{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R80",
  "content_hash": null,
  "slug": "bsm12-attempt-literature-audit",
  "type": "attempt",
  "title": "The closest literature treats broader query models",
  "summary": "Classical determining collections and spring-scale search use intersection counts, while their query restrictions and objectives differ from this finite adaptive problem.",
  "relevance": "For Optimal balanced-subset Mastermind on twelve points, record bsm12-attempt-literature-audit (“The closest literature treats broader query models”) documents a concrete method, search boundary, or failed route. The record states: Classical determining collections and spring-scale search use intersection counts, while their query restrictions and objectives differ from this finite adaptive problem.",
  "relevance_source": "recorded",
  "body": "Cantor and Mills study determining collections: fixed subsets \\(S_i\\) whose intersection cardinalities \\(|S_i\\cap T|\\) identify an arbitrary unknown subset \\(T\\). This supplies the classical nonadaptive form of the same observation model. Their queries and secrets may have arbitrary cardinalities.\n\nKarimi, Kazemi, Heidarzadeh, and Sprintson study adaptive subset weighing on a spring scale when the total integer weight is known. Their main objective is the expected number of weighings, and the weighed subsets may have arbitrary size. Black-peg Mastermind also returns an agreement count, though the AB variant studied by El Ouali and coauthors uses permutations rather than balanced binary vectors.\n\nSearches for the exact parameters \\((12,6)\\), balanced six-subset queries, spring-scale search, and binary black-peg Mastermind yielded no published value for \\(M_6\\). The certified interval in this record comes from the direct finite argument and computation.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.4153/CJM-1966-007-2",
      "locator": "Cantor and Mills, Canadian Journal of Mathematics 18 (1966), 42-48; Karimi et al., arXiv:1805.02977; El Ouali et al., arXiv:1611.05907"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4153/CJM-1966-007-2",
    "locator": "Cantor and Mills, Canadian Journal of Mathematics 18 (1966), 42-48; Karimi et al., arXiv:1805.02977; El Ouali et al., arXiv:1611.05907"
  },
  "models": [],
  "relations": [
    {
      "slug": "R81",
      "title": "The certified interval for M6 is 5 through 7",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "balanced-subset-mastermind-twelve",
      "title": "balanced subset mastermind twelve",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}