An improved lower bound for the Shannon capacity of $C_{11}$

A sequence of explicitly constructed independent sets in strong powers of $C_{11}$, with successive root improvements certified by exact integer comparisons, using cross-powers when dimensions differ. The current bound is $\Theta(C_{11}) \ge 5.295526013632343$, from an independent set in $C_{11}^{\boxtimes 213}$ (R10, 9 September 2026), improving the R3 result of $5.295492477500681$ in dimension 207 that this entry was first listed for, and the Buys-Polak-Zuiddam baseline of $5.295492315784620$. The intermediate steps R5 and R6 and the superseded R9 are recorded on the frontier. The exact capacity remains open, and no upper bound is claimed. The R5, R6, R9 and R10 builds carry disclosed native-evaluation dependencies rather than being kernel-only.

A sequence of explicitly constructed independent sets in strong powers of $C_{11}$, with successive root improvements certified by exact integer comparisons, using cross-powers when dimensions differ. The current bound is $\Theta(C_{11}) \ge 5.295526013632343$, from an independent set in $C_{11}^{\boxtimes 213}$ (R10, 9 September 2026), improving the R3 result of $5.295492477500681$ in dimension 207 that this entry was first listed for, and the Buys-Polak-Zuiddam baseline of $5.295492315784620$. The intermediate steps R5 and R6 and the superseded R9 are recorded on the frontier. The exact capacity remains open, and no upper bound is claimed. The R5, R6, R9 and R10 builds carry disclosed native-evaluation dependencies rather than being kernel-only.