Non-étale-trivializable reduction conjecture

In the variation setup, let $E$ be a numerically flat vector bundle on a smooth complex projective variety, with model $\mathcal E$ over $S$. Let $\Sigma^{\mathrm{net}}$ be the set of closed points $s\in S$ for which $\mathcal E_s$ is not étale trivializable. Non-étale-trivializable reduction conjecture. If $E$ itself is not étale trivializable, then $\Sigma^{\mathrm{net}}$ is infinite. In the ordinary-bundle examples discussed in the source, this is reformulated as infinitude of reductions with nontrivial nilpotent Frobenius action on $H^1(\mathcal O_{\mathcal X_s})$.