{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R22",
  "content_hash": null,
  "slug": "asq-attempt-balanced-family-reproduction",
  "type": "attempt",
  "title": "Reproduce the balanced-family table through maximum letter 8",
  "summary": "An exact depth-first sweep closed all ten primitive normalized reflection representatives in the balanced family through maximum letter 8 and matched the published maxima.",
  "relevance": "For Infinite additive-square avoidance over a finite integer alphabet, record asq-attempt-balanced-family-reproduction (“Reproduce the balanced-family table through maximum letter 8”) documents a concrete method, search boundary, or failed route. The record states: An exact depth-first sweep closed all ten primitive normalized reflection representatives in the balanced family through maximum letter 8 and matched the published maxima.",
  "relevance_source": "recorded",
  "body": "The sweep enumerated every A={0<a<b<c} with gcd(A)=1, c<=8, and c=a+b, then kept the lexicographically smaller of A and c-A. For each of ten representatives, a prefix-sum DFS visited every additive-square-free prefix until the search tree closed. The maxima, node counts, leaf counts, maximizer counts, and maximizer digests are recorded in the linked artifact. The compact six-field row digest was independently matched by a second operator implementation.",
  "status": "completed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "primitive normalized four-letter alphabets {0<a<b<c} with c=a+b, c at most 8, one representative under reflection",
    "bounds": {
      "alphabet_size": {
        "min": 4,
        "max": 4
      },
      "alphabet_maximum": {
        "min": 3,
        "max": 8
      },
      "alphabet_count": {
        "min": 10,
        "max": 10
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "attempt",
    "command": "PYTHONPATH=. python3 additive_square_sweep.py --max-value 8 --balanced-family-only --node-limit 100000000",
    "citation": {
      "locator": "Exact Python 3.9.6 execution on macOS arm64 on 2026-07-28; published comparison is Freedman and Brown, Integers 16 (2016), A33, Theorem 1 and pages 2-3"
    },
    "runtime_seconds": 80.48,
    "missing": [
      "source",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Exact Python 3.9.6 execution on macOS arm64 on 2026-07-28; published comparison is Freedman and Brown, Integers 16 (2016), A33, Theorem 1 and pages 2-3"
  },
  "models": [],
  "relations": [
    {
      "slug": "R29",
      "title": "The balanced four-letter family has finite maxima at most 60",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R17",
      "title": "Balanced-family alphabet enumerator",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R28",
      "title": "The exact finite maximum for {0,1,2,4} is 62",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "additive-square-finite-alphabet",
      "title": "additive square finite alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}