Positive matching decomposition conjecture for Cartesian products of cycles

Let $C_m$ and $C_n$ be cycles with $m,n\geq3$, and let $\mathrm{pmd}(G)$ denote the positive matching decomposition number. Positive matching decomposition conjecture for Cartesian products of cycles.

$$\mathrm{pmd}(C_m\square C_n)=6$$

for all $m,n\geq3$ such that $m+n$ is even, or such that $(m,n)\in\{(3,4),(3,6),(5,6)\}$. The supplied text presents this exact-value assertion after an analysis of positive matchings in the relevant Cartesian products; no resolution beyond that analysis is provided.