The self-audit: the instrument measured by its own rules

The note was written on 2026-10-20, before any run: the frozen set (the register at sha256 270094aa3c92…, 25 records), the five measurements with their definitions, the two laptop profiles and the hosted one, the mutation classes per record (119 mutable rows), the kill switches per phase, what is claimed and what is not, the holds, the output names. Every record below pins it by sha256; amend the note and every battery refuses until the records are regenerated — on purpose. Two things the note did not foresee are recorded as dated corrections, not silent edits: a stamp rule in the runner that was narrower than the note's (re-derived, no measurement touched), and the invariances a row admits, which must preserve every claim the row decides (negating a truth table flips its monotonicity claim; the class was replaced before the record was written).

The inventory (phase 1): 23 of the 25 records re-derive with one command (125 rows), 7 carry a standard-library verifier (50 rows), 1 a second implementation; 13 commands write their record and 10 only check it; 74 rows carry a per-row timing. The runner (phase 2, Apple M2, v24.14.1, Python 3.9.6, AC 100%): every command of the rerun kit under /usr/bin/time -l, one process at a time, twice under each profile — cold, then warm, never averaged. Under the portable profile the wall of 60 s is enforced by killing the process group at the cap: 5 records were REFUSED for resources (ledger.json (5.7 min, 1 row), horizon-ledger.json (2.2 min, 1 row), hseva-ledger.json (8.6 min, 1 row), gnnw-certificate.json (3.6 min, 1 row), polymaps-ledger.json (1.6 min, 8 rows)), exactly the 5 the inventory had timed over the cap. Under the extended profile every record ran and every one was reproducible: it differed from its pin only at its declared stamps, and the register rebuilt from it moved no row. Peak memory was at most 675 MiB, far from the 4 GiB the profile reports against.

One side effect is on the record and was restored each time: make engine rewrites certs/keller-certificate.json with the pins its sources listing has grown since the record was taken — a listing, nothing decided.

A mutant is a case derived from a row's pinned record entry by one named transformation of the note's class table. Its truth is fixed by construction and checked by a witness that shares no code with the decider (Python standard library, exact: Fractions, directed-rounding Decimal, Z[√2], Kronecker convolutions) — a FALSE mutant the witness cannot witness is DISCARDED and counted, never relabelled. The decider under test is the row's own re-derive path with the mutant in place of the pinned bytes; required words: FALSE → REFUTED, TRUE → CERTIFIED (an invariance keeps the original's own word, so a REPAIRED row's rigid motion is REPAIRED again), MALFORMED → REFUSED. The witness carries red controls every run: no violation on a CERTIFIED original or a TRUE mutant, one on the REFUTED original and on every family's control class.

Two defects, found and fixed. The campaign's first whole run came back with 28 false certifications and 49 malformed inputs answered REFUTED. The note's rule applied: fixed, recorded beside each mutant with the commit it was found at, the mutant kept, the count reported.

Still open, on the record: polymaps · exponent-missing → not as required (PARTIAL) × 1 — a partial decision that reads a term with a missing exponent silently (the evaluation zips the point against a short tuple); recorded, not yet fixed. The other outcomes that are not the required word are compositions, each listed in the record: refused 6, DISCARDED 27, not as required (REPAIRED) 17, not as required (UNWITNESSED) 1, not as required (PARTIAL) 1.

Not mutated, a reason per row (21 rows):

Classes excluded on rows that were mutated (16): tensor · coefficient-times-one-plus-1e-9 × 10 — no meaning over F₂: 1 + 10⁻⁹ is not an element of the field; the class is stated for Q and Z[i]; kissing · contact-sum × 1 — the configuration has no exact contact pair (no two rows at exactly 60°), so the sum of two contact vectors does not exist for it; shapes · printed-plus-one-unit × 1 — the row prints no value (the ledger certifies the exact value with no printed bar), so there is no printed digit to move; shapes · printed-minus-one-unit × 1 — the row prints no value; shapes · coordinate-perturbed-1e-12 × 2 — the hexagons' constraints (separation, containment) are cosines and sines of printed angles; a standard-library witness of a violated constraint would need certified trigonometry, which it does not have; polymaps · coefficient-plus-one × 1 — F7's determinant rests on the paper's lemma (the row is PARTIAL): a coefficient moved changes nothing the decider decides but the collision, which the witness-point class covers.

A double-precision checker written for the audit — no exact arithmetic, a tolerance τ on every constraint and on the bar, the natural numpy-style verification of each family — ran on every original and every mutant. On the 295 witnessed FALSE mutants it ACCEPTED 82 at τ = 10⁻⁶ (27.8 %), 33 at 10⁻⁹ (11.2 %), 7 at 10⁻¹² (2.4 %): a printed value one unit off in its seventh to tenth digit, a coefficient scaled by 1 + 10⁻⁹, a bar one unit above an entropy ratio's last printed digit, the published C* that is the naive double product — each inside what a tolerance admits. And the other side: it confirmed only 94 of the 97 TRUE originals at 10⁻⁶, 81 at 10⁻⁹, 72 at 10⁻¹² — among the polynomial maps, cancellation in float Gaussian elimination over hundreds to tens of thousands of terms puts the determinant past 10⁻⁶ of its constant on four of nine. A tolerance that admits a quarter of the false claims cannot confirm a quarter of the true ones. The exact deciders returned 0 false certifications on the same objects, and every original as the register says.

For every register row decided by two or more programs, the records were read and compared field by field: the word, the witness or the violating-pair count where one exists, the enclosure where one exists. 91 comparisons on 56 rows (40 2 implementations, field by field; 1 4 implementations, field by field; 1 3 implementations, field by field; 49 word-level: a standard-library verifier re-derives the record), 91 concordant, 0 disagreements. Nothing was re-run for this: the second implementations' own runs are on record, and so are the standard-library verifiers' exits in the rerun kit's run.

The hosted profile, carried in as recorded. 416 kernel challenges of the openai-math audit, decided on GitHub-hosted Linux runners (.github/workflows/openai-math-kernel.yml) with two kernels per run: 398 CERTIFIED, 18 REFUSED; wall seconds min 18, median 587, max 12453; peak RSS up to 13715 MiB. 435 runs exceed the laptop's portable wall and 413 its reported memory bound — which is why they are a profile of their own, never merged into the laptop table and never re-run here. The 18 refusals were for resources on the runner and stay refusals.

• Claimed. The counts above, per family, on this frozen set of 132 rows, on this machine, under the definitions fixed on paper first — and two defects found by those definitions, fixed and kept.
• Not claimed. A ranking of verification systems; independence from the author (every decider and every witness script is written here); anything about the 13 aggregate and reading rows; that passing M1 shows soundness beyond the classes listed.
• Held. The LLM-judge baseline (a spend); outside reruns (a send); the claim-to-statement track (two outside reviewers who did not build the benchmark); the register gap (a register change); the 54 undecided pre-registered claims (another front).