{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R489",
  "content_hash": null,
  "slug": "maj8torus-attempt-literature-and-counting-audit",
  "type": "attempt",
  "title": "The period theorem is classical; the size-eight basin count was not located",
  "summary": "The audit found the general finite symmetric-threshold theorem and modern majority-dynamics references, with no source reporting this exact numerator.",
  "relevance": "For Two-cycle probability for majority dynamics on the eight torus, record maj8torus-attempt-literature-and-counting-audit (“The period theorem is classical; the size-eight basin count was not located”) documents a concrete method, search boundary, or failed route. The record states: The audit found the general finite symmetric-threshold theorem and modern majority-dynamics references, with no source reporting this exact numerator.",
  "relevance_source": "recorded",
  "body": "The audit searched for synchronous majority dynamics on finite graphs, period-two behavior of symmetric threshold functions, toroidal majority cellular automata, and exact basin counts. The 1981 paper of Goles and Olivos supplies the general period-one-or-two theorem. Benjamini, Chan, O'Donnell, Tamuz, and Tan cite the finite period-two property while studying convergence on infinite unimodular graphs and random finite graphs.\n\nNo located primary source reports the basin numerator for \\(C_8\\square C_8\\) with retention on a four-neighbor tie. This is a search result rather than a proof of novelty. A complete entry needs a replayable symbolic count, such as a reduced decision diagram or transfer computation, whose fixed and two-cycle basin counts sum to \\(2^{64}\\).",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "a targeted literature search for the finite period theorem and an exact basin count for the stated C8 Cartesian C8 instance and tie convention, completed on 2026-07-25",
    "bounds": {
      "torus_side_length": {
        "min": 8,
        "max": 8
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1405.2486",
      "locator": "Targeted search completed 2026-07-25; finite period theorem at DOI 10.1016/0166-218X(81)90034-2; modern context in arXiv:1405.2486"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1405.2486",
    "locator": "Targeted search completed 2026-07-25; finite period theorem at DOI 10.1016/0166-218X(81)90034-2; modern context in arXiv:1405.2486"
  },
  "models": [],
  "relations": [
    {
      "slug": "R490",
      "title": "The exact numerator remains open, with a certified interval of 128 through 18,446,744,073,709,551,106",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "majority-eight-torus-two-cycle-probability",
      "title": "majority eight torus two cycle probability",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}