Continue the already-open kissing-5d campaign on wustep/maths. Do not mint a new problem folder. Covering and share/2026-08-16 stay frozen.

Published interval is still 40 ≤ τ₅ ≤ 44 (Tao C₂₉, Cohn table, Mittelmann–Vallentin s₁₄(5) ≈ 44.999, Cohn–Rajagopal). q1–q6 are on main. q6 (PR #101, merged) is residue: no 41-set and no unrestricted dual below 44. Restricted fact from q6: there is no leftover 41-set in the 1480-point (1/4)ℤ⁵ graph whose missed-root union sits in four D₅ coordinate-stars. So any remaining leftover 41-set has star-cover at least 5.

q6 leftovers to finish in compute/q7/:

1. Global leftover SAT on |U|=19 with star-cover ≥ 5 (Cadical/Kissat; store DRAT if unsat, or a 41-set if sat).
2. Five-star leftover-tight B&B / SAT (pools 528–625 extras). Store certificates.
3. Global leftover-tight extras B&B past the q6 200M-node cutoff, or a better prune.
4. Unrestricted dual below 44.

Dent = verified finite improvement of the published interval. Residue = incomplete search or a finite-graph fact that does not move 40–44. Do not claim τ₅ = 40. Do not treat extras ω as an unrestricted bound.