DIFFRACTION Abstract Asymmetrical Systems Modeling

DIFFRACTION: Abstract Asymmetrical Systems Modeling is the third manuscript in the DIFFRACTION research program. This work formalizes a framework for modeling asymmetrical systems whose state identity is preserved through reversible, admissibility-constrained transformations. The manuscript organizes the underlying source artifacts into a unified presentation centered on stepwise transforms, hidden-pair complex embeddings, spectral unfolding, coherence-aware constrained superposition, and three admissibility axioms: State Validity, Operator Closure, and Representation Fidelity. Rather than introducing new mathematics, this preprint consolidates and refines the existing theoretical framework into an IEEE-style manuscript. The discussion connects the preserved mathematical structure across signal processing, cryptographic transformations, runtime systems, quantum-inspired representations, complex vector embeddings, and abstract asymmetrical systems while maintaining a conservative interpretation of the underlying source material. Supporting computational appendices illustrate recurrence behavior and manifold construction used during development.