The conjecture that wild Schur algebras in the exceptional cases are τ-tilting finite

Let $S(n,r)$ be a wild Schur algebra over the field $\mathbb{F}$ of characteristic $p$, and let $(\star)$ denote the exceptional parameter cases

$$(\star)\quad\left\{\begin{aligned} p&=2,n=2, r=8, 17, 19; \\ p&=2,n=3, r=4;\\ p&=2,n\geqslant 5,r=5; \\ p&\geqslant 5, n=2,p^2\leqslant r\leqslant p^2+p-1. \end{aligned}\right.$$

Exceptional wild Schur algebra conjecture. All wild Schur algebras contained in $(\star)$ are $\tau$-tilting finite.

The conjecture concerns precisely the cases not determined by the paper's classification of wild Schur algebras. It is motivated by the absence of the identified $\tau$-tilting infinite quivers as subquivers, but the cases remain unresolved.