The discrete distributed spectral pair classification conjecture

Let $({\mathcal A},{\mathcal B})$ be a distributed spectral pair in $\{0,1,\ldots,M-1\}$. A distributed spectral pair classification conjecture. The pair $({\mathcal A},{\mathcal B})$ is either a spectral pair in $\mathbb Z_M$ or a spectral pair in $\mathbb Z_{M^2}$. The preceding classification suggests this conjecture; whether every distributed spectral pair has one of these two finite-group spectral structures remains open.