files / problems / unit-distance-509 / compute / search_summary.json

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{
  "published": {
    "source": "https://github.com/vasnesterov/HadwigerNelson/blob/master/vtx/509_parts.vtx",
    "sourced_from": "Polymath16 fifteenth thread, as cited by the Lean formalization README",
    "paper": "arXiv:2010.12665",
    "claimed_n": 509,
    "claimed_m": 2442,
    "verified_n": 509,
    "verified_m": 2442,
    "field": "Q(sqrt(3),sqrt(5),sqrt(11))",
    "split": {"unrotated_L": 374, "rho_S_minus_origin": 135}
  },
  "heule_510": {
    "source": "https://github.com/vasnesterov/HadwigerNelson/blob/master/vtx/510_heule.vtx",
    "identical_to_cnp_sat_510_vtx": true,
    "verified_n": 510,
    "verified_m": 2504
  },
  "four_color_unsat": {
    "solver": "Cadical 1.9.5 via python-sat",
    "vars": 2036,
    "clauses": 10280,
    "triangle": [0, 149, 152],
    "status": "UNSAT",
    "seconds": 2.455,
    "drat": "color509.drat",
    "drat_trim": "s VERIFIED",
    "clause_core": 9170
  },
  "vertex_critical": {
    "G_minus_v_SAT": 509,
    "G_minus_v_UNSAT": 0,
    "log": "shrink_singles.jsonl",
    "elapsed_seconds": 90.08
  },
  "lattice_reserve": {
    "r_max": 2.55,
    "unused_disk_or_rho": 156300,
    "deg_at_least_4": 677,
    "max_deg_into_G": 10,
    "file": "candidates.json"
  },
  "swaps": {
    "top12_extras_drop_one_lowdeg": {"tested": 24, "UNSAT": 0, "log": "expand_reduce.jsonl"},
    "full677_replace_v310": {"status": "UNSAT", "n": 1185},
    "binary_reduced_extras_for_v310": {"n_extra": 6, "n": 514, "file": "swap_v310_e6.vtx"},
    "G514_vertex_critical": {"SAT": 514, "UNSAT": 0},
    "one_extra_two_deg4": {"jobs": 10155, "hits": 0, "log": "double_swap_deg4.jsonl"},
    "one_extra_deg_ge6_two_deg4": {"jobs": 2925, "hits": 0, "log": "double_swap_noadj.jsonl"},
    "one_extra_two_deg_le5_adjacent": {"jobs": 68, "hits": 0, "log": "double_swap_d5adj.jsonl"}
  },
  "dent": false,
  "published_record_still": 509
}