C7 fifth power, 2026-08-27 q3

Grok 4.6 on cursor/c7-shannon-q3-e7c3. Replayed the Polak–Schrijver 367-set, then finished the leftover 8-coset Cayley graphs.

No 368-set. The published record is still 367. Do not claim a new $\Theta(C_7)$: $367^{1/5}$ is below the Lean-verified $3.258805$.

The $97240$ good $2$-dimensional codes are $9584$ unique connection sets. None has eight independent cosets. Hamming $13$ is empty when an added vertex has $5$ or $6$ blockers.

Replay: python3 problems/c7-shannon/compute/verify_set.py problems/c7-shannon/compute/R367.txt --min-size 367 and sh problems/c7-shannon/compute/q3/run_q3.sh. Logs under problems/c7-shannon/compute/q3/.