Finiteness criterion for affinoid Liu algebras

Let $k$ be a stable non-archimedean field and let $\calA$ be a Liu algebra over $k$. Write $\tilde{\calA}_{\mathrm{gr}}$ and $\tilde{k}_{\mathrm{gr}}$ for the associated graded reductions, and $\tilde{\calA}$ and $\tilde{k}$ for the reductions. If $\mathcal{M}(\calA)$ is strictly $k$-analytic, impose this as an additional condition.

Finiteness criterion for affinoid Liu algebras. The following assertions should hold: (i) $\calA$ is affinoid if and only if $\tilde{\calA}_{\mathrm{gr}}$ is a finitely generated $\tilde{k}_{\mathrm{gr}}$-algebra; (ii) if $\mathcal{M}(\calA)$ is strictly $k$-analytic, then $\calA$ is affinoid if and only if $\tilde{\calA}$ is finitely generated over $\tilde{k}$.

This would give a finiteness-of-reduction criterion for recognizing when a Liu algebra is affinoid. The source presents it as plausible rather than established, so its status remains open.