Hu–Ye multiplicity conjecture for hypermatrices

Let $\mathcal{M}$ be an order $h$ hypermatrix of dimension $n$, and let $\mu$ be an eigenvalue of $\mathcal{M}$. Write $am_{\mathcal{M}}(\mu)$ for its algebraic multiplicity and $gm_{\mathcal{M}}(\mu)$ for its geometric multiplicity. Hu–Ye multiplicity conjecture. One has

$$am_{\mathcal{M}}(\mu) \geq gm_{\mathcal{M}}(\mu)(h-1)^{gm_{\mathcal{M}}(\mu)-1}.$$

This conjecture relates algebraic and geometric multiplicities for eigenvalues of hypermatrices; the source gives no resolution.