{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R79",
  "content_hash": null,
  "slug": "bsm12-attempt-close-two-query-gap",
  "type": "attempt",
  "title": "Close the remaining two-query gap by certified minimax search",
  "summary": "A symmetry-aware feasibility search should test depth five first, then seek a depth-six tree or a second infeasibility certificate.",
  "relevance": "For Optimal balanced-subset Mastermind on twelve points, record bsm12-attempt-close-two-query-gap (“Close the remaining two-query gap by certified minimax search”) documents a concrete method, search boundary, or failed route. The record states: A symmetry-aware feasibility search should test depth five first, then seek a depth-six tree or a second infeasibility certificate.",
  "relevance_source": "recorded",
  "body": "The next computation should canonicalize each knowledge state under permutations of the twelve points and query complementation. For a remaining depth \\(d\\), reject a state immediately when it has more than \\(7^d\\) candidates. Cache every canonical state and record either a resolving query or the complete list of query-orbit failures.\n\nThe first run should decide whether depth five is feasible. An infeasibility result needs a replayable certificate containing each rejected canonical state, its stabilizer, the query-orbit representatives, and a child obstruction for every representative. If depth five fails, the same engine should search depth six and export the full decision tree when one exists. Independent certificate checking can then determine whether the answer is 6 or 7.",
  "status": "open_strategy",
  "evidence_grade": "proposed",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.4153/CJM-1966-007-2",
      "locator": "Research plan derived from the finite minimax formulation and the reproduced greedy tree"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4153/CJM-1966-007-2",
    "locator": "Research plan derived from the finite minimax formulation and the reproduced greedy tree"
  },
  "models": [],
  "relations": [
    {
      "slug": "R81",
      "title": "The certified interval for M6 is 5 through 7",
      "object_type": "claim",
      "relation": "targets",
      "direction": "outgoing"
    },
    {
      "slug": "balanced-subset-mastermind-twelve",
      "title": "balanced subset mastermind twelve",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}