Chou-Haag-Huryn-Ledoan Table 1 reproduces at all eleven rows after truncation, E(N)/(N^2 log^2 N) keeps rising to 0.244 at 10^7, odd separations carry nothing, and on even k the error is S(k)[R(N)+R(N-k)-R(k)], a k-resolved refinement of Korevaar and te Riele's Approximation 2.1 that explains 1 to 3 percent of E(N).
hunts/prime_pair_error (Record 92 of 98 in chronological sequence)
Guiding Question
Which separations k carry the Chou-Haag-Huryn-Ledoan error E(N), and is there one compact relationship, with the Hardy-Littlewood prediction held fixed, that accounts for a measurable part of psi_2(N, k) - S(k)(N - k)?
Method & Verification
FFT autocorrelation of Lambda through N=10^7 was cross-checked against pure-Python and direct pair sums, with a three-profile fit discovered on N<=10^6 and tested at the held-out cutoffs 3e6 and 1e7.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
Case-log status is settled as a reproduction plus one measured relationship, not new; mapped to completed. k divisible by 3 is one sixth of the separations and about half of the error. The directory at the pin later accumulated residue, wronskian, upper-bound, and factorial-certificate-frontier files; this row records the case-log reproduction, not those later arms. Nothing bears on RH.
Date Provenance
commit beee4fb4bbafd84ff71debd4951cfe7b3c2d9229, hunts/prime_pair_error/RESULTS.md, author 2026-09-06T01:30:13-05:00