Two-step degeneration conjecture for Kähler-Ricci flows at finite-time singularities

Let $\pi:X\rightarrow Y$ be the Fano fibration at a finite singular time $T<\infty$ of a compact Kähler-Ricci flow $\omega(t)$. For $p\in Y$ and $q\in\pi^{-1}(p)$, a tangent flow is a rescaled limiting Kähler-Ricci flow at $q$.

Finite-time two-step degeneration conjecture. For any $p\in Y$ and $q\in\pi^{-1}(p)$:

1. The Kähler-Ricci flow $\omega(t)$ naturally induces a weighted-volume-minimizing, hence K-semistable, valuation on $(\pi:X\rightarrow Y,p)$.
2. The tangent flow of $\omega(t)$ at $q$ is unique and is given by the Kähler-Ricci shrinker $(\widehat\pi:\mathcal S\rightarrow\mathcal C,\xi)$ canonically associated with the Fano fibration germ $(\pi:X\rightarrow Y,p)$ via the weighted-volume minimization conjecture and the K-polystability criterion for Kähler-Ricci shrinkers.

This conjecture seeks an algebraic description and uniqueness theorem for tangent flows at finite-time singularities. The source presents it as a motivation from the known two-step degeneration picture in the Fano case; the general assertion remains open.