# Gate-repair finale — the verify-the-verifier repairs land (2026-08-20) Agent: gate-repair finale implementer, branch opus-try. Authorities: the three committed verify-the-verifier reports (`verify-the-verifier-checks.md`, `verify-the-verifier-numbers.md`, `verify-the-verifier-embeds.md`). Discipline: repair → selftest fixture → gate green → next; the gate must end at FULL green (`node research/qc.js --full`, TOTAL 0), and no bound tail is invalidated — where a normalisation change moves a recorded hash, the affected tail is re-embedded with its recorded invocation, never left amber. STATUS: COMPLETE, 2026-08-20. `node research/qc.js --full` reads FULL GATE PASSED at the close: TOTAL 0 across the 11 checks, selftest 39 known positives firing and 32 controls silent, audit-numbers 246/246. ## Baseline (before any edit) - `node research/qc.js`: TOTAL 0 (11 checks). Advisory: 161 readings-not-traceable, 3 hand-pasted-tail (natal-cap-33-overnight, natal-cap-34-wrap-precision, natal-cap-37-at41-march — the three declared composites). - `node research/qc/selftest.js`: 24 known positives fire, 14 controls silent, plus 6 tailfmt normalisation cases. - `research/audit-numbers.js`: 243 checks (per the reconcile-bind ledger's closing gate it read 242; section X’s A048670 extension added one on 2026-08-20 — the exact count is re-measured at this pass's close). - One untracked file from a concurrent reader agent: `research/history/staging/redteam-0820-structural.md`. Not touched. ## Batch plan | batch | contents | status | |---|---|---| | A | tailfmt: OUT_HEAD tighten, writer/reader closing-rule clash, min-rule lookahead ("24.9 min wall"), Q6 secs-column widening, tokenizer false positives (hyphen-range, OEIS/DOI ids, exponent variants), raw body reader for the static out-sha check | DONE | | B | embed.js: static body verdict on --check, loud no-banner failure, --force stamp, inputs hashes, --check by recorded invocation, argv scope past `--`, env/node comparison, re-embed of a bound tail requires --force | DONE | | C | checks.js: embeds body-vs-out-sha (B1), binding-lost, no-output-block advisory count; refs whole-§ labels + section-into-unsectioned + fenced-example skip (B2/M26); adjudicated-pair-vanished (B3); quotes contiguity tier (B4); per-§ sourcing advisory (B5); calibration marker synonyms (B6); crosslinks real pointers (B7); absence-stale review dates (B8); paragraphIndex char class (B9); search-convention row scoping stated (B10); provenance mixed-provenance (B11); tails.js recorded-invocation parse | DONE | | D | migration/re-embeds forced by the normalisation change + acceptance tests | DONE (two-class --check verification in flight) | | E | multi-tail composite support (locateAll, embed --tail, embeds awareness, fixtures) | DONE (mechanism + fixtures; the 3 composites themselves not restructured — see below) | | F | audit-numbers: 6 echo→first-principles, new checks, tautology deletions, W1 phase-max | DONE (full-run verification in flight) | | G | mutation suite rebuilt from checks report §2/§6, re-run against the repaired gate; detection rate measured | DONE | ## Batch records ### A — tailfmt (the parser and the normalize rules) - `OUT_HEAD` tightened to `/^\s*\/\/\s*OUTPUT\s*(?:$|[—\-(])/`. Surveyed every banner first: zero real banners move; the one prose line the loose form matched (`h2-length-needed.js:27`) is excluded. The 1c42a16 wrap-steal shape (`// OUTPUT, which is a cross-check …`) can no longer capture a banner. - The min-rule's lookahead now lets `wall` through: `24.9 min wall` scrubs, `2 min(j` and the aligned-column `6 min` stay data. - Q6 implemented as settled (CHANGELOG 2026-08-20, "WIDEN the volatile list, timing-only"): a bare number under a table column literally headed `secs` (last header token) scrubs, scope ending at the first non-row line. The two-class ladder and import-stein §C3 shapes; a data table below a secs table is untouched (fixture). - Tokenizer classes closed in `figures()`/`presentIn()`: identifier digits (A048670, arXiv ids, DOI paths yield no token), hyphen-ranges (`1.54-2.27` never yields `-2.27`; a real `= -2.271` keeps its sign), exponent spellings (`3.0e8` matches `3.0e+08`). The readings advisory fell 161 → 156 on the spot. - New readers for the static custody check: `outputTextRaw` (rules KEPT — 62 bound bodies contain real rule lines), `outputBodyCandidates` (the legacy printed-READINGS ambiguity), `bodyMatchesRecorded` (the one-line static verdict), and a `body-lines:` fingerprint field that ends the READINGS-scan guessing for every new bind. - The perfold discovery: `attack-perfold-01/02` PRINT their readings on stdout, so the reader truncated their bound bodies at the printed READINGS line — 2 honest tails reading as unverifiable. Candidate parsing + `body-lines` stamps fixed both without re-running anything. ### B — embed.js (all nine ranked repairs) 1. `--check` now prints FOUR verdicts: code (static), body (static, against the block's own bytes), inputs (static), run. The forged-tail demonstration of the embeds report §1.4 now fails at `body` with nothing executed. 2. No banner: loud on BOTH streams, own exit code 4; `embed-backlog` counts the population (27 scripts today, was invisible at 3-of-40). 3. `--force` stamps `forced: , k of n figures in the replaced block not reproduced (first: …)` into the fingerprint. The two-class re-embed's stamp reads exactly the three wall-clock figures. 4. `inputs: path@sha12 …` recorded at bind for statically-resolvable `require`/`readFileSync` targets; `--check` compares them before running — the scratch dependency-edit demonstration now reads `input DIFFERS`. 5. `--check` re-runs the RECORDED invocation (env, node flags, args), warns when the caller's differs, scales its timeout from the recorded `elapsed`, and compares the recorded node version (warning). `qc/tails.js` gained the same authoritative-invocation parse (it used to re-run `node foo.js foo.js` on node-flag tails). 6. Flag scope stops at `--`: `-- --force` and `-- --check` reach the script, never the tool (verified on scratch). 7. Ambient environment guard: a bind refuses (exit 5) when the code reads an env var the shell sets undeclared; `--env` declares intent and lands in the invocation. Ubiquitous shell vars exempt. 8. Re-embedding a BOUND tail that changes the block requires `--force` and prints the figure diff first; an identical re-embed stays a no-op refresh. 9. The two consolidation-wave ledger corrections are recorded below rather than by editing history. ### C — the checkers - `embeds` now: code-sha per tail (multi-tail aware, code = bytes above the FIRST banner), body-vs-out-sha static verdict (`output-block-hand-edited`), and `binding-lost` for any file saying `OUTPUT — EMBEDDED` that no longer parses as bound (the 1c42a16 regression class fires the moment it lands). - `refs`: whole-label §s (dotted, lettered, `Theorem B` pairs), bold-led sub-item labels (`**4.5 …**`) and glossary-entry labels (`- **Stratum …**`) as addressable sections, `§§1-3` ranges, `§Q4.2` aliases, one-stopword prose (`in section 47`), `section-into-unsectioned-file` as its own kind, fenced examples skipped. Calibrating surfaced 13 live findings: 11 were the checker's own label-model gaps (fixed in the model), 2 were REAL dead pointers, both repaired: `IMPORT-MAP.md:404` §4 → §4.1 (Pippenger–Spencer lives under covering-dive §4.1), `origin-excess.md:696` `maier-matrix.md §F` → `maier-matrix.js` §F (the label names the SCRIPT's output part). - `transfers`: `adjudicated-pair-vanished` — every ADJUDICATED key matching no live candidate pair is a finding. Eight superseded re-keys moved to a new `ADJUDICATED_RETIRED` archive in ledgers.js, reasons intact, consulted by nothing. Description now states the check's honest scope. - `quotes`: the 95%-of-long-words tier is REPLACED by a contiguity tier (exact; or split-on-elision, all parts exact in order; or two exact halves with one bounded gap), and the description counts fuzzy clears. Calibrating surfaced 4 live firings: 2 were qc/README documenting its own examples (qc/ now excluded, same rule as `absence`), 2 were mention-shaped quote marks in live docs, both edited to stop quoting what they only name (SEARCH-CONVENTIONS.md:145, covering-dive.md:17). - `sourcing`: per-SECTION scope implemented as the `sourcing-backlog` ADVISORY (220 sections on landing day — a queue that size gated would teach everyone to ignore red; the counter should only fall, gate it in the tens). The gated file-level rule states its known weakness in its description. - `calibration`: `unmarked-strength-word` for ALL-CAPS settled-sounding words outside the vocabulary (ESTABLISHED, SETTLED, DEMONSTRATED, CONFIRMED, …). - `crosslinks`: reachability needs a real pointer (basename.md, backticked or bracketed stem, or a distinctive hyphenated stem ≥ 7 chars); `reachability-unprovable` for short-stem topic-word collisions. - `absence`: `absence-stale` when an ABSENCE_VERIFIED entry is older than 14 days (the suppression keeps suppressing; the staleness fires beside it). - `paragraphIndex`: a bullet needs its trailing space; `**Bold lead.**` no longer scopes its paragraph line-by-line (B9, the M08 false-positive root). - `provenance`: `mixed-provenance` when a note carries BOTH vocabularies — "p. 4" beside "ar5iv rendering" no longer clears silently. - `search-convention`: table rows were already row-scoped via paragraphIndex; the prose-paragraph limit is now stated in the description (B10). ### D — the normalize migration, and the two acceptance tests Changing VOLATILE moves hashes, so every bound tail whose recorded out-sha no longer reproduces from its own bytes was handled explicitly, never left amber: - 12 tails RESTAMPED after their bodies were verified byte-authentic under the normalize IN FORCE AT BIND TIME (9 pre-min-rule, 1 min-no-wall-rule natal-cap-27 — avoiding its 2 h re-run as instructed, 1 import-stein secs shape, 1 attack-growth-law closing-rule clash where the sha did not move). Each carries `body-lines:` and, where the hash moved, a dated `restamped:` note naming the rule it was verified under. A body matching NO bind-era rule would have been REPORTED, not restamped; there were none. - `two-class-lower-bounds.js` RE-EMBEDDED per the acceptance test (520.4 s, --force, stamp lists exactly the 3 bare-secs wall clocks); a full `--check` of the new binding is running at this batch's close. - Acceptance test 1 PASSED: `embed.js --check research/external-ladders-01.js` is flag-free — all four verdicts green, no readings advisory — without any edit to that file's prose ("048670" and hyphen-range tokens no longer exist to flag). - Static custody state at batch close: 219/219 bound tails green under `bodyMatchesRecorded` (218 before the two-class re-embed landed). ### E — multi-tail composites `tailfmt.locateAll` + `embed.js --tail N` + multi-tail-aware `embeds`. Each tail binds independently; the code hash covers the bytes above the FIRST banner for every tail; `--check --tail N` verifies one tail; binding without `--tail` on a multi-tail file refuses with a listing (exit 6). Selftest carries a two-tail fixture bound twice over (control) and with the second tail's block edited (fires on that tail alone). The three composites themselves (cap-33, cap-34, cap-37) are NOT restructured here: cap-33's reachable run needs a 100-minute prerequisite, cap-37's march is external by declaration, and cap-34's six stages cost ~37 minutes — the mechanism now exists for the wave that re-runs them. ### F — audit-numbers.js - U1: the Poisson-window check consumes the certificate walk's own `n - r0`. - U2: the printed `theta(x) − ln m = lnD` identity is now a check — `lnBig`, eleven checks' single point of failure, is under the gate. - U3: the two `e^{2g}/(kC2)` checks consume the COMPUTED C2; their §U duplicates deleted. - U4: 1.847 recomputed by `slope()` over A288815's nineteen terms n = 3..21 (the window was identified numerically: 1.847 is terms 3..21), with a 21-term array-length pin. - U5: the G2/h ratio table moved to the ladder section and divides the ladder's COMPUTED G2 by the COMPUTED h (h(31#)/h(37#) labelled TRANSCRIBED). - U6: `L.got[31] = max(internal, boundaryCheck(...))` — the discarded return value now participates, matching its three siblings. - NEW: A144311(n)+1 against our own FOURTEEN exact terms (12 computed in-run, 2 gap-certified); f(x, next-prime) by direct %-sieve at the five UNAFFECTED diagonal levels — 0.044444/0.048485/0.048844/0.031119/0.030660 reproduce a3-03 §3 exactly, and a second mod-32-class alias in any producer of that layer now disagrees here; `lastMulti < 499` (extinction vs out-of-range were one answer); the pi_2(1e10) anchor promoted from print to check; Y2(37) = computed G2(37#) − 1 by covering duality (a_p = 0 covers exactly the non-slots), replacing the `527 <= 527` tautology pair. - W1 phase-max: the T5 word is DERIVED by sieving Z/30 and the counting criterion runs at all three phases — 63/62/62, ceiling = max = 63; a future re-derivation from origin 17 or 29 can no longer redden the gate on a correct number. - DELETED (tautology list, all 9): `43·43/41·41`, `527 <= 527`, `528 − 1 === 527`, "the two differ", "capacity BELOW 19", the seam `/2` echo, the duplicate seam sum, and the two `e^{2g}` duplicates. The retired-number regression banners all stand (the retired /2, the retired 475/487, the retired 1.2417, the retired indexing). ### G — the mutation suite, re-run against the repaired gate The suite was rebuilt from verify-the-verifier-checks.md §2 (41 mutations — the report's 44 minus three subsumed variants; M09c is covered by M13b's same-wrong-number-both-sides shape). Each ran on a fresh APFS clone of a 17 MB snapshot of this tree (TOTAL 0 on its own), scored by the delta in gated findings and advisory counts. Driver and per-mutation results: session scratchpad `mut/drive.js`, `mut/results.json`. **Headline, before → after.** The report measured 11 of 44 firing, 31 invisible, 2 false positives. The rebuilt suite measures: - **23 of 41 fire in the GATE** (56%; was 25% counting controls) — every mutation of a class the repairs targeted now fires: the hand-edited bound block (M02), the banner steal (M17), the inserted "not" (M05), the changed number inside a quote (M05c), the dotted/lettered/unsectioned/stopword references (M06/M27/M24/M07), the vanished adjudication (M09f), the marker synonym (M12c), the page-beside-a-rendering note (M22), the short-stem orphan (M25). - **4 more are advisory-visible** (M01 readings figure, M10 pasted literature row, M15b deleted tail → no-output-block, M21 fabricated section → unsourced-section): 27 of 41 visible somewhere (66%). - **0 false positives** — the report's two (M26 fenced path, M08 bold-scoped convention) are both fixed and both now controls that stay silent. M28 (a dead quotation inside a CORRECTION paragraph) is silent BY THE HOUSE RULE (refutations stay visible), reclassified as a control. - All 12 re-run controls (M06b, M07b, M12, M14, M15f, M25b, M33, M34, M05b, M08, M26, M28) behave. **The 11 that still evade, each with its reason:** | # | mutation | why it evades | |---|---|---| | M03 | digit inside a LEGACY block | no fingerprint exists to bind it; only a re-run sees it. The fix is the migration backlog (3 composites left), not a check | | M04 | stale count word in prose | no producer for a count word; audit concern (report B12) | | M08b | convention-about-A clears ABSENT-about-B in a PROSE paragraph | stated limit of paragraph scoping (B10); table rows are row-scoped and covered | | M09b | hypothesis dropped from a single-sited claim | no pair to diff; outside `transfers` by construction, now said in its description | | M11 | live doc citing a spent staging report | no layer rule: 18 live docs legitimately cite history paths (measured), so a hard rule would misfire; stays a named-uncovered class | | M12b | single-sited overstatement vs its own artifact | needs the artifact read; structurally outside a cross-document check (B6) | | M13 | the same wrong constant in TWO documents | nothing diffs a document against a producer; audit-numbers holds its own literals. The corpus's largest unguarded class, named (B12) | | M21b | fabricated numbers beside `et al.` in the same section | the literature marker exempts its own section even under per-section scoping; scoping it tighter would fire on genuine literature sections | | M23 | invented ADJUDICATED entry whose key MATCHES the live pair | the ledger's reasons are the only audit for a fresh lie; `adjudicated-pair-vanished` covers stale keys, not invented ones | | M30 | absence claim naming no artifact | not checkable against a directory; dropped by design and now stated | | M32 | code edited + code-sha hand-recomputed, block internally consistent | any hash a tool computes a hand can compute. STATIC evasion only: `embed.js --check`'s run verdict reads `out-sha256 DIFFERS` on it | One incidental: M19 (a new artifact falsifying a dated absence) fires `uncited-script` on the new artifact — visibility by coincidence, not coverage; the mechanical falsification of a dated absence remains impossible, which the ledger and the `absence-stale` interval now both say. ## Ledger corrections carried here rather than by editing history Per the doc convention the history layer is not edited. The embeds report §6 item 9 records two corrections to `consolidation-wave.md` §2's table; they are restated here as the finale's record: - `a3-08-adjacent-pairs.js` is bound with the plain default invocation (89.6 s); the `-- --t31` + `--node-flag --max-old-space-size=8192` leg lives in its READINGS, not in the fingerprint. - `attack2-rankin2d.js` is bound with the plain default invocation (168.3 s); the `-- --deep` leg lives in its READINGS. ## Close **The gate at the close** (`node research/qc.js --full`, FULL GATE PASSED): - Fast gate: TOTAL 0 across all 11 checks. Advisory tier: 156 readings-not-traceable (was 161 — the tokenizer fixes), 27 no-output-block (newly counted; was invisible), 3 hand-pasted-tail (the three declared composites), 220 unsourced-section (newly counted per-section custody queue). The gate now states on every run what a zero certifies — a fast syntactic verdict — per the checks report §7. - Selftest: **39 known positives fire, 32 controls silent** (was 24/14). Every repair in this pass landed with its fixture in the same batch; the new positives cover output-block-hand-edited, binding-lost, no-output-block, multi-tail, the three tokenizer classes, the Q6 and min-wall normalize rules, body-lines parsing, dotted/lettered/unsectioned sections, the negated and exponent-mutated quotations, adjudicated-pair-vanished, unsourced-section, unmarked-strength-word, reachability-unprovable, absence-stale, mixed-provenance, the M26 fence control and the M08 bold control. - audit-numbers: **246/246 checks pass** (was 243: nine tautologies deleted, twelve first-principles checks added, six echoes converted in place). - Static custody: **all 219 bound tails hash to their own recorded out-sha** from bytes on disk, nothing executed; the two acceptance tests pass (`--check external-ladders-01.js` flag-free; the re-embedded two-class-lower-bounds fully green and stable under `--check`). - Mutation suite: **23/41 gated-caught, +4 advisory-caught, 0 false positives, 11 documented evaders** (§G above; report baseline was 11/44 with 2 false positives). **NOT reached / left open, deliberately:** - The three composites (cap-33, cap-34, cap-37) still carry hand-pasted tails: the multi-tail mechanism now exists, but their runs cost 100 min to 7 h and one is external by declaration. Pricing and per-file obstructions are in custody-overnight.md; binding them is a run-budget decision, not a tooling gap any more. - The 220-section sourcing queue and the 27 no-output-block scripts are counters that should only fall; gate them when they reach the tens. - The M11 layer rule (live doc citing spent staging) stays unimplemented on a measurement: 18 live docs legitimately cite history paths. - `qc/tails.js`'s substring figure-matching and 30 s default tier are unchanged beyond the invocation fix; the static body check has taken over its main job for bound tails. - The embeds report's §5.2 "observed inputs" variant (an fs/require shim logging what a run actually touches) was not built; the static `inputs:` field covers every literal dependency, not computed shard paths. - audit-numbers' §7.2 items priced "defer": the survival-trough triple (needs the curve) and a full A048670 h(31#) stream (offline job). - The environment guard whitelists ubiquitous shell variables by name; a script reading an exotic-but-common variable would still need `--env` discipline. **Restamp custody note.** Twelve out-sha256 values moved in this pass, every one on a body first verified byte-authentic against the normalize rule in force when it was bound, and every one now carries `body-lines:` plus a dated `restamped:` line in its own fingerprint. The alternative — leaving twelve tails permanently amber under rules adopted after they were written — is the state the embeds report §6 calls a checker people stop running.