{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R7",
  "content_hash": null,
  "slug": "ac0123-attempt-dated-source-and-live-audit",
  "type": "attempt",
  "title": "A 2026 source and live-state audit leaves the infinite case open",
  "summary": "The audit resolved one canonical TheoremDB problem with no attached research records and found a February 2025 primary source explicitly calling the {0,1,2,3} case unknown.",
  "relevance": "For Additive-cube avoidance on the alphabet zero through three, record ac0123-attempt-dated-source-and-live-audit (“A 2026 source and live-state audit leaves the infinite case open”) documents a concrete method, search boundary, or failed route. The record states: The audit resolved one canonical TheoremDB problem with no attached research records and found a February 2025 primary source explicitly calling the {0,1,2,3} case unknown.",
  "relevance_source": "recorded",
  "body": "The audit searched the live TheoremDB directory by exact title terms, object, parameter, and additive-cube aliases. It found one canonical target, problem 2826, and no attached research records. The exact slug search endpoint tokenized the query differently and returned zero, so the title-term result and canonical object were checked directly. No duplicate target or competing packet was found.\n\nThe literature pass started with Rao's 2015 paper, which asks the question and reports a finite word of about \\(1.4\\times10^5\\) letters. Lietard and Rosenfeld's 2020 classification makes the arithmetic-progression class the sole four-letter exception and reports finite words above \\(10^7\\). Lietard's thesis raises the finite construction to exactly 70,880,000. The 2022 survey repeats the open exception. Andrade and Mol explicitly call the case unknown in arXiv:2408.15390v2, revised February 2025. Popoli, Shallit, and Stipulanti address neighboring additive-complexity and Walnut questions.\n\nExact-title, exact-alphabet, finite-length, morphism, citation, arXiv, DOI, and author-page searches were run through 2026-07-28. The result is a dated search report. Its finite scope cannot establish the absence of later or unpublished work.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "the named live TheoremDB records and primary sources checked for the exact {0,1,2,3} additive-cube problem on 2026-07-28",
    "family": "the live target, attached research, cited primary papers, thesis, survey, later status paper, and author-hosted artifacts named in this record"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2408.15390v2",
      "locator": "Audit completed 2026-07-28 UTC; latest explicit status in Andrade and Mol, arXiv:2408.15390v2, Introduction, PDF page 2"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2408.15390v2",
    "locator": "Audit completed 2026-07-28 UTC; latest explicit status in Andrade and Mol, arXiv:2408.15390v2, Introduction, PDF page 2"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R12",
      "title": "A finite additive-cube-free word of length 70,880,000 is known",
      "object_type": "claim",
      "relation": "reports",
      "direction": "outgoing"
    },
    {
      "slug": "R11",
      "title": "The four-term progression is the remaining four-letter equivalence class",
      "object_type": "claim",
      "relation": "reports",
      "direction": "outgoing"
    },
    {
      "slug": "additive-cube-four-term-progression-alphabet",
      "title": "additive cube four term progression alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}