Hartl's maximality conjecture for the universal local system

Let $\breve{\cal{F}}^{wa}_b$ be the weakly admissible period space, let $\breve{\cal{F}}^0_b\subset\breve{\cal{F}}^{wa}_b$ be the intrinsic open $\breve E$-analytic subspace, and let ${\cal{V}}$ be the local system on $\breve{\cal{F}}^0_b$ whose fibers realize the crystalline representations attached to the corresponding filtered isocrystals.

Hartl's local-system maximality conjecture. The space $\breve{\cal{F}}^0_b$ is the largest open $\breve E$-analytic subspace of $\breve{\cal{F}}^{wa}_b$ carrying a local system ${\cal{V}}$ with the properties stated in the theorem.

The theorem in the paper constructs such a local system, while the conjecture asserts that its domain is maximal. Maximality is not proved in general.