{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R29",
  "content_hash": null,
  "slug": "asq-claim-balanced-family-maxima",
  "type": "claim",
  "title": "The balanced four-letter family has finite maxima at most 60",
  "summary": "Freedman and Brown determine the longest good words for four-letter sets satisfying the endpoint-sum equation; the ten primitive normalized reflection classes with maximum letter at most 8 have maxima between 50 and 60.",
  "relevance": "For Infinite additive-square avoidance over a finite integer alphabet, record asq-claim-balanced-family-maxima (“The balanced four-letter family has finite maxima at most 60”) records a bound, answer, status fact, or structural consequence. The record states: Freedman and Brown determine the longest good words for four-letter sets satisfying the endpoint-sum equation; the ten primitive normalized reflection classes with maximum letter at most 8 have maxima between 50 and 60.",
  "relevance_source": "recorded",
  "body": "This packet uses balanced family as shorthand for normalized four-letter alphabets A={0<a<b<c} satisfying 0+c=a+b. Freedman and Brown determine g(A), the maximum length of an additive-square-free finite word, for this family. For the ten primitive normalized representatives with c<=8 after identifying A with c-A, the ordered maxima are 50,55,55,55,60,60,60,58,60,60 for 0123,0134,0145,0235,0156,0167,0257,0347,0178,0358.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "four-letter integer alphabets satisfying the Freedman-Brown endpoint-sum equation",
    "family": "balanced four-letter alphabets with a+d=b+c"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://math.colgate.edu/~integers/q33/q33.pdf",
      "locator": "Allen R. Freedman and Thomas C. Brown, Sequences on Sets of Four Numbers, Integers 16 (2016), A33, Theorem 1 and the table on pages 2-3"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://math.colgate.edu/~integers/q33/q33.pdf",
    "locator": "Allen R. Freedman and Thomas C. Brown, Sequences on Sets of Four Numbers, Integers 16 (2016), A33, Theorem 1 and the table on pages 2-3"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R27",
      "title": "Audit sources, variants, duplicates, and target integrity",
      "object_type": "attempt",
      "relation": "reports",
      "direction": "incoming"
    },
    {
      "slug": "R22",
      "title": "Reproduce the balanced-family table through maximum letter 8",
      "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"
    }
  ]
}