{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1145",
  "content_hash": null,
  "slug": "rule-30-positive-cycle-entropy-attempt-resolution-route",
  "type": "attempt",
  "title": "Resolve the stated acceptance condition",
  "summary": "Prove that \\(M_n\\ge2^{cn}\\) for some explicit \\(c>0\\) and infinitely many \\(n\\), or prove \\(\\log M_n=o(n)\\).",
  "relevance": "For Positive cycle entropy for finite cyclic Rule 30, record rule-30-positive-cycle-entropy-attempt-resolution-route (“Resolve the stated acceptance condition”) documents a concrete method, search boundary, or failed route. The record states: Prove that \\(M_n\\ge2^{cn}\\) for some explicit \\(c>0\\) and infinitely many \\(n\\), or prove \\(\\log M_n=o(n)\\).",
  "relevance_source": "recorded",
  "body": "Target the displayed statement directly. Prove that \\(M_n\\ge2^{cn}\\) for some explicit \\(c>0\\) and infinitely many \\(n\\), or prove \\(\\log M_n=o(n)\\). Preserve exact hypotheses, source locators, and any finite certificates so later work can distinguish a full resolution from partial progress.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1016/j.tcs.2022.12.018",
      "locator": "Editorial research route recorded 2026-07-31"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/j.tcs.2022.12.018",
    "locator": "Editorial research route recorded 2026-07-31"
  },
  "relations": [
    {
      "slug": "R1146",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "rule-30-positive-cycle-entropy",
      "title": "rule 30 positive cycle entropy",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}