Lan-Sheng-Zuo's conjecture on nilpotent semistable Higgs bundles

Let $k$ be a field of positive characteristic, and let a Higgs bundle on a smooth projective variety over $k$ be nilpotent if its Higgs field is nilpotent, with its exponent defined as the least positive integer for which the corresponding iterated Higgs field vanishes. A Higgs bundle is strongly semistable if it is strongly semistable in the sense of Lan-Sheng-Zuo. Lan-Sheng-Zuo's conjecture. Any nilpotent semistable Higgs bundle of exponent less than the characteristic of the base field is a strongly semistable Higgs bundle. This conjecture seeks to extend the relationship between semistable Higgs bundles and representations to positive characteristic. The source does not provide evidence of a resolution, so its status remains open.