The soft-core Gibbs-to-non-Gibbs transition-time conjecture

Let $\beta$ be sufficiently large, let $\lambda$ be the soft-core parameter, and let $\mu\in\mathcal{G}(\gamma^{sc}_{\beta,\lambda,0})$. Let $t_{NG}(\beta)$ denote the exit time from the Gibbsian region for the Ising model with Hamiltonian

$$-\beta\sum_{i\sim j}1_{\omega_i\omega_j=-1}.$$

Soft-core transition-time conjecture. There exists a time $t_{NG}(\beta)$ such that the time-evolved measure is Gibbs for all $t<t_{NG}(\beta)$ and non-Gibbs for all $t>t_{NG}(\beta)$. The conjecture predicts a sharp Gibbs-to-non-Gibbs transition governed by the corresponding Ising-model exit time; the source gives no resolution.