Analytic and microscopic stability threshold conjecture

Let $(X,\Delta)$ be a log Fano manifold with vanishing Futaki character. Let $\gamma(X,\Delta)^{\mathcal{G}}$ denote the reduced Gibbs stability threshold and let $\delta^{\mathrm{A}}(X,\Delta)^{\mathcal{G}}$ denote the reduced analytic stability threshold. Reduced threshold conjecture. The invariants $\gamma(X,\Delta)^{\mathcal{G}}$ and $\delta^{\mathrm{A}}(X,\Delta)^{\mathcal{G}}$ coincide. This extends the previously cited conjectural equality between the unreduced analytic and Gibbs thresholds to the symmetry-reduced setting; the source provides no resolution.