{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R131",
  "content_hash": null,
  "slug": "cds-attempt-source-convention-audit",
  "type": "attempt",
  "title": "The source conjecture uses the floor-strength convention",
  "summary": "The primary source states CS(n) <= 1.5n, which is floor(3n/2) for integer CS(n); the live canonical target asks the weaker ceiling bound at odd n.",
  "relevance": "For The three-halves bound for distinct squares in circular words, record cds-attempt-source-convention-audit (“The source conjecture uses the floor-strength convention”) documents a concrete method, search boundary, or failed route. The record states: The primary source states CS(n) <= 1.5n, which is floor(3n/2) for integer CS(n); the live canonical target asks the weaker ceiling bound at odd n.",
  "relevance_source": "recorded",
  "body": "The live statement at revision tdbcr1:fd17647632161b23903c494cbd3f7f8404aec50a36197b28c3f7fc74e31db5fd asks s(w) <= ceil(3n/2). The CPM 2026 Final Remarks state the conjecture as CS(n) <= 1.5n. Because CS(n) is integer-valued, that source statement is equivalent to CS(n) <= floor(3n/2). The two versions differ by one when n is odd. Li and Song also describe the conjectured sharp upper bound as 1.5n and prove 5n/3.\n\nThe factor convention agrees across the sources and the live problem: a circular square is a square factor of a rotation, equivalently a square factor of ww of total length at most n. The dated search checked the CPM DOI page, PDF, and experimental HTML; arXiv:2605.12215 and its submission history; arXiv:1708.00639; exact-title and formula searches; DataCite metadata; the live TheoremDB directory; orient; and research search. TheoremDB contained one canonical target and zero attached research records. No later revision or later strengthening beyond 5n/3 appeared in the checked sources.\n\nThis mismatch blocks a universal resolution claim against the imported provenance until review aligns the canonical convention. The bounded computations in this packet state their literal finite regions and are valid under either convention.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "universal",
    "statement": "the checked source status, factor convention, and floor/ceiling wording of the three-halves circular-square conjecture as checked on 2026-07-28"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.4230/LIPIcs.CPM.2026.6",
      "locator": "CPM 2026 Final Remarks, page 6:12; arXiv:2605.12215v1 abstract, Main Theorem, and Conclusion; audit performed 2026-07-28 UTC"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4230/LIPIcs.CPM.2026.6",
    "locator": "CPM 2026 Final Remarks, page 6:12; arXiv:2605.12215v1 abstract, Main Theorem, and Conclusion; audit performed 2026-07-28 UTC"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R135",
      "title": "Five-thirds is the current checked upper bound",
      "object_type": "claim",
      "relation": "reports",
      "direction": "outgoing"
    },
    {
      "slug": "R134",
      "title": "Fibonacci constructions approach three halves",
      "object_type": "claim",
      "relation": "reports",
      "direction": "outgoing"
    },
    {
      "slug": "R129",
      "title": "Strengthen the primitive Rauzy split case",
      "object_type": "attempt",
      "relation": "constrains",
      "direction": "outgoing"
    },
    {
      "slug": "circular-distinct-squares-three-halves",
      "title": "circular distinct squares three halves",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}