Main conjecture on recovering the defect from its associated measure

Let $H\in C_N(s)$, where $s\in\mathbb N$ is chosen minimally, and let $\mu$ be the probability measure associated to the random variable counting the entries equal to $1$ after multiplying the rows and columns of $H$ by elements of $\mathbb Z_s$.

Main conjecture. For $H\in C_N(s)$, with $s\in\mathbb N$ chosen to be minimal, $d(H)$ can be recaptured from the knowledge of the associated measure $\mu$.

This is the source's conceptual reformulation and generalization of the preceding defect bounds in the Butson case. It does not specify a reconstruction procedure, and no resolution is supplied.