Output-sensitive classical algorithm conjecture for Kronecker coefficients

Let $\lambda$, $mu$, and $nu$ be partitions of $n$, and suppose that $f^{\lambda}\geq f^{mu}\geq f^{nu}$. Kronecker algorithm conjecture. The Kronecker coefficient $g(\lambda,mu,nu)$ can be computed by a classical algorithm in time

$$O\left(\frac{f^{\mu}f^{\nu}}{f^{\lambda}}\operatorname{poly}(n)\right).$$

The conjecture is posed as the opposite of the paper’s refuted expectation that no analogous classical algorithm exists for Kronecker coefficients. The paper proves efficient classical algorithms in substantial regimes, but the conjecture remains open in full generality.