{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R829",
  "content_hash": null,
  "slug": "vt0cr2-attempt-literature-audit",
  "type": "attempt",
  "title": "The focused literature search found deletion covering only",
  "summary": "Primary sources define the same VT code and study asymmetric errors or deletion covering; the exact ordinary Hamming radius was not located.",
  "relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
  "relevance_source": "derived",
  "body": "Varshamov and Tenengolts introduced the congruence code for single asymmetric errors in 1965. Lenz, Rashtchian, Siegel, and Yaakobi study covering codes under insertions and deletions. Their Definition 3 gives the same family \\(C_{VT}(n;a)\\), and Corollary 4 uses its perfect single-deletion property. Their introduction separately calls ordinary Hamming covering substitution covering.\n\nFocused searches combined the family names `Varshamov-Tenengolts`, `VT_0(n)`, and `Constantin-Rao` with `Hamming covering radius`, `covering radius 2`, and `quasi-perfect`. They located the 1965 construction, surveys of Hamming covering radius, and the insertion/deletion covering paper. The exact claim \\(\\rho_H(V_n)=2\\) did not appear in the sources found. This search cannot establish novelty, so the theorem above rests on the self-contained proof.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://cmrr-star.ucsd.edu/static/pubs/Covering_Codes_Using_Insertions_or_Deletions.pdf",
      "locator": "Andreas Lenz, Cyrus Rashtchian, Paul H. Siegel, and Eitan Yaakobi, Covering Codes Using Insertions or Deletions, IEEE Transactions on Information Theory 67(6), 3376-3388 (2021), especially introduction footnote 1, Definition 3, and Corollary 4"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://cmrr-star.ucsd.edu/static/pubs/Covering_Codes_Using_Insertions_or_Deletions.pdf",
    "locator": "Andreas Lenz, Cyrus Rashtchian, Paul H. Siegel, and Eitan Yaakobi, Covering Codes Using Insertions or Deletions, IEEE Transactions on Information Theory 67(6), 3376-3388 (2021), especially introduction footnote 1, Definition 3, and Corollary 4"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R830",
      "title": "The Hamming covering radius is exactly 2",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "vt-zero-covering-radius-two",
      "title": "vt zero covering radius two",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}