q2 — unrestricted dual hunt and exact 41-point searches

Replay:

sh compute/q2/run_all.sh

The published range is still $40\le\tau_5\le 44$ . This folder hunts either an exact Gegenbauer dual that is nonpositive on the whole interval $[-1,1/2]$ and has value $<44$ , or an explicit 41-point spherical code.

Script	What it does
`unrestricted_dual.py`	exact Delsarte duals forced $\le 0$ on $[-1,1/2]$
`dump_t5_pool.py`	Szöllősi $T^5$ pool (360 vectors; 5 of them universal)
`clique41.c`	exact 41-clique search on a dumped adjacency file
`sphere_clique.c`	kissing graph on $(1/d)\mathbb Z^5\cap\{\lvert x\rvert^2=2\}$
`layer_replace.py`	other hyperplane layer-swaps of $D_5$ and $L_5$
`verify.py`	replay any dual JSON under `certs/` and any claimed 41-set
`t5_clique.json`	no 41-clique in the 355-point remainder (607171 nodes)
`sphere_d2.json`	no 41-clique on the 200-point half-integer sphere
`q5cap_clique.json`	no 41-clique in the 320-point $Q_5$ -cap orbit
`t5_36_residue.json`	36-clique hunt that would give a 41-set; incomplete
`sphere_d4.json`	$(1/4)\mathbb Z^5$ 41-search; incomplete

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.