Maximal-period invariants conjecture for irreducible quantum processes

Let $\opL$ be an irreducible object with associated set $\Lambda_\opL$, preorder $\preceq$, period $N_\alpha$, and invariant $\varsigma_\alpha$ for each $\alpha\in\Lambda_\opL$. Maximal-period invariants conjecture. If $\alpha,\gamma\in\Lambda_\opL$ are maximal with respect to $\preceq$, then

$$N_\alpha=N_\gamma\quad\text{and}\quad\varsigma_\alpha=\varsigma_\gamma.$$

The conjecture is motivated by an ordering intended to capture the periodicity encoded by $\alpha$ and $\gamma$. The supplied text says it is unproved, although it notes that it holds when $\GammaGroup$ is torsion.