q1 — re-optimize Hou–Zhao vector smoothing

Same lemma as Hou–Zhao arXiv:2607.01169v2 Lemma 2.1. Their certificate is eight symmetric kernels at m=32, L=4. The 2026-08-17 campaign certified those kernels at L=6. This folder searches the leftover handles: free histograms instead of six-mode profiles, more kernels, a resampled finer grid, and dropped kernel symmetry.

Certified

certs/joint_r8_L6.json is an eight-kernel rational certificate at m=32, L=6. The kernels are free symmetric histograms, not the published six-mode shapes. Exact arithmetic gives

√(ab) = 0.9432425309706136 < 0.94325 < 0.9435.

So

F(N) ≤ √N + 0.94325 N^{1/4} + O(1)

for all large N. This beats Hou–Zhao’s published four-decimal statement 0.9435, not just their exact γ0. SHA-256 of the JSON is edcc2c973809c4bb8a3f25233ffc80e6b5ce432a70c4d01697a3ba8ead8beda5.

Three checks that do not share covering code:

./run_all.sh

that is: parent verify_certificate.py (nested (q,i) loop), verify_q1.py (Fraction convolution), and verify_q1.c (GMP nested sum). All three report min slack 0 and ab < (0.94325)^2.

A floating γ is not a bound. The search log is search.jsonl.