Geometric Architecture of Wave Homeostasis: Axiomatic Translation of the McEc Model Into Dynamical Systems Theory

This paper provides a complete non-perturbative axiomatic mathematical formulation of the Morphological Energy Coherence (MCEC-2) framework. We generalize the principles of topological wave stability and dynamic homeostasis by migrating the constitutive equations from structural mechanics to the differential geometry of non-linear dynamical systems on Riemannian manifolds and Banach spaces. We prove three foundational theorems of micro-regularity: first, the construction of a topological dissipation functional driven by a pseudo-differential metric latency operator, regulated by a Hodge-de Rham spectral eigenvalue; second, the uniform invariance of the spectral Rayleigh quotient under a harmonic stationarity limit condition, establishing the exact algebraic cancellation of the inertial mass coordinate through the four-dimensional conformal symmetry of the Hodge star operator; third, the compactness of the flow boundary resolvent on the codimension boundary submanifolds, driving the algebraic collapse of boundary extension areas. This coordinate-free formulation proves that the smooth manifold acts as a self-organizing morphological processor, suppressing singular energy accumulation and establishing total wave transparency.