Odaka's product behavior conjecture for minimally non-collapsing limits

Let $(\mathcal X^*,\mathcal L^*)\to\Delta^*$ be a degeneration satisfying the paper's special maximal-degeneration expectation, and let $(S,M)$ be a fixed pointed polarized $m$-dimensional Calabi–Yau variety with point $s'$. Consider the product degeneration with fibers $\mathcal X_t\times S$ and polarization $p_1^*\mathcal L\otimes p_2^*M$. Product behavior conjecture for minimally non-collapsing limits. The minimal non-collapsing limit of the fiber Ricci-flat Kähler metrics is isometric to the metric product of the minimal non-collapsing pointed Gromov–Hausdorff limit of $\mathcal X_t$ at $s(t)$ and the metric tangent cone of $S$ at $s'$. This expectation is proposed as a counterexample to extending the preceding special-degeneration expectation to general products, and is said to be easily verified for degenerating polarized abelian varieties; the source gives no resolution.