This paper develops a multivariate generalization of derivative-order geometry. It introduces lattice cocycles and closure ideals to describe the multi-dimensional flow of derivative-order ladders. The work establishes fiberwise collapse laws and derives anisotropic fingerprints that recover the entire multivariate packet from finite jets. These results show that lattice cocycles and closure identities lead to exact fiberwise collapse and anisotropic recovery across variables.
Mohammad Abu-Ghuwaleh (Tue,) studied this question.