Mulmuley–Sohoni occurrence-obstruction conjecture

For $n>m$, let $Z_{n,m}$ be the orbit closure of the padded permanent $X_{11}^{n-m}\mathrm{per}_m$ in $\mathsf{Sym}^n\mathbb{C}^{n^2}$, and let ${{\mathcal{D}}et}_n$ be the orbit closure of the determinant. A partition $\lambda$ occurs in a coordinate ring when the corresponding irreducible polynomial representation occurs in that coordinate ring. Mulmuley–Sohoni's occurrence-obstruction conjecture. For every $c\in\mathbb{N}_{\ge 1}$, for infinitely many $m$, there exists a partition $\lambda$ occurring in $\mathbb{C}[Z_{m^c,m}]$ but not in \mathbb{C}[{{\mathcal{D}}et_{m^c}]. The existence of such a partition would obstruct the containment $Z_{m^c,m}\subseteq{{\mathcal{D}}et}_{m^c}$ and hence yield a lower bound for the determinantal complexity of the permanent. The conjecture was proposed as a strategy for proving the border determinantal complexity conjecture, but the source explicitly states that it is false.