Gabber–Abe conjecture on Ψ-factorizability of Ψ-good pairs

Let $f$ be a morphism and $K$ a sheaf. A pair $(f,K)$ is Ψ-good if it satisfies the Ψ-goodness condition used for nearby cycles. For a composition of specializations $s\rightarrow t\rightarrow u$, let $R(\Psi_f)_u^t K$ denote the corresponding nearby-cycle complex.

Gabber–Abe conjecture. If $(f,K)$ is Ψ-good, then $(f,R(\Psi_f)_u^tK)$ is Ψ-good and $(f,K)$ is Ψ-factorizable.

This result was announced by Gabber and Abe as a theorem in the étale-sheaf setting, but the source presents the statement here without a supplied resolution status or a proof in the stated generality.