Observational_Collapse_Invariants_in_Modular_Dynamical_Systems

We introduce the Observational Collapse Invariant (OCI), a structural invariant for discrete dynamical systems under modular observation. Unlike classical invariants such as entropy or spectral data, OCI captures the structure of equivalence classes induced by observational collapse.

We establish a kernel classification theorem for linear recurrence systems under modular projection, showing that OCI characterizes observational equivalence classes. We further prove that OCI is independent from entropy and spectral invariants, providing a complementary perspective on dynamical complexity.

Computational evidence on classical sequences, including Fibonacci, Padovan, and Tribonacci systems modulo 9, illustrates that OCI distinguishes systems that are indistinguishable via entropy or spectral data. A categorical formulation via an observation functor is also introduced, framing OCI as a structural invariant of the kernel of the observation process.

These results suggest that observational collapse provides a natural and robust framework for analyzing dynamical systems under finite-resolution measurements.