Fibonacci dimension conjecture for multiple t-values

Let $\mathcal T$ be the $\mathbb Q$-subalgebra of $\mathbb R$ generated by $1$ and the multiple $t$-values, and let $\mathcal T_n$ be the subspace of $\mathcal T$ spanned by all multiple $t$-values of weight $n$. Let $F_n$ denote the $n$th Fibonacci number. Fibonacci dimension conjecture. For every integer $n\geq 2$,

$$\operatorname{dim}\mathcal T_n=F_n.$$

This predicts the exact dimensions of the weight-graded pieces of the algebra of multiple $t$-values. The corresponding dimension statement for multiple zeta values is described in the source as generally believed but not yet proved, while the multiple $t$-value dimension formula remains conjectural.