Spectrality and equi-positivity for Hadamard triple towers

Let $\mu(N_n,B_n)$ be the Cantor–Moran measure associated with a sequence $\{(N_n,B_n,L_n)\}$ forming a Hadamard triple tower, and let $\nu_{>n}$ denote the pulled-back tail measures. Assume that $\gcd(B_n)=1$ for all $n$ and that $\mu(N_n,B_n)$ has compact support. Spectrality and equi-positivity conjecture. The measure $\mu(N_n,B_n)$ always has the no-overlap condition, and it is a spectral measure if and only if $\{\nu_{>n}\}$ has an equi-positive subsequence. The conjecture proposes a criterion connecting the no-overlap property and spectrality of Cantor–Moran measures with equi-positivity of their tail measures; the supplied text gives no resolution or further known cases.