Compute — five-dimensional kissing number

Replay (creates .venv on first run):

sh compute/run_all.sh

Independent certificate check only:

compute/.venv/bin/python compute/verify_certificates.py

Script	What it certifies
`verify_configs.py`	$D_5,L_5,Q_5,R_5$ are 40-point kissing codes matching Cohn–Rajagopal Table 2.1
`extend_d5.py`	$D_5$ admits no 41st point ( $4/5>1/2$ )
`levenshtein.py`	$L_5(5,1/2)=48$
`d4_equator.py`	Rankin $A(4,0)\le 8$ ; 24-cell holes have independence number 8
`q5_extend.py`	no equatorial 41st point on $Q_5$ ; $A_4\not\subset D_4$
`certs/restricted_delsarte.json`	exact Gegenbauer duals for $T_{D_5}$ (bound 42) and $T_{L_5}$ (bound $239925/5456$ )
`verify_certificates.py`	replays those duals from the recurrence, no other imports
`integer_d5.py`	integer distance distributions for $T_{D_5}$ : 42, 43, 44 empty; 41 only with 20 antipodes
`exact_duals.py`	interpolation that found the duals
`q1/polar_vertices.py`	polars of $D_5,L_5,Q_5,R_5$ have $\max\\|x\\|^2=5/4<2$
`q1/integer_q5_44.c`	integer $T_{Q_5}$ slice empty at $N=44$

The unrestricted range remains $40\le\tau_5\le 44$ .

27 August continuation lives in q1/ (polar maximality, $T_{Q_5}$ integer 44), q2/ (unrestricted dual hunt and exact 41-point searches), q3/ (leftover $(1/4)\mathbb Z^5$ / $T^5$ 36-clique handles, larger exact pools), and q4/ (leftover finite graphs, exact Bachoc–Vallentin matrices over the rationals, and a parallel dual / 41-code hunt). The unrestricted dual hunt is q4/dual_exact.py; nothing certified below 44.

Later search: sh compute/q4/run_all.sh. q5 leftover slices: sh compute/q5/run_all.sh. The 355-point $T^5$ remainder has no 36-clique (native CaDiCaL DRAT, drat-trim verified). The $n_1\le 21$ slice of the 1480-graph is unfinished after four-star leftover emptiness (sh compute/q6/run_all.sh). Later leftover search with star-cover at least 5 lives in q7/ (sh compute/q7/run_all.sh): type- $(2,1)$ and type- $(1,3)$ five-star leftover hosts are empty (native CaDiCaL DRAT verified). The remaining type- $(0,5)$ hosts and the global $|U|=19$ leftover SAT live in q8/ (sh compute/q8/run_all.sh); those SAT hunts did not finish (no stored verified DRAT). The unrestricted range remains $40\le\tau_5\le 44$ .