can be applied. Takens' theorem generically proves that the state space of a dynamical system can be reconstructed from a single observed time series of the system, . This reconstructed or shadow manifold is diffeomorphic to the true manifold, , preserving instrinsic state space properties of in .

Convergent Cross Mapping (CCM) leverages a corollary to the Generalized Takens Theorem that it should be possible to cross predict or cross map between variables observed