The BCOV slope formula for semi-stable Calabi–Yau degenerations

Let $f\colon \mathcal{X}\to S$ be a relatively minimal family, let $s_i\in S$ be a point such that the singular fiber $f^{-1}(s_i)$ is semi-stable, let $a_i$ denote its BCOV invariant slope, and let $\chi_2^i$ and $I_2^i$ be the associated topological and intersection data. The BCOV slope conjecture. If $f$ is relatively minimal and the singular fiber $f^{-1}(s_i)$ is semi-stable, then

$$12a_i=\chi_2^i-3I_2^i.$$

This conjecture predicts that the BCOV invariant slope is determined by topological and intersection-theoretic data of the singular fiber; the surrounding discussion notes that the corresponding summed identity is known, while the asserted individual formula is proposed by comparison.