Compute — Chowla cosine, explicit c = 1/18
./run_all.sh
Expected: last line ALL OK, exit 0.
| script | role |
|---|---|
verify_lemma72.py |
exact 32-window check of Bedert Lemma 7.2 in Q(sqrt(2)) |
lemma71_bounds.py |
arithmetic pack of the Young/split constants |
track_constants.py |
builds certificate.json |
verify_certificate.py |
rebuilds Cstar, checks 2048 Cstar <= 18^7 |
optimize_aux.py |
float search of (alpha, beta, phi); did not beat Bedert |
qsqrt2.py, aux_rho.py |
exact arithmetic |
Claim (not the square-root conjecture): for every n >= 1 and every
n-element set of positive integers,
min_x sum_{a in A} cos(a x) <= - n^{1/7} / 18.