Continue SuperGrok’s existing campaign on the five-dimensional kissing number in https://github.com/wustep/maths. Start from main. Open a PR.

Folder: problems/kissing-5d/ Read AGENTS.md, PROBLEM.md, ATTACK.md, WALKTHROUGH.md, and compute/ first. New compute/qN/ for this run. Update ATTACK.md. Commit often.

Current record: 40 ≤ τ5 ≤ 44. Four 40-point codes D5, L5, Q5, R5 already replayed. Restricted Delsarte: TD5 bound 42, TL5 bound 239925/5456 < 44. Mittelmann–Vallentin published upper bound is 44. D5 is maximal. Q5 equator is not a 24-cell minus two pairs. Numerical SDP without an exact positivity certificate is residue.

Outcome that counts: an exact dual certificate excluding some k in {41,42,43,44}, or a new exact spherical code of size >40 on S^4. Do not claim τ5 = 40.

Public README: ordinary English only. Do not touch covering.