Unified Gravitational, Electromagnetic, and Spin Dynamics from Fermi–Walker Geometrodynamics Constrained by the Particle’s S¹ Compton Clock Fiber

We present a four-dimensional spacetime-geometrodynamical description of electromagnetism as a \(U(1)\) holonomy, formulated in parallel with standard gravitational geometrodynamics. According to the Hamilton--Jacobi optomechanical analogy, interactions admit a dual reading: dynamically, as local changes of four-momentum; geometrically, as local modulations of spacetime recurrences. Spacetime curvature induces redshift and ruler deformation, reproducing gravitational interaction. Similarly, Local Lorentz Transformations associated to a congruence of observer-adapted Fermi--Walker accelerated frames induce local modulations of spacetime recurrences, analogous to the precession of a gyroscope. This yields an effective Abelian connection that reproduces the Lorentz force as a Coriolis-like inertial effect and leads to Maxwell equations for the induced \(U(1)\) curvature. At leading order, the observer-adapted local Lorentz transport generator \(\Omega^{EM}_{\mu\nu}\) determines the electromagnetic field strength through the geometrodynamical identity \(qF_{\mu\nu}\simeq - m \Omega^{EM}_{\mu\nu}\), up to integrable contributions generating \(U(1)\) gauge orbits. These results emerge within a field description implementing "Phase Harmony'', \ie covariant Periodic Boundary Conditions imposed consistently with the variational principle, thereby tracking the relativistic transformations of the natural Compton proper-time recurrence associated with the particle's mass, namely the "particle's internal Compton clock''. The resulting effective \(S^1\) fiber attached to each spacetime point allows a purely four-dimensional reinterpretation of the Kaluza--Klein mechanism and, in turn, a derivation of the Maxwell kinetic term directly from the Ricci tensor. By construction, the same local-isometry structure that governs electromagnetism also governs spin transport, yielding a unified kinematical and dynamical description of Thomas precession and the Bargmann--Michel--Telegdi equation. This suggests a possible geometrodynamical carrier for the anomalous magnetic-moment \(g-2\).