q4 — leftover (1/4)Z^5 slice and T^5 36-clique

Replay:

sh compute/q4/run_all.sh

The published range is still $40\le\tau_5\le 44$ . This folder records the leftover finite graphs from the previous campaign and a parallel hunt for an exact unrestricted dual below 44 or an explicit 41-point code. Neither endpoint moved.

Script	What it does
`analyze_stars.py`	the ten octads are the $D_5$ coordinate-stars
`n1_le32.c` / `n1_check.py`	complete $n_1=32$ slice (C + Python)
`n1_complete.c`	seed-union BFS; $k\le 12$ stored in `n1_complete_k12.json`
`n1_dfs.c`	hash-free canonical DFS; $k\le 18$ in `n1_dfs_k18.json`
`verify_n1.rs`	independent star pools, $\omega=8$
`t5_omega.py`	35-colour / SAT 36-clique of the $T^5$ remainder
`t5_share.c`	exact high-share 36-cliques against published 35s (24–30 empty)
`n1_ilp.py`	star-free seed count, HiGHS; k=4..7 empty, k≥8 cutoff
`bv.py` / `dual_exact.py`	exact $S_k^5$ and unrestricted dual hunt
`construct41.py`	algebraic 41-point ansätze outside the leftover graphs
`verify.py`	replay colourings, 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.