Geometric-Spectral Derivation of the Precession Anomaly in Relativistic Circular Motion

We present a non-perturbative derivation of the precession anomaly observed in confined relativistic systems, focusing on the case experimentally known as the muon $g-2$ factor anomaly. The analysis proceeds exclusively from the Geometric Spectral Stability Principle (GSSP), formulated as a fundamental variational functional, and from its minimal dynamic realization within the Foundations of Spectral Fields (FSF) formalism. We demonstrate that the total phase correction accumulated in relativistic circular motion decomposes uniquely into two contributions: (i) an absorbable term, which coincides exactly with Thomas precession, and (ii) a residual term of spectral origin, invariant under kinematic redefinitions. We show that only the residual term survives as a physical observable. By specializing this result for real systems in storage rings, we quantitatively identify the observed muon anomaly as the direct manifestation of a fourth-order geometric sampling error of spacetime. No additional field, virtual particle, or adjustable parameter is introduced.