A Three-Layer Differential Framework: Lorentz Geometry, Dirac Dynamics, and C6 Phase Topology as Independent but Unified Geometric Layers

Abstract We introduce a differential-geometric framework in which Lorentz geometry, Dirac spinor dynamics, and the six-fold analytic phase topology of C6 appear as three independent but coexisting layers of a single underlying space. Unlike traditional approaches—where metric structure, spinor dynamics, and complex phases are treated as separate algebraic extensions—the present model exhibits a structural duality: each layer preserves its algebraic identity, yet physical observables emerge only when all layers are projected onto the same visible subspace. The resulting structure reconciles Lorentz invariance, Dirac symmetry, and internal cyclic curvature without algebraic mixing. We show that the hidden phase topology induces a geometric time potential, redshift offsets (z ≈ 0.16–0.19), and phase–curvature modifications to long-time evolution, all while maintaining strict Lorentz and Dirac consistency. This modular but unified structure provides a candidate foundation for a broader class of analytic-curvature models and phase-topological extensions of quantum theory.