Dimension-dependent boundedness conjecture for torus exceptional degree

Let $\mathcal{T}(X,B)$ denote the torus exceptional degree of a log Calabi--Yau pair $(X,B)$. Torus exceptional degree boundedness conjecture. For every positive integer $n$, there exists a positive integer $t_n$ depending only on $n$ such that, for every log Calabi--Yau pair $(X,B)$ of dimension $n$, index one, and birational complexity zero,

$$\mathcal{T}(X,B)\leq t_n.$$

The conjecture extends the proved surface bound $\mathcal{T}(X,B)\leq 9$ to every fixed dimension. The paper also notes that the total torus exceptional degree can be unbounded even for surfaces, so the asserted uniform bound concerns $\mathcal{T}$ itself.