Holomorphic quantum unique ergodicity for quaternionic Shimura curves

Let $(\boldsymbol{\times}_k)_k$ be a sequence, indexed by sufficiently large even integers $k$, of nonzero cuspidal holomorphic Hecke eigenforms on the quotient $\mathbf{Y}$, and let $\Psi:\mathbf{Y}\to\mathbb{C}$ be bounded and continuous. The measure associated with $\varphi_k$ is

$$\frac{y^k|\varphi_k(z)|^2\,dx\,dy/y^2}{\int_{\mathbf{Y}}y^k|\varphi_k(z)|^2\,dx\,dy/y^2}.$$

Holomorphic mass equidistribution conjecture. For every such $\Psi$,

$$\frac{\int_{\mathbf{Y}}y^k|\varphi_k(z)|^2\Psi(z)\,\frac{dx\,dy}{y^2}}{\int_{\mathbf{Y}}y^k|\varphi_k(z)|^2\,\frac{dx\,dy}{y^2}}\longrightarrow\frac{\int_{\mathbf{Y}}\Psi(z)\,\frac{dx\,dy}{y^2}}{\int_{\mathbf{Y}}\frac{dx\,dy}{y^2}}\qquad (k\to\infty).$$

This is the holomorphic analogue of quantum unique ergodicity for cuspidal Hecke--Laplace eigenfunctions, previously proved in the cited setting by Lindenstrauss and Soundararajan. The source presents this as the main expected equidistribution statement; its resolution is not specified here.