Linear-bound multiset reconstruction conjecture for tableau minors

Let $k\geq 1$ and let $T\in\operatorname{YT}(n)$, where $n\geq k+4$. Here $\operatorname{mM}_k(T)$ denotes the multiset of $k$-minors of the standard Young tableau $T$. Multiset reconstruction conjecture. The multiset $\operatorname{mM}_k(T)$ determines $T$. This proposed linear bound is supported by computer verification for $k\leq 5$, and concerns reconstructibility from multisets of $k$-minors.