{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R825",
  "content_hash": null,
  "slug": "vt0-attempt-literature-logconcavity-audit",
  "type": "attempt",
  "title": "Primary sources supply the coefficient formula",
  "summary": "The checked papers derive the VT weight distribution. Their stated results leave this bounded log-concavity question to direct computation.",
  "relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
  "relevance_source": "derived",
  "body": "Bibak, Kapron, and Srinivasan translate fixed-weight VT words into distinct positive solutions of a congruence and derive the individual coefficient formula in Corollary 3.12. Bibak and Milenkovic derive a generating polynomial in Theorem IV.7 and extract the same coefficient formula in Theorem IV.8.\n\nA focused search using the terms `Varshamov-Tenengolts`, `weight distribution`, `weight enumerator`, `log-concave`, and `unimodal` found these coefficient results and no theorem asserting the requested log-concavity range. The exact finite sweep therefore supplies the result for \\(7\\leq n\\leq2000\\). This search record makes no claim about lengths beyond 2000.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "primary literature checked for the VT weight enumerator, individual weight coefficients, and a log-concavity result for the zero-syndrome coefficients",
    "bounds": {
      "publication_year": {
        "min": 2018,
        "max": 2019
      },
      "target_length": {
        "min": 7,
        "max": 2000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1007/s10623-017-0428-3",
      "locator": "Khodakhast Bibak, Bruce M. Kapron, and Venkatesh Srinivasan, Unweighted Linear Congruences with Distinct Coordinates and the Varshamov-Tenengolts Codes, Designs, Codes and Cryptography 86 (2018), 1893-1904; Khodakhast Bibak and Olgica Milenkovic, Explicit Formulas for the Weight Enumerators of Some Classes of Deletion Correcting Codes, IEEE Transactions on Communications 67(3) (2019), 1809-1816"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s10623-017-0428-3",
    "locator": "Khodakhast Bibak, Bruce M. Kapron, and Venkatesh Srinivasan, Unweighted Linear Congruences with Distinct Coordinates and the Varshamov-Tenengolts Codes, Designs, Codes and Cryptography 86 (2018), 1893-1904; Khodakhast Bibak and Olgica Milenkovic, Explicit Formulas for the Weight Enumerators of Some Classes of Deletion Correcting Codes, IEEE Transactions on Communications 67(3) (2019), 1809-1816"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R827",
      "title": "The truncated VT zero-syndrome weight sequence is log-concave through length 2000",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "vt-zero-weight-log-concavity",
      "title": "vt zero weight log concavity",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}