{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1390",
  "content_hash": null,
  "slug": "binary-code-weight-enumerator-equality-complexity-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: Evaluating weight enumerators and finding minimum distance have strong hardness results, while the recent MathOverflow thread gives no reduction or algorithm for equality of the full polynomials. Exact unresolved remainder: Give a deterministic polynomial-time algorithm with proof, or prove hardness under a named standard reduction and place the problem in the strongest justified upper complexity class. A hardness proof must map every input to two explicitly constructible binary generator matrices and prove equality of their entire weight enumerators exactly when the source instance is a yes-instance.",
  "relevance": "For Complexity of equality for binary-code weight enumerators, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: Evaluating weight enumerators and finding minimum distance have strong hardness results, while the recent MathOverflow thread gives no reduction or algorithm for equality of the full polynomials.\n\nExact unresolved remainder: Give a deterministic polynomial-time algorithm with proof, or prove hardness under a named standard reduction and place the problem in the strongest justified upper complexity class. A hardness proof must map every input to two explicitly constructible binary generator matrices and prove equality of their entire weight enumerators exactly when the source instance is a yes-instance.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/cs/0304044",
      "locator": "abstract and main hardness results for exact and additive-approximate evaluation of a binary-code weight enumerator"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/cs/0304044",
    "locator": "abstract and main hardness results for exact and additive-approximate evaluation of a binary-code weight enumerator"
  },
  "relations": [
    {
      "slug": "R1285",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "binary-code-weight-enumerator-equality-complexity",
      "title": "binary code weight enumerator equality complexity",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}