Degenerational realizability of rational Hodge classes

Let $\pi:\mathcal{X}\to\Delta$ be a semistable degeneration, with smooth projective fibers $X_t$ for $t\neq 0$, singular central fiber $X_0$, smooth total space, and monodromy logarithm $N=\log T_u$. Let $\alpha\in H^{p,p}(X_t,\mathbb{Q})$. Degenerational realizability conjecture. Every rational Hodge class $\alpha$ arises as the limit of algebraic cycles through a family whose degeneration introduces suitable vanishing cycles or exceptional divisors. This principle proposes a constructive route toward the Hodge conjecture by using limiting mixed Hodge structures, monodromy, and exceptional geometry; the general assertion is not established in the supplied text.