Calderón sum formula conjecture for discrete wavelet frames

Let $A$ be an invertible matrix, let $\Gamma$ be a lattice in $\mathbb{R}^n$, let $B=A^T$, and let $\Psi=\\{\psi_1,\dots,\psi_L\\}$ generate the wavelet system $\mathcal{A}(\Psi,A,\Gamma)$. A wavelet system is formed from the dilates and lattice translates of the functions in $\Psi$. Calderón sum formula conjecture. If $\mathcal{A}(\Psi,A,\Gamma)$ is an orthonormal basis, or more generally a Parseval frame, for $L^2(\mathbb{R}^n)$, then

$$\sum_{l=1}^L \sum_{j\in \mathbb{Z}} |\hat\psi_l(B^{-j}\xi)|^2=1$$

for almost every $\xi\in\mathbb{R}^n$. The formula is known when the lattice counting estimate holds, and hence in one dimension, but remains open in general; it is also known for continuous wavelet systems. In particular, it is not known whether the discrete orthonormal or Parseval-frame hypothesis alone forces $|\det A|\ne 1$.