Output-sensitive classical algorithm conjecture for Littlewood–Richardson coefficients

Let $\lambda$, $mu$, and $nu$ be partitions such that $|\lambda|=|mu|+|nu|$. Assume $c^{\lambda}_{mu,nu}>0$. Output-sensitive Littlewood–Richardson conjecture. There exists a classical algorithm running in time

$$O\left(c^{\lambda}_{\mu\nu}\operatorname{poly}(n)\right)$$

that computes $c^{\lambda}_{\mu\nu}$. This is stated as a stronger conjecture because $c^{\lambda}_{\mu\nu}\leq f^{\lambda}/(f^{\mu}f^{\nu})$; it is known in restricted settings, including fixed-length cases, but remains open in general.