GEOMETRIC ARCHITECTURE OF WAVE HOMEOSTASIS: AXIOMATIC TRANSLATION OF THE MCEC MODEL INTO DYNAMICAL SYSTEMS THEORY
Abstract
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.
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BibTeX
@misc{chianura2026geometric,
title = {{GEOMETRIC ARCHITECTURE OF WAVE HOMEOSTASIS: AXIOMATIC TRANSLATION OF THE MCEC MODEL INTO DYNAMICAL SYSTEMS THEORY}},
author = {Piergiuseppe Chianura},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23530005},
url = {https://zenodo.org/records/23530005},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GEOMETRIC ARCHITECTURE OF WAVE HOMEOSTASIS: AXIOMATIC TRANSLATION OF THE MCEC MODEL INTO DYNAMICAL SYSTEMS THEORY
AU - Piergiuseppe Chianura
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23530005
UR - https://zenodo.org/records/23530005
AB - 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.
ER -