Divisorial polystability threshold conjecture

Let $(X,\Delta)$ be a log Fano manifold with vanishing Futaki character. Define the divisorial polystability threshold $\delta(X,\Delta)_{\mathrm{ps}}$ as the infimum of the ratio of averaged log discrepancies to non-Archimedean pluricomplex energy over semistable finite-support probability measures on divisorial valuations. Let $\gamma^{(N)}(X,\Delta)^{\mathcal{G}}$ and $\delta^{\mathrm{A}}(X,\Delta)^{\mathcal{G}}$ be the reduced Gibbs and analytic stability thresholds. Divisorial polystability threshold conjecture.

$$(X,\Delta)\text{ is K-polystable}\iff\delta(X,\Delta)_{\mathrm{ps}}>1,$$ $$\lim_{N\to\infty}\gamma^{(N)}(X,\Delta)^{\mathcal{G}}=\delta(X,\Delta)_{\mathrm{ps}},$$

and

$$\delta^{\mathrm{A}}(X,\Delta)^{\mathcal{G}}=\delta(X,\Delta)_{\mathrm{ps}}.$$

When the symmetry group is trivial, the proposed threshold agrees with the standard stability threshold; its validity would imply the earlier log-canonical-threshold stability conjecture. The source provides no resolution.