the assay office / record

The Certificate Nobody Stress-Tests

Written 2026-08-24. Claims re-read against their sources on 2026-09-27: 7 checked, 4 confirmed, 0 wrong, 3 unverifiable. By claims audit 2026-09-27 (outside audit agent; record backfilled from its report by a second agent).

Control-sample audit (research/claims-audit/PREREG.md), 2026-09-27, findings condensed in research/claims-audit/findings/r6.md. Reader check, partial by design: the published verify.mjs alone fails (ERR_MODULE_NOT_FOUND, and it needs public/ and src/content paths), which the page discloses; the repository copy passes 32/32. distinct-coverings.mjs with engine.mjs from /checks/ runs alone and reproduces the committed output exactly. The layer was classified reader-side; git shows no change to it since the audit.

Claims

• CONFIRMED C(9,4,3) = 25
  research/twenty-five-blocks/ (the engine's 25 blocks) : lower bound recomputed by hand (ceil 7/2 = 4, ceil 32/3 = 11, ceil 99/4 = 25); all 84 triples covered by the engine's 25 blocks, checked with the auditor's own loop
• CONFIRMED 126 = C(9,4), 84 = C(9,3), 300 = C(25,2), 2300 = C(25,3), 100 = 25 x 4 triple slots
  public/strata/twenty-five-blocks/index.html : all correct
• CONFIRMED Schonheim 1966, "On maximal systems of k-tuples", Studia Sci. Math. Hungar. 1, 363-368
  research/twenty-five-blocks/README.md (the citation checked; confirmed against standard bibliographies via web search, the report gives no URL) : citation correct apart from the initial (see Findings)
• CONFIRMED "140 distinct 25-block coverings carrying 20 distinct deletion fingerprints"
  research/twenty-five-blocks/distinct-coverings.txt : reproduced exactly by node distinct-coverings.mjs 3000
• UNVERIFIABLE The La Jolla Covering Repository tabulation
  ljcr.dmgordon.org : DNS failure and 502
• UNVERIFIABLE "which no published table records"
  no test possible : a negative claim with no way to test it
• UNVERIFIABLE Ox Alpha as independent author of engine-b
  internal to the site : cannot be checked from outside

What was done

• [declined] MINOR two check statements pull against each other (index.html:91 "runs offline with node and re-derives everything above" against the placard's "Running it needs the repository around it"): left as is; minor, and both are true inside the repository, which the placard says is needed.
• [declined] MINOR the page says the run's output is "committed beside it as distinct-coverings.txt", which is 404 under /checks/ while the .mjs beside it is served: left as is; minor, the file is committed in the repository as stated.
• [declined] MINOR research/twenty-five-blocks/README.md gives the author as "S. Schoenheim"; he is J. (Johanan) Schonheim: left as is, a research-file slip; the page does not carry it.