Prompt (q4)

Attack kissing number $\tau_5$ on https://github.com/wustep/maths. Read AGENTS.md, problems/kissing-5d/PROBLEM.md, ATTACK.md, and compute/q3 first. Covering/share/2026-08-16 stay frozen. Do not start a new problem.

On main after q3: unrestricted interval still $40\le\tau_5\le 44$. No exact dual below 44 on $[-1,1/2]$. No 41-point code. Certified: the leftover 1480-point $(1/4)\mathbb Z^5$ graph has no 41-clique that uses $n_1\ge 33$ $D_5$-type points. Unfinished leftovers: the $n_1\le 32$ slice of that graph, and the 36-clique in the 355-point $T^5$ remainder.

This is q4. Aim for a real jump: either exclude 41–44 unrestricted, or produce a 41-code.

Targets: finish the $n_1\le 32$ slice; finish the $T^5$ 36-clique; in parallel hunt an exact unrestricted dual $<44$ or a certified 41-code. Do not claim $\tau_5=40$. Residue if the interval does not move.