Mulmuley's #P conjecture for Kronecker coefficients

For partitions $\lambda$, $\mu$, and $\nu$ of the same integer, let $g(\lambda,\mu,\nu)$ denote the Kronecker coefficient, and let ${\textsc{Kron}}$ be the problem of computing this coefficient from the binary-encoded input. Mulmuley's conjecture.

$${\textsc{Kron}}\in {\rm{\textsf{\#P}}}.$$

The paper has the unconditional upper bound ${\textsc{Kron}}\in {\rm{\textsf{GapP}}}$; the conjecture asks for the stronger counting-class upper bound.