q2 — grow free histograms from the q1 mix

Same lemma as Hou–Zhao arXiv:2607.01169v2 Lemma 2.1. q1 leftover refine and dropped-symmetry never finished; this folder does not continue those two phases.

certs/r11_m48_L6.json is an eleven-kernel rational certificate at m=48, L=6. The kernels are free symmetric histograms, grown from the q1 mix and then reshaped on a 48-bin grid. Exact arithmetic gives

√(ab) = 0.943006169985179 < 0.94301 < 0.94325 < 0.9435.

So

F(N) ≤ √N + 0.94301 N^{1/4} + O(1)

for all large N. This beats the folder record 0.94325 and Hou–Zhao’s published 0.9435. SHA-256 of the JSON is 341cba5bd8364cd315561d1b89ad3e3ba0c9d5160047781d86c40213b53b02c6.

Three checks that do not share covering code:

./run_all.sh

that is: leftover check of the q1 log, parent nested-loop and this folder’s exact matrix-vector verifier on the q1 certificate (do not regress C<0.94325), then the same two Python checks plus the GMP nested-sum verifier on certs/r11_m48_L6.json with ab < (0.94301)^2.

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