{
  "checked_at": "2026-08-29T00:00:00Z",
  "source": "https://arxiv.org/abs/2607.21508",
  "method": "Independent exact enumeration using the power-sum expansion of the chromatic symmetric function and Murnaghan–Nakayama characters.",
  "results": {
    "G1": { "vertices": 12, "edges": 22, "schur_partition": [3, 3, 3, 3], "coefficient": -64 },
    "G2": { "vertices": 12, "edges": 21, "schur_partition": [3, 3, 3, 3], "coefficient": -40 }
  },
  "conclusion": "Both coefficients are negative, reproducing the two stated counterexamples to claw-free Schur positivity.",
  "source_code": "/scripts/reproduce/claw-free-schur.cpp"
}