{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R12",
  "content_hash": null,
  "slug": "ac0123-claim-seventy-million-finite-word",
  "type": "claim",
  "title": "A finite additive-cube-free word of length 70,880,000 is known",
  "summary": "Lietard's 2020 thesis Proposition 6.4.1 gives a word of exactly 70,880,000 letters over {0,1,2,3} with no additive cube; the infinite case remains open.",
  "relevance": "For Additive-cube avoidance on the alphabet zero through three, record ac0123-claim-seventy-million-finite-word (“A finite additive-cube-free word of length 70,880,000 is known”) records a bound, answer, status fact, or structural consequence. The record states: Lietard's 2020 thesis Proposition 6.4.1 gives a word of exactly 70,880,000 letters over {0,1,2,3} with no additive cube; the infinite case remains open.",
  "relevance_source": "recorded",
  "body": "Proposition 6.4.1 of Lietard's thesis states that there is a 70,880,000-letter word over \\(\\{0,1,2,3\\}\\) containing no three consecutive equal-length blocks with equal sums. Chapter 6 constructs the word with the deterministic Up and Down method, which alternates the letter priority \\(0,1,2,3\\) and \\(3,2,1,0\\) after a failure threshold and a fixed retreat. Section 6.4.2 reports that the computation took several weeks.\n\nThis is the strongest finite construction located in the dated audit. It supplies no infinite word or impossibility proof. The thesis page for the word and program currently points to a file-share URL that returned HTTP 404 on 2026-07-28. The proposition is therefore recorded as sourced evidence without an independent replay of the 70,880,000-letter artifact.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the source-reported 70,880,000-letter word over the literal integer alphabet {0,1,2,3}",
    "bounds": {
      "word_length": {
        "min": 70880000,
        "max": 70880000
      },
      "alphabet_size": {
        "min": 4,
        "max": 4
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://docnum.univ-lorraine.fr/public/DDOC_T_2020_0259_LIETARD.pdf",
      "locator": "Florian Lietard, Evitabilite de puissances additives en combinatoire des mots, doctoral thesis, Universite de Lorraine, 2020, Proposition 6.4.1 on PDF page 119 (printed page 100), construction in Sections 6.2-6.4, and conclusion on PDF page 125"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://docnum.univ-lorraine.fr/public/DDOC_T_2020_0259_LIETARD.pdf",
    "locator": "Florian Lietard, Evitabilite de puissances additives en combinatoire des mots, doctoral thesis, Universite de Lorraine, 2020, Proposition 6.4.1 on PDF page 119 (printed page 100), construction in Sections 6.2-6.4, and conclusion on PDF page 125"
  },
  "relations": [
    {
      "slug": "R7",
      "title": "A 2026 source and live-state audit leaves the infinite case open",
      "object_type": "attempt",
      "relation": "reports",
      "direction": "incoming"
    },
    {
      "slug": "R9",
      "title": "The source-informed finite construction reaches one million",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "R10",
      "title": "The reconstructed method produces a checked million-letter word",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "additive-cube-four-term-progression-alphabet",
      "title": "additive cube four term progression alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}