Triangular-lattice q0 convergence conjecture

Let $q_0(L)$ denote the crossing for a triangular-lattice strip of width $L$ with fully periodic boundary conditions, and let $q_{\rm B}\simeq3.8196717312$ be the value where Baxter's analytically determined bulk free-energy eigenvalues become equimodular. Triangular-lattice $q_0$ convergence conjecture. For widths $L=3p$, the limit

$$q_0(\mathrm{tri})=\lim_{p\to\infty}q_0(L)$$

exists and equals $q_{\rm B}$; moreover, the sequence $q_0(3p)$ is monotonically increasing in $p$. This is supported by numerical agreement with Baxter's value, but remains unproved in the source.