The conjecture on specialization of 1-cycles

Let $X$ be as in the cited theorem of Kollár--Tian, with generic fiber $X_K$ and integer $n$ as in that theorem. Write $C\!H_2(X)$ and $C\!H_1(X_K)$ for the relevant Chow groups, and $A_1(X_K)$ for the group of algebraically trivial 1-cycles. The specialization conjecture for 1-cycles. The natural homomorphisms

$$C\!H_2(X)/n\to C\!H_1(X_K)/n\to A_1(X_K)/n$$

are isomorphisms.

This concerns specialization and algebraic equivalence of 1-cycles in the degeneration considered by the paper. The source gives no resolution status for the assertion.