The pointwise base-point-freeness conjecture for adjoint bundles

Let $Y$ be a smooth projective variety, let $y\in Y$ be a point, and let $L$ be a nef and big line bundle on $Y$. Assume that for every irreducible subvariety $Z$ with $y\in Z\subsetneqq Y$,

$$(L^{\dim Z}\mathbin{.}Z)\geqslant(\dim Y)^{\dim Z},$$

and that

$$(L^{\dim Y})>(\dim Y)^{\dim Y}.$$

The pointwise base-point-freeness conjecture. The adjoint line bundle $K_Y+L$ is base point free at $y$. The source presents this as a known generalization of Fujita's base point freeness conjecture; no resolution status for this precise formulation is supplied in the excerpt.