Ross's sub-lattice conjecture for periodic framework rigidity

Let $\tilde{G}(\mathbf{p},\mathbf{L})$ be an infinitesimally rigid periodic framework with periodic graph $(\tilde{G},\varphi)$. Let $\Lambda<\mathbb{Z}^2$ be any sub-lattice, and define $(\tilde{G},\varphi')$ to be the periodic graph obtained by replacing the $\mathbb{Z}^2$-action $\varphi$ with the induced $\Lambda$-action $\varphi'$. Ross's conjecture. Then $\tilde{G}(\mathbf{p},\mathbf{L})$ is an infinitesimally rigid realization of the induced abstract periodic framework on $(\tilde{G},\varphi')$. Informally, this says that a generic rigid periodic framework remains rigid when the periodicity constraint is relaxed to a sub-lattice, enlarging the class of allowed motions. The conjecture concerns whether infinitesimal rigidity is preserved under passage from the original lattice to any sub-lattice; its resolution is not given here.