{
  "campaign": "heesch-leader-optimality",
  "leader_verified": true,
  "leader_hc_verified": 4,
  "leader_ring5_coverage": "251/254",
  "leader_score": 4.988189,
  "leader_score_full_precision": 4.988188976377953,
  "best_found_coverage": "251/254",
  "best_found_score": 4.988189,
  "beat_leader": false,
  "verdict": "holds",
  "verdict_scope": "No outer-ring re-choice beats the leader with rings 0..2 fixed (rings 3,4,5 all free), hence also with rings 0..3 fixed (rings 4,5 free) or ring 5 alone. Space NOT covered: freeing rings <=2 (f<=2) — host RAM. Solver-trust UNSATs (incremental CaDiCaL, no DRAT emitted); encoding soundness per gsqs README premises.",
  "search_completed": {
    "ring5_only_exact_maxsat": "optimum uncovered = 3 (certified by RC2) — leader ties, cannot be beaten",
    "free_from_4_rings0to3fixed": {
      "control_decide_3/254": "SAT, official defect 3/254, score 4.988189",
      "decide_2/1_pockets_counted": "UNSAT (16 cuts, 3s)",
      "decide_3/255_pockets_counted": "UNSAT (32 cuts, 7s)",
      "r_only_0/339": "UNSAT (0 cuts, 11s) — max R < 339 rules out D>=4"
    },
    "free_from_3_rings0to2fixed": {
      "control_decide_3/254": "SAT, official defect 3/254, score 4.988189",
      "decide_2/1_pockets_counted": "UNSAT (11 cuts, 18s)",
      "decide_3/255_pockets_counted": "UNSAT (43 cuts, 39s)",
      "decide_4/339_pockets_counted": "UNSAT (0 cuts, 62s)",
      "r_only_0/360": "UNSAT (83 cuts, 207s) — max R <= 359 < 424 rules out D>=5"
    },
    "free_from_2_attempted": "OOM-killed during solve: 1,053,736 vars / 7,553,966 clauses, 2.4 GB encode peak on a ~3 GB host. Space not covered by this run."
  },
  "commands": [
    "pip install python-sat   # into /workspace/venv — solver dep, NON-stdlib",
    "bash tools/build_checkers.sh   # drat-trim + lrat-check built; cake_lpr skipped (x86-64 only)",
    "python -m heesch_verify submission/best.heesch",
    "python scripts/score_driver.py submission/best.heesch   # verify_witness+verify_defect+yukon_score (harness path)",
    "python -m harness.verify   # REJECTED: CHECKER_UNAVAILABLE cake_lpr (aarch64) — expected off x86-64 Linux",
    "cd gsqs/solver && python corona_opt.py heesch/submission/best.heesch --out runs/corona_opt_best.heesch",
    "python joint_multi.py heesch/submission/best.heesch --free-from 4 --count-pockets --decide 3/254   # control: SAT 4.988189",
    "python joint_multi.py heesch/submission/best.heesch --free-from 4 --count-pockets --decide 2/1     # UNSAT",
    "python joint_multi.py heesch/submission/best.heesch --free-from 4 --count-pockets --decide 3/255   # UNSAT",
    "python joint_multi.py heesch/submission/best.heesch --free-from 4 --r-only --decide 0/339          # UNSAT",
    "python joint_multi.py heesch/submission/best.heesch --free-from 3 --count-pockets --decide 3/254   # control: SAT 4.988189",
    "python joint_multi.py heesch/submission/best.heesch --free-from 3 --count-pockets --decide 2/1     # UNSAT",
    "python joint_multi.py heesch/submission/best.heesch --free-from 3 --count-pockets --decide 3/255   # UNSAT",
    "python joint_multi.py heesch/submission/best.heesch --free-from 3 --count-pockets --decide 4/339   # UNSAT",
    "python joint_multi.py heesch/submission/best.heesch --free-from 3 --r-only --decide 0/360          # UNSAT",
    "python joint_multi.py heesch/submission/best.heesch --free-from 2 --count-pockets --decide 3/254   # OOM-killed (3 GB host)"
  ],
  "wall_seconds": 675,
  "wall_seconds_note": "sum of run wall times incl. encoding (~510s solver) + ~180s OOM-killed f=2 attempt; reproduction commands add ~6s",
  "witness_sha256": {
    "leader_heesch/submission/best.heesch": "87d35cd173835f0f775cc632921423f6d511dea88352eca30124010cb02b3572",
    "leader_proof.drat.xz": "1cefa72c2147ab6e1aa9b02c9f4715f07c82a6fb9aa5175097cddf632102b10e",
    "gsqs_decide_control.heesch": "162c7a26ca90cbb421a382890303b6b592add98e44444b3698ffa0169aa3202e",
    "gsqs_hex15-kaplan-a.joint.heesch (NOTE: different witness, score 4.9573)": "ec1a065f15486aa31b7fc7753d52bafc0dba95fef83c198dba5bf50f6ffa3642"
  },
  "artifact_sha256": {
    "REPRODUCE-LOG.txt": "8ae5ad9c2b4d7828505efa744e4e5601279f24550f8f9e338905a5b9c338ac87",
    "SEARCH-LOG.txt": "a2e768c094e3553e60523b753cd201a304c701c608ce72f3f42cc2b7f54a9770",
    "scripts/score_driver.py": "f23fbfe339f049988e775ed04adb60ac06cfed6343bec86b396915645b74730a",
    "runs/01_corona_opt.log": "e5733fcb6cd3d2bc06e6d8ff13f05954670a2ca68e54134637cbe9d0b29b042d",
    "runs/02_f4_control.log": "0f1c7d743d371ae96c664cfe5d61bd2975dd9ac95b1dfea949af3e76f76b859c",
    "runs/03_f4_d2.log": "620b1696cc50178dca1258514e02cd49eaf1813c95a68bef53380da4b06fd792",
    "runs/04_f4_d3r255.log": "a1c2e4387d54e3fb4b6a7dd64b956dae4390cdb9944b11d015f6a6d526c99d5a",
    "runs/05_f4_rmax339.log": "d95443c074d323bab7f239aabfb247f5db09f3994d1eb8ea67c2ac98e6647106",
    "runs/06_f3_control.log": "e7485493cf108f2ed0f4f38873a105e61ef7fe2a9a3800101588a0b6d14da0c0",
    "runs/07_f3_d2.log": "65f6b5e71f55279ea49a783523fb7f2360be2733e74200f9411cfd15b61737fe",
    "runs/08_f3_d3r255.log": "1933e40fee11fd5e44e2591af24a932479e304e92c72a9b84da2a399836fe3a9",
    "runs/09_f3_d4r339.log": "9471276b10e08b4cdc6f54f16656d759d5bf6ebd0b3a47c6625ce0498b229512",
    "runs/10_f3_rmax360.log": "424d4dc4479bcf65ba256c471a5a041fb3b33d8c943e8de7a0c3adb71d286250",
    "runs/11_f2_control.log": "75bfb89446af6ecff7fd35ae40c85cfef5ed93000dcf94263d27029db75024a7",
    "runs/repro_cli_leader.json": "ba120bbb078e9e7e6f9703b965c15c16c8db3414590f76ef5edba1e562cb21eb",
    "runs/repro_score_leader.json": "e977c3ef5f720a204385ca2a4ef3edcadf6a7c5bf5d46a83a09c4db6a10477f6"
  },
  "cross_check": "repro_cli_leader.json sha256 ba120bbb078e9e7e6f9703b965c15c16c8db3414590f76ef5edba1e562cb21eb is byte-identical to Kannaka's published control.official.json evidence artifact on the ledger",
  "environment": {
    "arch": "aarch64",
    "python": "3.11.2",
    "ram_gb": 3,
    "deps": "challenge harness stdlib-only; solver repo requires python-sat 1.9.dev15 (installed in /workspace/venv)",
    "proof_gate": "not run — cake_lpr is x86-64-only; drat-trim/lrat-check built successfully"
  },
  "new_witness": null
}