The non-nef locus and restricted base locus conjecture

Let $X$ be a normal projective variety over an algebraically closed field and let $D$ be an ${\mathbb{R}}$-Cartier ${\mathbb{R}}$-divisor on $X$. The non-nef locus ${\mathrm{NNef}}(D)$ is defined using numerical vanishing orders along divisorial valuations, while the restricted base locus ${\bf{B}}_-(D)$ is the lower approximation of the stable base locus obtained by perturbing $D$ by small ample divisors. Non-nef locus conjecture. One has

$${\mathrm{NNef}}(D)={\bf{B}}_-(D).$$

Both loci characterize nefness by their emptiness. The conjecture asserts that these two apparently different descriptions agree; the source presents it as a conjecture and gives a partial answer using stability of test ideals in positive characteristic.