5D Geometrodynamic Architecture on an S¹/Z₂ Orbifold: 3-Form Gauge Coupling, Selected Scalar Sector, Kaluza-Klein Reduction, Radion Decomposition, Electromagnetic Coupling and Transient Topological Signatures

This paper develops a speculative 5D geometrodynamic framework parameterising the universe as a pentadimensional manifold compactified via an S¹/Z2 orbifold. A zero-mode sector of a geometric curvature field (3-form) is rigorously selected, which under strict algebraic conditions in Cl1,4 behaves as a 4D scalar field coupled to the brane's electromagnetic field. Version 5.0.1.8 represents the stabilization of the framework into a Preliminary Effective Model, mathematically audited and ready for experimental injection. Specifically, it provides: Geophysical Transfer Resolution & Surface Amplification: The scalar approximation was replaced by a Stratified Spherical Model (TMM). It is mathematically demonstrated that at low frequencies (10⁻² ~ 10⁻¹ Hz), induced eddy currents inside the Earth generate a constructive surface reflection coefficient (RB ≈ 1), effectively doubling the anomaly's amplitude (T(ω) ≈ 2.0) at the surface rather than attenuating it. This establishes a strict operational guideline for SuperMAG and GNOME pipelines. Absolute Stability of the Scalar Sector: Exact elimination of the radion-scalar cross-mixing (κφχ = 0) in the Minimal Model, proving that the kinetic matrix is strictly diagonal (G > 0) and mathematically eradicating the possibility of ghost states. Convergent Planck Mass: Analytical resolution of the 5D curvature factor (Randall-Sundrum rigid limit) guaranteeing a convergent and strictly positive effective mass even in the asymptotic limit. Top-to-Bottom Mathematical Audit: Consolidation of dimensional consistencies, rigorous bounding of the local axion canonization (ac), and the exact normalization of the Bayesian marginal evidence (Z₀) for empirical testing. The framework includes a comprehensive falsifiability matrix and empirical geomagnetic prediction models designed for testing transient topological signatures using extreme low-frequency (ELF) magnetometer stations.