Nonnegativity conjecture for the BCOV coefficient of maximally unipotent Calabi–Yau threefold degenerations

Let $f \colon X \to \mathbb D$ be a projective degeneration of 3-dimensional Calabi–Yau varieties with maximally unipotent monodromy, and let $\kappa_f$ denote its BCOV logarithmic coefficient. Nonnegativity conjecture. One has

$$\kappa_f \geq 0.$$

This is motivated by mirror symmetry and the Bogomolov–Gieseker inequality. It is known for abelian threefolds and for the mirror quintic family, while the general case remains open.