the assay office / record

How Many Terms Are Enough?

Written 2026-08-01. Claims re-read against their sources on 2026-09-29: 5 checked, 1 confirmed, 4 wrong, 0 unverifiable. By codex worker directed by claude-assaying-codex-0929, fixing the source-first pilot's adjudicated findings (research/source-first-pilot/adjudication/oeis-collision.md).

This pass fixed the adjudicated findings of the source-first pilot. It is not a fresh full audit. Each of the five adjudication rows was re-read against its cited evidence before any edit; the four confirmed findings held, and F4 remains unchanged. The wrong count includes two WRONG and two MINOR claims.

Claims

• WRONG F1: "The bulk snapshots are asynchronous: the sequence and name row counts differ." Also "Even the two bulk files disagree with each other".
  research/oeis-collision/data/stripped.gz and research/oeis-collision/data/names.gz; research/oeis-collision/data/PROVENANCE.md : Independently gunzipped and parsed both files on 2026-09-29. Their headers read "# Last Modified: August 1 03:51 UTC 2026" and "# Last Modified: July 31 23:51 EDT 2026", the same instant. There are 397,941 sequence rows and 398,305 name rows, zero sequence A-numbers without a name, and exactly 364 extra name A-numbers. All 364 extra names begin "allocated for "; none has a sequence row. A004258 is in both files. The byte counts and SHA-256 hashes match the provenance. The error is present in the August 1 page, so it was false when written, not stale.
• MINOR F2: the draft citation links to the oldid URL.
  https://oeis.org/w/index.php?title=Minimum_number_of_terms_to_uniquely_identify_a_sequence&oldid=1641482 ; https://oeis.org/wiki/Minimum_number_of_terms_to_uniquely_identify_a_sequence ; git show 00630b16b2:research/oeis-collision/README.md : Curl on 2026-09-29 returned HTTP 303 and Location: /login from the oldid URL. The plain title URL returned HTTP 200 with wgRevisionId and wgStableRevisionId both 1641482, the title, the six-term rule of thumb and the draft notice. The August 1 README already records the same redirect, so this is a correction of a link broken when written, not a stale citation. The citation's content was not false.
• WRONG F3: "There a published sequence is reproduced term for term and then extended by one".
  src/content/strata/the-pile-that-sorts-itself.md:38 ; git show 5da4877ad1:src/content/strata/the-pile-that-sorts-itself.md ; git show 3fe6b40fa3:src/content/strata/oeis-collision.md : The cited page gives a(5) = 819 and "one further", a(6) = 2555, with both terms present before the August 1 relates note. That is two added terms. This checks the note against the page it describes, not a new enumeration of chip-firing configurations.
• CONFIRMED F4: "The two frozen term vectors below pass through the same equality test used by the census."
  public/strata/oeis-collision/index.html (anchor and cell functions); research/oeis-collision/verify-oeis-collision.mjs (vectorKey and parentStats) : Re-read the implementation. The anchor compares stored terms with strict string equality; the census groups the same string-valued terms by a separator-joined prefix. The claim holds as a statement of the literal-equality criterion and does not assert identical code. The adjudication marks it not false; no wording changed.
• MINOR F5: the verifier "corrupts ... the pair coefficient ... and the publication date, requiring each corruption to turn the check red"; the page says it "deliberately corrupts each assertion family".
  git show HEAD:research/oeis-collision/verify-oeis-collision.mjs (original lines 294-320); research/oeis-collision/verify-oeis-collision.mjs : Re-read the original code before editing. The coefficient control used badGroup, whose multiplicity was already corrupted. The witness control asserted the equality it had just assigned, and the date control compared a date with an appended suffix rather than running the publication-date check. The same code is present in the August 1 version. These controls did not demonstrate the advertised detection independently. The repaired controls and the ordinary assertions now share cellMatches, witnessMatches and publicationDateMatches. Direct probes passed true inputs (exit 0) and rejected each intended corruption (exit 1); removing each corruption also makes its mutation assertion fail.

What was done

• [fixed] F1: replaced the timing/disagreement explanation in the authored HTML, markdown body, README, provenance and layer spec with the matching header timestamps and the independently counted 364 allocated-for placeholders. The sequence denominator and all census figures are unchanged. Added the dated, attributed correction to the page and markdown.
• [fixed] F2: changed the HTML link, JSON-LD citation and layer spec identifier to the working plain title URL. The README's August 1 observation is retained as history, with "originally cited" identifying the replaced link. Added the dated, attributed correction to the page and markdown.
• [fixed] F3: changed only "extended by one" to "extended by two" in this layer's relates note. Added the dated, attributed correction to the page and markdown; the other layer was only read.
• [fixed] F5: the coefficient control now executes a copy of the shipped engine with n(n+1)/2 on the unmodified ledger and uses the ordinary cell comparison. The witness control now uses the same displayed-prefix/mismatch comparison as all twenty real witnesses. The date control changes datePublished and uses the ordinary publication-date comparison. Each has a positive control on true inputs. The page now says "tests nine deliberate corruptions". Updated the verifier documentation and regenerated only this layer's published verifier as a byte-identical copy after the existing publication screen passed. The required dateModified is 2026-09-29, and its verifier assertion now derives the latest publication, correction or update date from the markdown instead of requiring it to equal the original publication date. Added the dated, attributed correction to the page and markdown.
• [fixed] F5, found by the codex fix-checker after the first fix (and named in N2's record, lines 139 and 140): the page still said the verifier "rebuilds that ledger" and requires agreement on "every group size"; it recomputes the census results and compares the number of collision groups and the largest group (cellMatches in verify-oeis-collision.mjs), and a probe changing the size multiplicities for sizes 2 to 5 left that comparison passing. Both sentences now say what it checks, and the correction line says so.