{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R492",
  "content_hash": null,
  "slug": "maj8torus-claim-reported-fifty-thousand-sample",
  "type": "claim",
  "title": "The candidate run reported 8,391 two-cycle outcomes among 50,000 starts",
  "summary": "The observed proportion was 0.16782, and every sampled orbit settled within 17 updates.",
  "relevance": "For Two-cycle probability for majority dynamics on the eight torus, record maj8torus-claim-reported-fifty-thousand-sample (“The candidate run reported 8,391 two-cycle outcomes among 50,000 starts”) records a bound, answer, status fact, or structural consequence. The record states: The observed proportion was 0.16782, and every sampled orbit settled within 17 updates.",
  "relevance_source": "recorded",
  "body": "The candidate-generation record reports a run with seed 20260724. Of 50,000 sampled initial states, 41,609 reached fixed points and 8,391 reached genuine two-cycles. The observed two-cycle proportion was\n\\[\n\\frac{8391}{50000}=0.16782.\n\\]\nEvery sampled trajectory settled within 17 synchronous updates.\n\nThe generation record did not preserve the pseudorandom generator or a digest of the sampled states. These figures are therefore reported evidence rather than a replayable exact certificate. They do not determine the numerator over \\(2^{64}\\).",
  "status": "reported",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "the 50,000 seeded 8 by 8 initial configurations reported in the candidate-generation record",
    "bounds": {
      "sample_size": {
        "min": 50000,
        "max": 50000
      },
      "vertices_per_configuration": {
        "min": 64,
        "max": 64
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1016/0166-218X(81)90034-2",
      "locator": "api/app/data/agent_candidate_problems_v4.jsonl, record candidate.majority-eight-torus-two-cycle-probability"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/0166-218X(81)90034-2",
    "locator": "api/app/data/agent_candidate_problems_v4.jsonl, record candidate.majority-eight-torus-two-cycle-probability"
  },
  "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"
    }
  ]
}