Odd-width square-lattice strip conjecture for the critical crossing

Let $q_0(L)$ denote the maximum real value in the limiting curve for a square-lattice strip of width $L$ with fully periodic boundary conditions. Odd-width square-lattice conjecture. For widths $L=2p+1$ with $p\geq 1$, one has $q_0(L)=3$. This identifies an infinite sequence of strip widths whose crossing value equals the expected square-lattice critical value $q_{\rm c}(\mathrm{sq})=3$; the source reports exact values through width $11$, but gives no resolution of the conjecture.