{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R373",
  "content_hash": null,
  "slug": "heilbronn10-attempt-unrestricted-global-certificate",
  "type": "attempt",
  "title": "Run the unrestricted Sudermann-Merx global model at n = 10",
  "summary": "Pin the public model and exact incumbent, retain only proved symmetry reductions, and export enough solver state for independent interval or rational checking.",
  "relevance": "For Exact ten-point Heilbronn number in the unit square, record heilbronn10-attempt-unrestricted-global-certificate (“Run the unrestricted Sudermann-Merx global model at n = 10”) documents a concrete method, search boundary, or failed route. The record states: Pin the public model and exact incumbent, retain only proved symmetry reductions, and export enough solver state for independent interval or rational checking.",
  "relevance_source": "recorded",
  "body": "Use companion repository commit \\(4e725664b35a6e5640876e56b1cd0ec3aeeef6e5\\) and set \\(n=10\\) in \\(optimization_models/heilbronn_final.py\\). Seed the exact Comellas–Yebra coordinates and value as the incumbent. Retain the proved five-boundary-point canonicalization from Proposition 2. Run the full \\(P_\\Delta^*\\) model over arbitrary ten-point configurations. Leave out the Monji-Modir-Kocuk two-points-per-edge conjecture and \\(y_5\\le1/2\\) restriction.\n\nA first budget is 24 wall-clock hours with at most 16 threads and 64 GiB RAM. Record Python, Gurobi, operating system, CPU, model parameters, deterministic seed, primal and dual bounds, node counts, logs, checkpoints, and the final solver status. Export each incumbent as exact decimal strings and save every certificate or box description needed for independent interval or rational checking.\n\nA universal upper bound of 0.04654 is a useful intermediate result. A timeout or resource limit should become an explicit attempt record with its last certified upper bound. Keep the problem open until a universal exact or rigorous interval upper bound matches the exact construction value.",
  "status": "next_experiment",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "universal",
    "statement": "all configurations of ten distinct points in the unit square, without structural symmetry or boundary-pattern assumptions"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://github.com/spiralulam/heilbronn/tree/4e725664b35a6e5640876e56b1cd0ec3aeeef6e5",
      "locator": "Plan checked against theoremdb on 2026-07-28; model and repository audited at the pinned public commit"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://github.com/spiralulam/heilbronn/tree/4e725664b35a6e5640876e56b1cd0ec3aeeef6e5",
    "locator": "Plan checked against theoremdb on 2026-07-28; model and repository audited at the pinned public commit"
  },
  "relations": [
    {
      "slug": "R371",
      "title": "Audit the live record, primary sources, and current arXiv frontier",
      "object_type": "attempt",
      "relation": "constrains",
      "direction": "incoming"
    },
    {
      "slug": "R375",
      "title": "The best-known ten-point area is 0.0465374195825..., with global optimality open",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R374",
      "title": "The exact Comellas–Yebra construction has minimum area 0.0465374195825...",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R376",
      "title": "The Comellas–Yebra three-parameter family has exact maximum 0.0465374195825...",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R372",
      "title": "Cover the symmetric family by exact determinant intervals",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "heilbronn-square-ten",
      "title": "heilbronn square ten",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}