Finite Cores Exhaustion and the Failure of Strict Sequential-Pressure Approximation in Coded Shifts

Let $X=X(\mathcal{G})$ be a coded shift whose generating set uniquely represents its concatenation set. We prove that, for every continuous potential $φ$, the pressures of the finite-generator subshifts (the finite cores) converge to the sequential pressure $P_{\mathrm{seq}}(φ,\mathcal{G})$, the sup