Heterogeneous Composite Discrete Dynamical Framework

This technical report presents a five-layer architecture for deterministic discrete evolution, operator composition, composite dynamics, stability structures, and compatible realizations. Version 2.0 integrates revised mathematical proofs and reproducible examples, distinguishing declared structural components from conclusions that require additional assumptions. The framework’s three foundation conditions concern unique evolution, a supplied shared representation, and reconstruction into the legal evolution domain. Their irredundancy is established relative to these declared capabilities. Further results establish finite composition closure, conditional Lipschitz bounds, invariant-set preservation, reconstruction-error bounds, and transitivity of commuting maps. The accompanying package contains twelve exact synthetic checks, including exhaustive verification of 27 finite self-maps, 729 ordered pairs, and 19,683 ordered triples. All checks passed. Negative controls demonstrate that individually stable operators can have an unstable composite, legal reconstruction need not preserve accuracy, and noninvertible commuting maps need not preserve full system identity. The report organizes established mathematical principles into a scoped architectural framework. It does not claim an absolute minimal axiom system, unconditional composite stability, or general cross-domain equivalence. Offline HTML, executable verification code, reference results, and integrity hashes support reproducibility.