Conditional periodic equidistribution conjecture for tracial states

Let $C^*(\mathbb{Z}[1/6])$ be regarded as a subalgebra of $C^*(\mathfrak{F}_{2,3})$, let $\operatorname{TSt}(C^*(\mathfrak{F}_{2,3}))$ denote the tracial states, call a state conditionally finite-dimensional when the image of $C^*(\mathbb{Z}[1/6])$ in its GNS representation has finite dimension, let $\operatorname{cndm}(\Phi)$ be that dimension, and let $\Delta$ be the distinguished state from the source. Conditional periodic equidistribution conjecture. If $(\Phi_n)_{n\in\mathbb{N}}$ is a sequence of extreme conditionally finite-dimensional elements of $\operatorname{TSt}(C^*(\mathfrak{F}_{2,3}))$ with $\lim_{n\to\infty}\operatorname{cndm}(\Phi_n)=\infty$, then $(\Phi_n)$ converges pointwise to $\Delta$. The source gives no evidence of resolution.