{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R451",
  "content_hash": null,
  "slug": "levine-attempt-current-source-and-duplicate-audit",
  "type": "attempt",
  "title": "The 2026 source audit retains the exact two-player value as an open conjecture",
  "summary": "A dated audit found the April 2026 primary revision, no later checked resolution, and no second TheoremDB target for the same Borel two-player game.",
  "relevance": "For The value of Levine's two-player coin-index game, record levine-attempt-current-source-and-duplicate-audit (“The 2026 source audit retains the exact two-player value as an open conjecture”) documents a concrete method, search boundary, or failed route. The record states: A dated audit found the April 2026 primary revision, no later checked resolution, and no second TheoremDB target for the same Borel two-player game.",
  "relevance_source": "recorded",
  "body": "The audit began with MathOverflow question 326669 and both visible answers, then checked the current versions of arXiv:1407.4711 and arXiv:2508.01737. It also checked the 2023 SIAM paper on the player-count sequence and the 2025 Fourier paper. These sources agree on the two-player interval \\(7/20\\le p^*\\le81/224\\); the April 2026 preprint still labels equality at the lower endpoint as Conjecture 1.\n\nThe later-citation check used OpenAlex and DataCite records for arXiv:2508.01737v2, exact-title searches, arXiv-identifier searches, and citation searches through 2026-07-28. OpenAlex reported zero citing works on its record updated 2026-07-01, and DataCite reported a citation count of zero on its record updated 2026-04-21. Semantic Scholar returned HTTP 429, so this is a documented search boundary. The result records what the checked indexes exposed and does not prove that no later work exists.\n\nLocal searches of canonical records, candidate files, and research fixtures, followed by production API searches for `Levine hats`, `guessing coins`, `7/20`, and `two-player coin`, found this canonical prospect and no duplicate target. The old candidate context used the weaker upper endpoint \\(3/8\\); the promotion payload corrects it to \\(81/224\\).",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "the two-player fair Levine game and directly neighboring finite-stack and multi-player formulations",
    "family": "Levine hat and coin-index problems in the checked primary literature and TheoremDB corpus"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2508.01737",
      "locator": "Primary and citation audit completed 2026-07-28 against arXiv:2508.01737v2 dated 2026-04-19"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2508.01737",
    "locator": "Primary and citation audit completed 2026-07-28 against arXiv:2508.01737v2 dated 2026-04-19"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R455",
      "title": "The checked interval is 7/20 through 81/224, and equality at 7/20 remains open",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R454",
      "title": "Borel infinite-stack strategies have the same supremum as finite-stack strategies",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "levine-two-player-seven-twentieths",
      "title": "levine two player seven twentieths",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}