{
 "what": "Google's 18 Ramsey lower-bound graphs for AlphaEvolve (arXiv 2603.09172), each decided by an exhaustive clique search written here from the definition: a file R(s, t) >= m is CERTIFIED when its graph on m - 1 vertices has no s-clique and no independent t-set, both searched to the end. Written by tools/run-ramsey-ledger.py.",
 "source": {
  "repository": "https://github.com/google-research/google-research",
  "commit": "0d94f8c4d92678ce5f7a0eacae725f79174cfb03",
  "directory": "ramsey_number_bounds/improved_bounds",
  "pins": "corpus/ramsey/alphaevolve/PINS.json"
 },
 "method": {
  "kernel": "instruments/ramsey/clique.c",
  "reference": "instruments/ramsey/clique.py",
  "refMax": 250,
  "order": "smallest-last (ties by smallest label); roots in rank order with their later neighbours",
  "bounds": "greedy colouring of the candidates (lowest label first), walked backwards; size + colour < k closes the branch",
  "orbital": {
   "kernel": "instruments/ramsey/orbital.c",
   "reference": "instruments/ramsey/orbital.py",
   "battery": "instruments/ramsey/battery-orbital.py",
   "what": "one root (vertex 0) when a transitive group of checked automorphisms is given, one piece per orbit of a checked stabilizer of 0 on its neighbours; every piece relabelled core first (the reverse of its smallest-last order) and searched by clique.py's algorithm; with no maps (plain) the whole graph is the one piece",
   "sides": [
    "R_8_18_ge_1052 I (plain)",
    "R(3, 33) >= 241 I (orbital)"
   ]
  }
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  "instruments/ramsey/clique.py": "dd6ef69e4d750a5f2b432365b5c046df4a493a9c8b2294205e56caf790dd0316",
  "instruments/ramsey/graph.py": "5aa0a9e27a38f3ddf36294c2f4b9c8ad00db2a4d2406ee348f4b62ece34f99f9",
  "instruments/ramsey/orbital.c": "e6b135b7e7e71fd6ec8f9e75102ebdeffb910703d9f5f159fe145b38c2c9957c",
  "instruments/ramsey/orbital.py": "bd9956d0207ffea4f6576844cb380fbb092a7f18984435b7eed5e3e479446512",
  "instruments/ramsey/satpath.py": "46a337319694f98caf2666f9943ebaf98280e32a9eabdf24a26d64587f121223",
  "tools/run-ramsey-ledger.py": "3a355cf11866febd05a6d06d5e7925c88583722a338868835d01d7a1f41a547a"
 },
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  "compiler": "Apple clang version 21.0.0 (clang-2100.0.123.102)",
  "threads": 8
 },
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  "REFUSED": 1
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}