Time Crystals--Null--Modular $\mathbb{Z

Construct theoretical chain unifying discrete/continuous time crystals with Null--Modular Z_2 holonomy, bulk-integral Z_2--BF choice, and relative cohomology invariant. Closed system side, provide rigidity and stability of prethermal discrete time crystals in exponentially long time windows via high-frequency Floquet--Magnus and Lieb--Robinson constraints; under strong disorder provide necessary and sufficient structure for \pi spectral pairing and eigenstate time crystalline order. Open system