{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R10",
  "content_hash": null,
  "slug": "ac0123-claim-million-letter-construction",
  "type": "claim",
  "title": "The reconstructed method produces a checked million-letter word",
  "summary": "A deterministic Up-and-Down reconstruction produced a 1,000,000-letter word over {0,1,2,3}, and two differently ordered exact scans found no additive cube.",
  "relevance": "For Additive-cube avoidance on the alphabet zero through three, record ac0123-claim-million-letter-construction (“The reconstructed method produces a checked million-letter word”) records a bound, answer, status fact, or structural consequence. The record states: A deterministic Up-and-Down reconstruction produced a 1,000,000-letter word over {0,1,2,3}, and two differently ordered exact scans found no additive cube.",
  "relevance_source": "recorded",
  "body": "With failure threshold 1,209, retreat length 100, and checkpoint spacing 10,000, the constructor reached length 1,000,000 after testing 2,480,028 candidate letters. The output file, including its final line feed, has SHA-256 digest `15d439b42fefa8501203775cf0b4457f7eaf19bae14ae5797b5d405e03ed1846`.\n\nThe constructor's internal scan checked every end position and block length. The independent checker scanned every block length and start position. Each covered all 166,666,500,000 admissible factor specifications and found no additive cube. The symbol counts are 282,092 zeros, 217,686 ones, 217,697 twos, and 282,525 threes. Lietard's source-reported word has length 70,880,000. The acceptance condition still asks for an infinite word or an impossibility proof.",
  "status": "observed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "the single recorded deterministic word of length 1,000,000 over the literal integer alphabet {0,1,2,3}",
    "bounds": {
      "word_length": {
        "min": 1000000,
        "max": 1000000
      },
      "alphabet_size": {
        "min": 4,
        "max": 4
      },
      "candidate_factor_pairs": {
        "min": 166666500000,
        "max": 166666500000
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "locator": "ac0123-artifact-updown-constructor and ac0123-artifact-independent-full-scan"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "ac0123-artifact-updown-constructor and ac0123-artifact-independent-full-scan"
  },
  "relations": [
    {
      "slug": "R5",
      "title": "Deterministic Up-and-Down finite-word constructor",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R3",
      "title": "Independent exact full-word checker",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R9",
      "title": "The source-informed finite construction reaches one million",
      "object_type": "attempt",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R12",
      "title": "A finite additive-cube-free word of length 70,880,000 is known",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R6",
      "title": "Search beyond image length seven with a decision certificate",
      "object_type": "attempt",
      "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"
    }
  ]
}