{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R441",
  "content_hash": null,
  "slug": "lat7-attempt-literature-audit",
  "type": "attempt",
  "title": "A public finite-torus table already records the same period",
  "summary": "A 2019 computation lists 64,165,598 for the 7 by 7 square torus; peer-reviewed sources found in the search discuss broader ant dynamics.",
  "relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
  "relevance_source": "derived",
  "body": "A Mathematics Stack Exchange answer published in July 2019 gives a rectangular-torus table under the same all-white, original-position, original-direction recurrence convention. Its 7 by 7 entry is `[7] 64,165,598`, where the bracket records seven symmetry-based quasi-recurrences before the full labeled return. The value agrees with the independent certificate here.\n\nLangton introduced the mobile automaton in 1986. Later work proves complexity and recurrence results for related Lorentz lattice-gas models, while the focused search found no peer-reviewed table of these small square-torus periods. The exact value therefore has a prior public computation. This entry adds a compact full-state encoding, cycle parameters, replay assertions, and trace digests.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://math.stackexchange.com/questions/3296855/what-is-the-period-of-langtons-ant-on-a-torus",
      "locator": "Stack Overflown, answer posted July 18, 2019, rectangular recurrence table; Christopher G. Langton, Studying artificial life with cellular automata, Physica D 22 (1986), 120-149, DOI 10.1016/0167-2789(86)90237-X; Takeo Hagiwara, Tatsuie Tsukiji, and Zhi-Zhong Chen, IEICE Transactions E99.A (2016), 1034-1049, DOI 10.1587/transfun.E99.A.1034"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://math.stackexchange.com/questions/3296855/what-is-the-period-of-langtons-ant-on-a-torus",
    "locator": "Stack Overflown, answer posted July 18, 2019, rectangular recurrence table; Christopher G. Langton, Studying artificial life with cellular automata, Physica D 22 (1986), 120-149, DOI 10.1016/0167-2789(86)90237-X; Takeo Hagiwara, Tatsuie Tsukiji, and Zhi-Zhong Chen, IEICE Transactions E99.A (2016), 1034-1049, DOI 10.1587/transfun.E99.A.1034"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R442",
      "title": "The complete initial state first returns after 64,165,598 updates",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R440",
      "title": "Bit-packed cycle detection and direct replay certificate",
      "object_type": "artifact",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "langton-ant-seven-torus-return",
      "title": "langton ant seven torus return",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}