From Classical Dynamics to the Resonance Tower: Foundations of the Harmonic Universe Model

This paper establishes the classical backbone of the Harmonic Universe Model by deriving the modal structure that underlies its unification programme. Starting from a minimal harmonic action on M 4 ×K, we obtain the harmonic field equation, linearize around a stable background, and perform a controlled modal reduction. The internal dynamics reduce to a self-adjoint Sturm–Liouville problem whose discrete spectrum generates a tower of effective four-dimensional resonances. The spacing, degeneracies, and selection rules of this tower are fixed by the internal realization (interval or circle) and by admissible boundary or periodicity conditions, providing a falsifiable structure independent of detailed microphysics.We clarify the adiabatic regime in which the tower remains approximately diagonal and derive the minimal form of mode mixing outside that limit. Classical interaction operators reduce to overlap integrals that enforce robust selection rules and generate correlated coupling hierarchies. These structures supply the precise mathematical counterpart of the modal unification picture developed in the earlier Modelo Armónico del Universo manuscript: extended, flat, smooth, and localized internal profiles arise here as classical eigenfunctions of the internal operator.The classical framework developed in this article serves as the basis for the next article, where the resonant tower is quantized and coupled to a minimal matter sector similar to the Standard Model. It also provides the necessary modal infrastructure for the gravitational and cosmological developments in subsequent articles.