{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R28",
  "content_hash": null,
  "slug": "asq-claim-alphabet-0124-maximum-62",
  "type": "claim",
  "title": "The exact finite maximum for {0,1,2,4} is 62",
  "summary": "Every additive-square-free word over {0,1,2,4} has length at most 62. Exactly two length-62 words occur in the complete search tree, and they form one reversal orbit.",
  "relevance": "For Infinite additive-square avoidance over a finite integer alphabet, record asq-claim-alphabet-0124-maximum-62 (“The exact finite maximum for {0,1,2,4} is 62”) records a bound, answer, status fact, or structural consequence. The record states: Every additive-square-free word over {0,1,2,4} has length at most 62.",
  "relevance_source": "recorded",
  "body": "After normalizing by translation and gcd and identifying reflections, {0,1,2,4} is the first primitive four-letter alphabet outside the balanced family when alphabets are ordered by maximum letter and then lexicographically. Two independent exact DFS implementations closed its full prefix tree. Each visited 19,097,778 nodes and 5,350,440 terminal leaves. The deepest level is 62 and contains two words. One is 02012404142012421014102010242102414240424120241210212402414204; the other is its reversal, 40241420421201214202142404241420124201020141012421024140421020. This result concerns one finite alphabet. It leaves the existence question over other finite alphabets open.",
  "status": "supported",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "all finite additive-square-free words over the exact integer alphabet {0,1,2,4}, including the empty word",
    "bounds": {
      "alphabet_size": {
        "min": 4,
        "max": 4
      },
      "alphabet_maximum": {
        "min": 4,
        "max": 4
      },
      "word_length": {
        "min": 0,
        "max": 62
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "locator": "Independent exact Python and C++20 exhaustive searches executed on macOS arm64 on 2026-07-28"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Independent exact Python and C++20 exhaustive searches executed on macOS arm64 on 2026-07-28"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R30",
      "title": "Any positive construction needs at least four letters",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R22",
      "title": "Reproduce the balanced-family table through maximum letter 8",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R19",
      "title": "Exact additive-square-free prefix-tree enumerator",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R18",
      "title": "Independent C++ exact search for {0,1,2,4}",
      "object_type": "artifact",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "R24",
      "title": "Search for a low-expansion morphism and certify it",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "additive-square-finite-alphabet",
      "title": "additive square finite alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}