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Sixty-Five Thousand Contestants, One Crown

Written 2026-08-25. Claims re-read against their sources on 2026-09-27: 6 checked, 2 confirmed, 4 wrong, 0 unverifiable. By claims-audit controls 2026-09-27 (audit agent + fix agent).

Audit finding set research/claims-audit/findings/r4.md (## sixty-five-thousand-contestants), each finding re-read by the fix agent. The grim-trigger claim was recomputed independently: table 65520 (defect unless the last round was mutual cooperation, under the encoding in public/strata/sixty-five-thousand-contestants/reference.js) was played against all 65,536 opponents for 100 rounds beside an unbounded grim trigger, with 0 mismatches.

Claims

• WRONG "Strategies that need unlimited memory, like the grim trigger, are not in this field"
  public/strata/sixty-five-thousand-contestants/reference.js : grim is memory-one (cooperate iff the last round was CC); table 0xFFF0 = 65520 reproduces it exactly against every opponent over 100 rounds (fix agent's own replay, 0 mismatches)
• WRONG Dek: "all 65,536 strategies that can be built from the previous round's outcome"
  research/sixty-five-thousand-contestants/README.md : one round gives a 4-entry table (32 strategies with a first-move bit); 65,536 needs the last two rounds' joint outcomes, as the README and reference.js say
• WRONG Famous tournaments had "a dozen or so" (dek), "about fifteen" (seo, plain), "about twenty" (og, twitter), "a couple of dozen" (footer) entrants
  https://www2.econ.iastate.edu/classes/econ308/tesfatsion/axeltmts.pdf : first tournament 14 entries (plus RANDOM per https://axelrod.readthedocs.io/en/stable/discussion/overview_of_past_tournaments.html), second "Sixty-two entries, plus RANDOM" (63 strategies per https://arxiv.org/abs/2510.15438)
• MINOR This page enters "every strategy of the same memory class" as the famous tournaments
  https://raw.githubusercontent.com/Axelrod-Python/Axelrod/dev/axelrod/strategies/axelrod_first.py : several first-tournament entries (Davis, Tullock, Stein and Rapoport, others) are implemented with memory_depth inf; entries were unrestricted programs; counted as wrong
• CONFIRMED 65,536 strategies and 2,147,516,416 matches of 100 rounds at T=5, R=3, P=1, S=0
  research/sixty-five-thousand-contestants/verify-sixty-five-thousand-contestants.mjs : 2^16 = 65,536; 65,536 x 65,537 / 2 = 2,147,516,416; asserted by the verifier against the page
• CONFIRMED 214,751,641,600 rounds in all
  research/sixty-five-thousand-contestants/README.md : 2,147,516,416 x 100 = 214,751,641,600

What was done

• [fixed] HIGH grim trigger: the "Excluded by the memory class" note now says grim is in the field (table 65520) and names what is really excluded; dated correction line in the page footer
• [fixed] HIGH dek "previous round's outcome" now "last two rounds' outcomes"
• [fixed] MED entrant counts: dek, seoDescription, plain (and its aw-plain copy), og and twitter descriptions, the page dek and the sources footer now give Axelrod's 14 and 62 submitted entries, with two sources cited in the footer (the footer no longer says nothing is cited)
• [fixed] MINOR "same memory class" replaced with "every deterministic strategy that looks back two rounds" in the page dek, og and twitter; the exclusion note says many submitted entries could consult the whole history
• [fixed] MED reader: with the pinned clang present but the repository's build script absent, the reproducible-build check FAILED instead of taking the documented SKIP; the verifier now skips in that case, the README says so, and the page says the offline verifier runs inside the repository (its check placard already said it needs the repository)