{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R372",
  "content_hash": null,
  "slug": "heilbronn10-attempt-symmetric-family-cover",
  "type": "attempt",
  "title": "Cover the symmetric family by exact determinant intervals",
  "summary": "The exact cover succeeds 1.8 × 10⁻⁷ above the construction value. A run 1.3 × 10⁻⁷ above it leaves 35 boxes after 650,000 nodes, exposing rapid scaling near the optimum.",
  "relevance": "For Exact ten-point Heilbronn number in the unit square, record heilbronn10-attempt-symmetric-family-cover (“Cover the symmetric family by exact determinant intervals”) documents a concrete method, search boundary, or failed route. The record states: The exact cover succeeds 1.8 × 10⁻⁷ above the construction value.",
  "relevance_source": "recorded",
  "body": "A deterministic depth-first branch-and-bound used exact rational interval bounds and five witness triangles. Thresholds were tightened through 0.046539, 0.0465385, 0.046538, 0.04653775, and 0.0465376. The final completed run at 0.0465376 visited 649,645 nodes and closed every ordered box. This is 0.000000180417458... above the exact construction value.\n\nAt threshold 0.04653755, only 0.000000130417458... above the exact value, a 650,000-node cap left 35 boxes open at depth 64. The capped run is a budget-exhaustion trace. It supplies no counterexample. The coordinate ansatz also covers only a symmetric three-parameter family, so this route cannot certify the canonical unrestricted problem without a separate reduction theorem. The analytic argument in `heilbronn10-claim-symmetric-family-exact` settles the family exactly.",
  "status": "inconclusive",
  "evidence_grade": "computational",
  "scope": {
    "kind": "family",
    "statement": "all ordered parameters 0 <= x <= y <= z <= 1/2 in the listed ten-point affine boundary ansatz near the exact construction threshold",
    "family": "Comellas-Yebra diagonal-reflection and half-turn symmetric three-parameter boundary family"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Exact interval runs and replay artifact executed 2026-07-28 UTC"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Exact interval runs and replay artifact executed 2026-07-28 UTC"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R370",
      "title": "Exact rational interval cover for the symmetric family",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R376",
      "title": "The Comellas–Yebra three-parameter family has exact maximum 0.0465374195825...",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "R373",
      "title": "Run the unrestricted Sudermann-Merx global model at n = 10",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "heilbronn-square-ten",
      "title": "heilbronn square ten",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}