The Sato–Tate equidistribution conjecture

Under the algebraic Sato–Tate setup, let $\operatorname{ST}_K(V,\psi)$ be the associated compact Sato–Tate group. For a prime $v$ of $K$, let $s_v$ be the semisimple part of the normalized Frobenius element, viewed in $\operatorname{ST}_K(V,\psi)$. Sato–Tate conjecture. The conjugacy classes $\operatorname{conj}(s_v)$ in $\operatorname{ST}_K(V,\psi)$ are equidistributed in $\operatorname{conj}(\operatorname{ST}_K(V,\psi))$ with respect to the measure induced by Haar measure. This is the expected Frobenius equidistribution statement and is open in the stated generality.