels / five ratios — the caveat that p moves with x *is* carried correctly); and "the **58** exact terms … 6.17 at p = 11 to 252.12 at p = 271", whose endpoints span 54 (the 22% and the 41-fold lever are both verified correct). **Two out-of-scope observations TA raised**, offered as routing rather than findings: `research/oeis-G2-submission.md` COMMENTS states the reduction as `a(n) < prime(n+1)^2 − prime(n)` against the settled `x′² − 2`; and `G2-STATE.md`:529 still says full decoupling "**halves** the open band" against the settled ~71% carried at `G2-STATE.md`:803 and `ZONE-POSTULATE.md`:249. Both are outside every partition's file set this wave. --- # PART 3 — TB, the sieve and moiré leaves Files: `sift-limit-attack.md`, `bv-import-survey.md`, `dhr-verification.md`, `maier-matrix.md`, `origin-excess.md`, `LOCALIZED-GAP.md`, `localized-single-alignment.md`, `a3-03-f-from-census.md`, `a3-09-histogram-operator.md`, `d2-d4-bijection.md`, `two-moire-argument.md`. Four scripts re-run (`maier-matrix.js`, `origin-excess.js`, `sift-limit-attack.js`, `localized-single-alignment.js` at 307 and 1613). ## TB-1 (HIGH). "Untried in tile form", eight minutes before it was tried. `bv-import-survey.md` §4: "The vector sieve (Brüdern–Fouvry style, two combs sieved jointly) is the natural follow-on and **is untried in tile form**. [ASSESSMENT]" **HOME: `sift-limit-attack.md` §4.5 + `research/sift-limit-attack.js`**, which "built the actual Rosser supports, machine-verified the sandwich Λ⁻ ≤ θ ≤ Λ⁺ at every integer scanned, and measured the certificate T(x) … directly". Run here: 2.1 s, thirteen configured rows including exhaustive full-period scans of the p < 20 tile. `theta-ladder.md` carries the same family to z = 71. `bv-import-survey.md` is timestamped Aug 14 21:50 and `sift-limit-attack.js` Aug 14 21:58 — **it went stale eight minutes after it was written** and has stayed stale. ## TB-2 (HIGH). A "largest single event" superlative refuted by the event log it is read from. `localized-single-alignment.md` §6: "p = 739 creates the record patch … jumping 1266 → 1848 **(0.379 nats, the largest single event on the ladder)**." The script's own event log, from a re-run at x = 1613 (36.7 s, all controls passed), prints `53 BOUNDARY 204 -> 300` alongside it. **ln(300/204) = 0.3857 > ln(1848/1266) = 0.3782.** The p = 53 event is inside the measured window (x₀ = 53) and is one of the nine BOUNDARY events §3 P4 counts. Under the alternative reading of "the ladder" as all 253 folds, p = 7 (12 → 30) is **0.916** nats. The superlative fails either way. ## TB-3 (HIGH). A number that reproduces from nothing, and a blanket claim the omitted third of its own output refutes. `origin-excess.md` reading 6: "At S = x′² the class a_q = 0 is the **worst of the q classes** at the smallest prime (rank 17/17 at y = 13, x = 23; 16/17 and **13/13** at y = 11)." The document's own pasted output prints, for y = 11, x = 23: `rank of a=0: **11 of 13**`. "13/13" appears nowhere. And the §4 paste **silently omits a third block the script prints**: `y=11 x=19 S=529 q=13: rank of a=0: **6 of 13**`. So at the smallest prime, a = 0 is worst in **1 of 3** computed cases, 11th of 13 in the second, and **mid-pack in the third — the one not pasted**. §4's prose ("At the smallest prime, the one that matters, a = 0 is the worst class of the q") and §0 item 3 inherit the overreach. **HOME:** `origin-excess.js` section D. ## TB-4 (MED-HIGH). h₂'s exponent attached to G₂. `sift-limit-attack.md` §3: "…where the direct ratio **G₂/(x ln²x)** wobbles … the control-corrected growth exponent is **1.57** central". **HOME: `exponent-control.md` §5**, which tabulates 1.57 ± 0.06 for **h2** and 1.54 ± 0.09 for **G2**, and instructs in bold: "**Quote 1.57 for h2 and 1.54 for G2**". `paper/beta2-note.md` repeats the split. The sentence's subject here is unambiguously G₂. The campaign's already-settled distinction, surviving at this site. ## TB-5 (MED-HIGH). "The grain census distribution remains lawless pending the correlation computation." `d2-d4-bijection.md` §Status. `research/grain-census.js` — committed **fourteen minutes after this file** — carries the correlation computation and an exact law in its own header: "count(d) = Σ_{S ⊆ …} (−1)^{|S|} N({0} ∪ S ∪ {d}) … **an identity, not a model** … **This turns 'forced equality' into a finite check.**" `a3-03-f-from-census.md` states it plainly: "`research/grain-census.js` **proved** an exact finite identity for count_x(d)". The census is not lawless, the computation is not pending, and "no forced equal-count law exists" is now decidable rather than asserted. ## TB-6 (MED-HIGH). "The nearest unclaimed theorem" has been claimed, in this repo's own paper. `two-moire-argument.md`: "**The nearest unclaimed theorem:** the two-classes-per-prime Jacobsthal upper bound is **open at ANY exponent** … **Any upper bound at all would be new**." `paper/beta2-note.md` now states its own Theorem and calls it "**first published upper bound of any exponent for the two-class problem**". **NEEDS CHRIS'S JUDGEMENT, and the reason is precise.** The literature half survives: `covering-dive.md` §2.1 still carries "[ABSENT]" with a search log. But beta2-note bounds **G₂** while two-moire's sentence names **h₂**, and `exponent-control.md` records G₂ ≤ h₂ pointwise, so a G₂ bound is not an h₂ bound. What is definitely stale is the framing — the nearest unclaimed theorem has been claimed in the repo's own paper file and this document does not know it. ## TB-7 to TB-13 (MEDIUM) - **`origin-excess.md` §0**: "ρ(2) < 1, measured directly at **eighteen levels** … **0.79303 at x = 1487**". 0.79303 is the single best of eighteen; the column *rises away* from e^{2γ}/4 monotonically thereafter (0.79475, 0.79668, 0.79863, 0.79922). "VERIFIED to four digits" holds at one crossing, not as a converging measurement. Separately, §5's table is an **unmarked 11-of-18 excerpt** — the document explicitly marks its *other* truncation but not this one, so a reader cannot tell that seven rows exist below x = 29. `maier-matrix.md` §5 inherits the top-five quote without the "of eighteen" scope. - **`localized-single-alignment.md` §4**: "folds moving M at all | **21 of 253**". The script prints `folds measured: 240 … (folds moving M at all: 21)` with `meas = rows.filter(r => r.p >= 53)`. The correct pair is *21 of 240* or *28 of 253* (§6 gets the latter right); "21 of 253" is neither. The same table's next row is correct. - **`localized-single-alignment.md` §4 and §7**: "total spend from x = 53 | 2.001 nats = **45% fixed-window + 55% boundary**". The script prints 1.086 + 1.301 = **2.387**, not 2.001 — the per-fold increments are `max`-ed and do not partition the cumulative growth. 45% of 2.001 is 0.90, but §1 of the same document quotes the fixed-window spend correctly as 1.09 nats. §1 and §4 disagree about one quantity and §4's equation is arithmetically false as written. - **`a3-09-histogram-operator.md`**: "m̄/ln²p **falls** 3.70, 2.85, 2.61, 2.50, **2.49**, 2.42 … VERIFIED by exact computation of W/D: … **2.5024** … which **reproduces the six values above digit for digit**". Recomputed from scratch: 2.5024 rounds to **2.50**, not 2.49, and the exact sequence *rises* from 2.4954 (p = 97) to 2.5024 (p = 199). The prose hides the rise and supports the word "falls"; "digit for digit" is false at the fifth entry. - **`maier-matrix.md` §4a item 1**: "VERIFIED at **3 of 3** cells with S > y′²" and, four lines later, "fails in **6 of the 8** test cells with S > y′²". Same population, two sizes. `maier-matrix.js` re-run: it contains **no S > y′² test at all** (section F hard-codes `S = yp*yp`). `grep -rn "1210"` over the repo returns one hit, this line. The named cell's arithmetic is right (y = 7, x = 19, S = 1210: L = 43 against bound 10); neither count has a computing artifact. **NEEDS COMPUTE OR CHRIS'S JUDGEMENT.** - **`maier-matrix.md` §5**: "**ρ has its minimum at u = 2**", flat, in the section it calls "the headline". **HOME `origin-excess.md` §0**: "**The third, that ρ attains its minimum exactly at u = 2, is INFERRED** from the squared-Buchstab form and **is not proven here**; the measured trough … sits at **u = 2.0903**." `origin-excess.md` §8 keeps the hedge ("*Asymptotically* ρ has its minimum at u = 2"). (`FOLD-PROFILE.md` §9 also states it flat, so which file is home for the argmin may need Chris's call — but `origin-excess.md` is the only one that looked and it says INFERRED.) - **`maier-matrix.md` READING 4**: "the origin … **carries ρ(2) = e^{2γ}/4 = 0.79305 of the mean density**". **HOME `origin-excess.md` §5, boxed**: "The origin ceiling (MEASURED, **HL-conditional in its exact value**)". The raw measured ρ_x(x′²) is **0.91207** at x = 6037; 0.79305 appears only after dividing out a separately measured HL factor of 1.14120. maier-matrix's §5 body carries the caveat; the READING — the line designed to be quoted onward — drops it and states a bare equality 15% from the raw measurement. ## TB-14 to TB-21 (LOW-MED and LOW) - **`sift-limit-attack.md` §4.5**: "at exponent **2.2, below β₂/2 and below the Ziller-Morack conjectural p² ceiling**". β₂/2 = **2.1332** and the p² ceiling is exponent **2**; 2.2 exceeds both. `sift-limit-attack.js` carries the identical error twice, so the .md is copying rather than flattening — but the arithmetic is wrong in both. **NEEDS CHRIS'S JUDGEMENT** (the u = 1.8 row *is* below both). - **`a3-03-f-from-census.md` §Lemma A**: "for all **302** primes from 5 to 1999". The loop is `PR.filter(q => q >= 5 && q <= 2000)`; π(1999) = 303, so the count is **301**. Verified by sieve. The 302 is a hard-coded string in three places in the script, never computed from `PR.filter(...).length`. - **`sift-limit-attack.md` §3**: "K\* = **0, 0, 2, 10** escalates" drops the levels and truncates at four of six. `NATAL-CAP-CAMPAIGN.md` says "0, 0, 2, 10 **at @11..@19**"; `GLOSSARY.md` says "**0, 0, 2, 10, 27, 69**". Direction is against the document's own argument, so consequence is low. - **`sift-limit-attack.md` §4.5**: "γ = **0.23..0.33** measured" excludes the z = 50, u = 2.8, s = 1.4 row at **0.380** (thirteen values re-run). Nothing says that row is excluded by intent. - **`origin-excess.md` §5**: "**all fifteen readings** agreeing on one constant", followed by a six-row table and six ratios. The fifteen may live in the run log; nothing in the document lets a reader check it. - **`origin-excess.md` §5 and `maier-matrix.md` §5**: "the constant's **fifth** independent appearance in the repo". No enumeration exists to adjudicate it, `grep` finds e^{2γ}/4 at more than five sites, several descend from one home (the β-limit chain), and the origin's own ρ(2) is *identified* with `FOLD-PROFILE.md` §9's trough constant two sentences later. **NEEDS CHRIS'S JUDGEMENT**; agreement descending from one home is not independence. - **`bv-import-survey.md` throughout**: `anchored-note.md`, `staircase-note.md` and `beta2-note.md` cited bare from `research/` where all three live in `paper/`. - **Adjacent, reported because it is a named companion**: `a3-09-histogram-operator.js`'s READINGS block still carries "**e^{2 gamma}/(4 C_2) = 1.20**", the retired factor-2-slipped value the campaign settled against e^{2γ}/(2C₂) = 2.4026. The `.md` is correct; the script is not. --- # PART 4 — TC, the natal-cap leaves Files: `natal-cap-04/10/12/14/19/21/23/26/30/31/32/36-*.md`, `anchored-windows.md`, `SCRIPTS.md`. No scripts re-run; every check is arithmetic done from scratch or a comparison against a committed OUTPUT/READINGS block or a `wave7-logs/` file. ## TC-1 (HIGH). **CONTRADICTS A SETTLED VALUE.** Max VR is enumerated at @19, it reads 2.293, and it breaks the trend three documents rest on. **`natal-cap-31-calm-vs-kill.md` §Theorem 2, "Scope, exactly":** > "that maximum is **enumerated at @11, @13 and @17 only** — the three levels this > file walks in full … so the theorem is established at those three levels **and > nowhere else**." and the conjecture box: "Its whole support is two measured trends over three points: **max VR falls, 2.78 / 2.35 / 2.14**, and the driver S̄/√(K·V̄) rises, 3.1 / 4.9 / 9.8." **Against `natal-cap-19-calm-lemma.js` PART A @19, its committed OUTPUT block:** ``` ===== PART A @19: W=9699690 N=252450 K=435 scour (23..3109) — full ensemble, all 9699690 rotations ===== W/2 (predicted loudest): VR(W/2)=2.293 rank-from-top 0/9699690 (ties 1) ``` `rank-from-top 0` is an enumerated maximum over all 9,699,690 rotations, and `natal-cap-19-calm-lemma.md`'s own closing paragraph says so in prose: "W/2 the single loudest rotation for the **third level running**". **The convention was checked before the claim was made.** At @17, √(K·V̄·VRmax) = √(120 × 1144.40 × 2.143) = **542.5**, reproducing cap-31's "542" to the digit, and the driver 3614.93/√(120×1144.40) = **9.755** reproduces its "9.8". Same ensemble, same normalisation. **Two defects in one paragraph.** (a) A false absence: the enumeration exists and ran. (b) **The trend is refuted by the fourth point**: 2.78 → 2.35 → 2.14 → **2.293** goes *up*. **This overrides a value the campaign settled.** Wave 4's R-2 and this wave's briefs all carry "enumerated at @11, @13 and @17 — three levels", and `TODO.md`, `GLOSSARY.md` and both papers carry the three-level form. **Nothing should be applied from this finding until the @19 enumeration is confirmed at the artifact by a second reader.** **What TC computed and did not commit to**, offered as routing only: all ingredients for the theorem at @19 are already in the corpus (K = 435, V̄ = 8944.60, VRmax = 2.293 from cap-19.js Part A; S̄ = 49,238.76 from `research/wave7-logs/cap35-x-multiplicity.log` PART 6, whose @11/@13/@17 rows match cap-31's table exactly). **HOME:** `natal-cap-19-calm-lemma.js` PART A owns the enumerated maximum; `natal-cap-31-calm-vs-kill.md` governs the theorem's scope statement and is the site. ## TC-2 (HIGH). The wrap identity has been found, implemented and run — one line below the wave-4 fix. **`natal-cap-21-beyond-chebyshev.md` §Next steps item 2**: "**Find** the 4-point wrap identity … **the only route** to @17's 4.9e16-term sum", and §"The @13/@17 blocker": "@17 … **needs a genuinely new identity**". **Against `natal-cap-32-wrap-identity.md`'s own one-line abstract**: "The 4-point identity cap-27 asked for **exists**, is verified through @13 against the certified value, and turns @17's 'dead' T4 into an **11-minute computation** … T4@17 = **4,616,850,623,332** ± 4e−4 rel." `TODO.md` item 6 already carries it. **Item 1's wave-4 fix landed correctly** and was verified; item 2 was not touched. The superlative "**the only route**" is separately falsified by `natal-cap-34-wrap-precision.js` stage [K], which prices the κ₄ road ("at @17 a mere SIGN (kappa4 ≤ 0) would give P(S=0) <= 3Var²/μ⁴ = 3.05e−8 outright"), and κ₄ is negative at both certified levels (recomputed: @11 −1.14, @13 −0.48). Same site, LOW-MED: item 1's "Only the @17 **rerun** is outstanding" — @17 never ran, and `TODO.md` says "the @17 rerun, **which never started**". "Rerun" without that clause reads as a repeat of a completed pass. ## TC-3 (HIGH). The kill shadow was retired by a theorem-grade result. `anchored-windows.md` still calls it new and unexplained. **`anchored-windows.md` §5 heading**: "**New object: the kill shadow (measured, unexplained)**", with "The shadow constant ≈ 0.85 and its k → ∞ recovery rate are **new measurable objects; we found no prior study**", and §7: "**New measured object: the kill shadow ≈ 0.85 just past every zone.**" **`GLOSSARY.md` §Deprecated**: "**'Kill shadow' → absorbed into the Unification Law (kept only historically).**" **`ATTACKS2.md` row 5**: "✅ **DONE, CLOSED** … **THE UNIFICATION LAW** … Unifies … **the kill shadow (= curve average over first octave — no longer a separate object)**." The script agrees: `attack2-05-07-integral-ladder.js` reading A5-2, "The kill shadow is no longer a separate object". **The pointer runs the wrong way, which is the diagnostic.** `SCRIPTS.md` lists `attack2-05-07-integral-ladder.js` with **companion prose `research/anchored-windows.md`** — the script that dissolved the object names this file as its prose, and this file has never heard of it. ## TC-4 (HIGH). Both of cap-14's named next steps were executed by cap-21, and step 1's named outcome was refuted. **`natal-cap-14-discrepancy-lemma.md` §Next steps**: "1. Exact E[v_k²] … (**the quadruple sum should collapse by CRT as the pair sum did**) → **an unconditional ensemble theorem beyond Chebyshev, the first rung of the ladder**. 2. The ℓ∞ lemma … max_c|Y_c − 2N/q| **≤ 7√(N/q)** is a finite verified fact at **three levels**". **`natal-cap-21-beyond-chebyshev.md`**, whose dateline reads "executes cap-14's two named next steps": Prop 4 computed E[v_k²] **exactly** and found the per-step route "**dead** for structural reasons … Beyond-Chebyshev lives at the endpoint (Theorem 2), not in the chain", and blocker 2 refutes the CRT prediction outright ("**No CRT closed form**"). Route B measures the step-1 constant at **four** levels (2.893 / 2.299 / 2.488 / 2.011), with the reading that "step 1 needs only C₁ ≈ 2–2.9 — **the marchwide constant 7.34 is dominated by EVOLVED sets, not the natal start**". So the section is a live to-do list instructing a future agent to redo done and partly refuted work, and its stated constant overstates the truth by 2.4× while its level count is one short. ## TC-5 (MED-HIGH). SETTLEMENT DELIVERED: the Anchored Typicality Measurement is **two levels, not three**. Wave 4 left this open and asked for the home to be opened. `natal-cap-19-calm-lemma.md` §"What Lemmas 1–3 do and do not give" says, and only says: "Σ dev(0,q)² / Σ V_fused = **0.935 @13, 0.939 @17**". `anchored-calm.md`'s status row says "@13, @17, **@19**". **The artifact settles it.** `natal-cap-19-calm-lemma.js` OUTPUT: @13 and @17 are full scours (34/34 and 120/120 primes) at 0.9352 and 0.9392; **@19 is a 6-of-435 sample and reads 0.2941**, with a mean percentile of 35.2% against 47.9/47.8. The @19 datum does not merely fail to support "the anchor is position-typical" — it points the other way, and cannot be a third supporting level under any reading. **Two consequences.** `anchored-calm.md`'s scope cell must come down to @13, @17 (its own "The two numbers the table stands on" already lists only two, so the file contradicts itself). And **the home is silent about the @19 sample** — it reports @19 elsewhere but never records that the typicality statistic was sampled there and came back at 0.2941. A home that omits the datum deciding its own scope is how the downstream three-level form survived. **Whether the @19 sample is reported as a caveat or omitted with a stated reason is Chris's call; the scope cell is settled.** ## TC-6 to TC-9 (MED-HIGH) - **`natal-cap-04-packing-notes.md`**: "@17 the cap fails **for every q ≤ 211**". The script's OUTPUT enumerates: "DEFINITIVE cap failures … **38 primes** [19,…,211]". π(211) − π(17) = **40**, and **193 and 199 are absent from the list**. The `.js`'s own summary line ("all 38 primes q ≤ 211") is itself inconsistent with its enumeration. Per the enumeration-is-authority rule, the `.md` restated a 38-element list as a universal. Needs a one-line recheck of 193/199. - **`natal-cap-10-sieve-cap.md` §3**: "Σcap crosses N at q = 97, **the 23rd of 120 primes**". The script's READINGS say "**18th** of 120", and an independent recount from the @17 scour's start at 19 puts 97 at index **18**. (113 is the 23rd — a plausible source of the slip.) MED-HIGH because this number is the file's stated evidence for "cap-mass at small q". - **`natal-cap-36-skeleton-door.md` intro**: "reproducing @23 as its control **(18.5 min)**". The `.js` header — the artifact that owns the runtime — reads "plus **11.3 min** for --at29, measured 2026-08-17; an earlier run of the same pass took 18.5 min **on a loaded machine**", and its output prints `[658s]` = 11.0 min. This is one of wave 4's settled values still live at one site, and it puts two files in direct disagreement, since `natal-cap-30-skeleton-bound.md` already carries 11.3 min. (`wave7-logs/cap36-at29.log` shows 1111.9 s — that is the loaded-machine run the header explicitly demotes, so the log is not the authority here.) - **`natal-cap-32-wrap-identity.md` §"The honest wall"**: "2D class histograms over prime pairs — **identified, not implemented**". `natal-cap-34-wrap-precision.js` stage [J] builds them and computes the contraction cost **exactly** at @13, @17 and @19, and `wave7-logs/cap34-exact13.log` refutes the cheap form ("a pure class-histogram count … **−64.36% of the layer**"). `TODO.md` item 6 has absorbed it: "**The class-histogram shortcut is REFUTED**". More broadly, cap-32.md carries **no reference to cap-34 at all**, though cap-34 exists solely to grade cap-32's engines. ## TC-10 to TC-16 (MEDIUM and below) - **`natal-cap-31-calm-vs-kill.md`**: "Measured X(0)/X̄ = 1.45 / 0.991 / 0.948, **descending**". `wave7-logs/cap35-x-multiplicity.log` PART 6 (whose @11/@13/@17 rows reproduce cap-31 exactly) adds @19 at **0.9558** — up. `TODO.md` §X already records the correct reading and names `(X̄−X(0))/S̄` as the better statistic, "exactly the form Assumption A is stated in", which is the form cap-31's own X-floor box uses. cap-31 carries no pointer to cap-35 anywhere. - **`natal-cap-30-skeleton-bound.md` Prop C.1** merges two different bounds: the displayed bound **has L in it** (`L/4 + lB/2`) and the next sentence calls it "**L-free**". The L-free bound is `natal-cap-36-skeleton-door.md` **Corollary B**, whose aggregate is 5.7e2 @11 / 5.6e4 @23 — cap-30's quoted 18.2 and 1593 are cap-26's Abel numbers. And **cap-36 has no section titled "The per-branch bound"**; the phrase is a bolded sentence inside Corollary B, and both files point at a section name neither has. - **`natal-cap-30-skeleton-bound.md` §Next**: "Cap-36 measures that door open at M = 30, 210 and 2310 **with square-root cancellation**" drops the home's "**from @19 on**". At @17 the M = 30 ratio is 1.16e−1 against K^{−1/2} = 9.1e−2 — above square-root strength. `TODO.md` says "moduli 30 and 210", a third variant. - **`natal-cap-31-calm-vs-kill.md` reading 3**: "splits as **−567 from overlap credit versus −51 from strikes**". The script prints `S−S̄ = −515.9 = X̂(−566.7) − D̂(−50.8)` — a **difference**. Read additively the prose gives −618, and the strike channel's contribution is **+50.8**, i.e. it offsets. A reader gets the sign backwards on the channel the file's whole thesis is about. - **`natal-cap-36-skeleton-door.md` intro**: "the aggregate anticorrelation is a **theorem at every x ≤ 29**", against the settled "**certified** at every computed level, @11 through @29" and `anchored-calm.md`'s "**six computed levels only**". "Every x ≤ 29" reads as covering all levels below 29 including @7, which is not in the table. Low consequence — those levels exhaust the primes in [11, 29] — but it is the exact phrasing the campaign retired. - **`anchored-windows.md` §7 "Verification code"**: cites "full source: **scratchpad/anchored-check.js** (run 2026-08-13)". The file does not exist anywhere, and `git log --all -- '*anchored-check*'` returns nothing: never committed. Its outputs are §3's life-cycle numbers and the whole §5 shadow table. This is the same hollow-reproduction shape commit 7e6e49f fixed in `U-FRAME.md`, surviving here, and it falsifies `SCRIPTS.md`'s opening claim that "**Every number in this body of work was produced by one of the scripts below.**" - **`natal-cap-19-calm-lemma.md`**: "six counterexample primes … (**cap-23's verdict table**, cap-30 Prop D)". cap-23's verdict table covers **four** levels and four exceptions; the six-across-six statement lives in cap-23's later section. Count and scope right, pointer wrong. --- # Coverage: what I did NOT sweep, and why **Swept end to end, by me:** `U-FRAME.md`, `kappa-not-L.md`, `operator-and-pair-count.md`, `f-decays.md`, `FOLD-PROFILE.md`, `OBSERVATIONS.md`, `ATTACKS.md`, `ATTACKS2.md`, `ATTACKS3.md`. **Swept by the three delegated sub-sweeps**, file lists at the head of Parts 2–4. I did not re-derive their findings; provenance is marked per entry and the artifact each was settled against is named. **TC-1 in particular contradicts a value this campaign settled and must be confirmed at the artifact by a second reader before anything moves.** **Not swept at all, and each is a real gap:** - **`research/*.js`, still.** R named this as the coverage gap to spend a wave on and it is still open. I opened seven scripts and **two of my four highest findings came out of them** (T-1 from `attack2-rich-vein.js`, T-3 from running `fold-profile-08`), plus the retraction in T-11 and the count in T-5. That is a hit rate high enough to say the surface is not merely unswept but productive. There are ~128 scripts and I opened `a3-04`, `a3-10`, `attack2-rich-vein`, `fold-profile-08`, `fold-profile-07`, `fold-profile-13`, `lucky-control` and `verify-ladder{,-big}`. Everything else is untouched. - **The natal-cap `.js` layer specifically.** 37 scripts, the campaign with the largest gap between what its scripts print and what its summaries carry, and wave 4's R-1 came out of exactly there. - **`research/wave7-logs/`** — eight run logs, not opened by any wave. They are the primary record for cap-34, cap-35, cap-36 and the Lemma V pilot, and a log is the one artifact that cannot have been edited to agree with a summary. - **`research/natal-cap-33-overnight.txt`, `natal5-17tile-scour.txt`, `natal5-variance.txt`** — three `.txt` outputs cited by nothing I checked. - **`research/a3-*.md`** beyond the two I read at the line I needed (`a3-03-f-from-census.md`, `a3-09-histogram-operator.md` went to a sub-sweep; `a3-05-bound-L.md` is P's). - **`research/history/`** — out of scope by the doc convention, and correctly so, but it means I could not check whether any of T-1 through T-15 was already adjudicated and reverted. I checked the thirteen `ADJUDICATED` pairs in `research/qc/checks.js` and none of my fifteen appears there. - **`web/`, `attestation/`** — out of scope by construction. - **The homes I opened only at the line I needed**: `NATAL-CAP-CAMPAIGN.md`, `paper/moire-primes.md`, `paper/anchored-note.md`, `THE-DIALS.md`, `a3-05-bound-L.md`, `certificate-engine.md`, `SCRIPTS.md`. A scope error *inside* any of them would not have been seen from here. **Gaps the three sub-sweeps reported honestly, carried up verbatim in substance:** - **The literature layer is unaudited, everywhere.** No sub-sweep had web access. `covering-dive.md`'s ~40 cited PDFs and every `[ABSENT]` verdict in its Q1–Q5, `sift-limit-attack.md` §2's Ford and Franze quotations, `natal-cap-10-sieve-cap.md` §5's six literature-access claims (all six flagged [UNVERIFIED] by the file itself), and `natal-cap-04`'s OEIS "0 hits" searches all rest on searches nobody could repeat. TB did corroborate Franze's β₂ values against `dhr-verification.md` independently; Ford's Table 1 is unconfirmed. - **`d2-d4-bijection.md`'s verification block has no runnable script** — its code fence reads "(script as run 2026-08-14; see conversation for full listing)". TB recomputed the P = 30 layer and all four ∏(p−2) predictions by hand; the triples-count = 0 claim and the P = 210 bijection are checked only in the small case. - **`natal-cap-36-skeleton-door.md` Measurement D's "separate census (not in the script, same method) … nine levels through @41, 1,117,909 scour primes"** has no artifact in the repo and cannot be verified from it. The file discloses this, so TC did not report it as a defect. - **`natal-cap-34-wrap-precision.js` has no pasted OUTPUT/READINGS block**, unusual for the house format, so the exact @13 layer split lives only in `wave7-logs/cap34-exact13.log` and in `TODO.md` prose. That is the evidentiary basis for TC-9. - **`gate-multiplies.md` §6's twelve-row recursion table** — twelve verdicts, each pointing at a different home section — was not verified row by row. TA names it as the place in that file where a dropped scope would do the most damage. - **`cap-31` ↔ `cap-35` is unfinished** and TC names it as the largest thing it leaves open: cap-35 extended cap-31 to @19 across its whole measurement table, and only the two rows bearing on TC-1 and TC-10 were compared. Further stale trend readings in cap-31 §Readings are likely. - **`LOCALIZED-GAP.md` §3's "x = 13933 (VERIFIED)" and §§5–6's measured tables** were not run against `localized-01/02/04`; §7's A5/A9 cross-checks and §8's boundary sweep are unrun. - **`theta-ladder.md`'s dependence on `sift-limit-attack.md` §4.5** is spot-checked only. §7 explicitly names that file as "the home and the authority" and its whole accounting table was not verified row by row. - **Numbers with no parent in any pasted output**, found and not chased: cap-31's c_obs = 1.25/1.46/2.06; cap-12's "−139,799 / +140,148" head/bulk split; cap-19's "q = 19 @17: R = 0.15"; `bv-import-survey.md` §§3.1–3.3's Staircase tail constants and the x = 149 crossover. **Four method notes for the shepherd.** 1. **The false-absence grep works, and it needs a second pattern.** Grepping "not yet run / never / nobody has / does not exist / the only one" over my surface returned about forty hits, and thirty-five of them were *mathematical* absences ("there is no such constant", "there is no drift left to happen") which are not the defect. The two that mattered, T-1 and T-4, used neither phrasing: they said **"unexplained"** and **"unexplored"**. Those two words, plus "unexamined", "untouched", "open", "not yet", "remains" and "still has to be", are the second pattern, and they are the ones a scoreboard uses. Both of my hits were in scoreboard-shaped documents with one verdict per row, which is the shape R predicted would lose a scope in transit. 2. **Running the artifact beat reading it, twice, and cheaply.** T-3 took one `node research/fold-profile-08-*.js` (30 s) and could not have been found any other way: there is no near-duplicate to diff, the numbers printed are all correct, and the only defect is which five of ten appear. T-13 took one `node lucky-control.js` (64 s) and converted an unsourced table into a verified one. Wave 4 bounded lesson 2 by saying five of P's fourteen needed the home opened; I would add that **for a document quoting a subset of a script's output, the script must be run, because the subset is invisible from the text.** 3. **Wrong counts keep arriving by one mechanism**, and this partition found them in every one of the four sweeps: **a count correct on a narrow grid, carried onto a wider one when the grid grew, with the scope sentence updated and the count not**. T-5 is the clean specimen — "strictly smaller at three folds" is right on a five-fold grid and becomes five when the grid extends to nine, and the prose kept three. TA-4, TC-6 and TC-7 are the same shape in three other files. In every case the correct value is a one-line recount from a series the corpus already prints, so it is worth asking whether `audit-numbers.js` can hold the *series* rather than the counts derived from them. 4. **The "next steps" section is a defect generator and should be treated as one.** Of the eleven HIGH findings across the four sweeps, three (TC-2, TC-4, TA-1) live in a *Next steps* / *What this note owes other files* section, one more (TA-8, MEDIUM) in *Realistic targets*, and two (T-1, T-4) in scoreboard status cells. These sections are written to describe the future, they are never re-read when the future arrives, and **nothing in the repo links a "do X" to the artifact that later did X**. If one structural change comes out of this wave, that is the highest-value one: a next-step item is either struck with a pointer to its artifact or is not there. `natal-cap-21` item 1 shows it works — wave 4 struck it correctly and it now reads "DONE, by `natal-cap-27-t4-at13.js`". Item 2, one line below, is TC-2. --- *This is a wave-5 partition report. Findings are stated for adjudication; no replacement text is supplied and nothing in the corpus was edited.*