Leftover n1 ≤ 21, star-cover ≥ 4

Replay:

sh compute/q6/run_all.sh

The published range is still $40\le\tau_5\le 44$ . After the $T^5$ remainder 36-clique DRAT and the 3-star leftover emptiness, this folder records the leftover $n_1\le 21$ slice of the 1480-point $(1/4)\mathbb Z^5$ graph and a parallel hunt for an exact unrestricted dual below 44.

C leftover-tight branch-and-bound empties every 4-star host (four_star_extras.json). A covering Python leftover-tight sample matches (replay_four_star.json). A remaining 41-set in that graph has star-cover at least 5. Global leftover SAT on that slice did not finish. No unrestricted dual below 44.

Script	What it does
`four_star_color.py`	greedy colouring of extras in each 4-star pool
`four_star_extras.c` / `.py`	leftover-tight extras B&B / SAT on each 4-star pool
`replay_four_star.py`	independent leftover-tight Python sample
`two_axis_extras.py`	the ten $k=28$ two-axis pools (four-seeds only)
`star_cover_min.py`	min $
`five_star_color.py` / `five_star_census.py`	5-star colouring and part-count
`leftover_sat.py`	global SAT, $n_1\le 21$ , star-cover at least 5
`leftover_global.c`	leftover-tight extras B&B with a 4-star grow-prune
`dual_more.py`	further exact unrestricted dual attempts
`verify.py`	replay any claimed 41-set and dual JSON

A numerical SDP that does not become an exact positivity certificate is an incomplete search. The unrestricted range remains $40\le\tau_5\le 44$ unless a verifier-plus-certificate pair here says otherwise.