Bost's tensor-product minimal-height conjecture for rigid adelic spaces

Let $E$ and $F$ be rigid analytic spaces over a number field $K$, and let $H_{\min}(E)$ denote the minimal height arising from the slope filtration of $E$. Bost's conjecture. The minimal height of the tensor product satisfies

$$H_{\min}(E\otimes F)=H_{\min}(E)H_{\min}(F).$$

The conjecture concerns the elusive behavior of slope filtrations under tensor products. It is known when one factor is multiplicity-free as a $K[G]$-module, while the unrestricted statement remains open.