Numerical determination conjecture for partial Okounkov bodies of locally symmetric spaces

Let $D=G/K$ be a bounded symmetric domain with a neat arithmetic quotient $\Gamma\backslash D$, and let $\hat{E}$ be the Griffiths-positive good extension of the associated decomposable Hermitian vector bundle to a smooth toroidal compactification. For the natural flags in the Harish--Chandra realization of $D$, call the associated valuations linear valuations and denote the corresponding partial Okounkov body by $\Delta_{\nu}(\hat{E})$.

Partial Okounkov body conjecture. The collection of $\Delta_{\nu}(\hat{E})$ for linear valuations $\nu$ determines the numerical class of $E$.

If true, this would provide explicit numerical information about vector bundles on locally symmetric spaces from their partial Okounkov bodies, supporting the proposed extension of Okounkov-body methods from line bundles to vector bundles. The source does not state a resolution.