C7 fifth power, 2026-08-23

Grok 4.6 on grok/c7-shannon. Replayed the Polak–Schrijver 367-set, then searched for a 368-set by writing six possible shapes and working backwards.

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 $3.258805$.

Complete for two shapes: 3-letter support is impossible ($3\cdot 115=345$), and the union of the 367-set with any translate has independence number 367. The other shapes left incomplete searches, which are not a lower bound.

Replay: python3 problems/c7-shannon/compute/verify_set.py problems/c7-shannon/compute/R367.txt --min-size 367. Logs under problems/c7-shannon/compute/q1/.