Incidentally periodic rigidity conjecture

A framework $(\langle G,m\rangle,p)$ consists of a periodic graph with placement, and $(\widetilde G,\widetilde p)$ denotes its associated infinite incidentally periodic framework. The flexible torus allows the torus lattice to vary, whereas an incidentally periodic framework is considered with respect to all infinitesimal motions, not only those preserving periodicity.

Incidentally periodic rigidity conjecture. If $(\langle G,m\rangle,p)$ is infinitesimally rigid on the flexible torus, then it is infinitesimally rigid as an incidentally periodic infinite framework $(\widetilde G,\widetilde p)$.

This conjecture asks whether rigidity under periodicity-preserving motions on the flexible torus rules out all infinitesimal flexes of the corresponding infinite framework, including flexes that do not preserve periodicity. The source presents this as an open question.