Topological Complex Electrodynamics and Phase-Locked Resonance: A Unifying Geometric Architecture for Subatomic Solitons, Quantized Impedance, and Entanglement

Abstract We present the Topological Complex Electrodynamics and Phase-Locked Resonance (TCER) framework, a deterministic, non-singular field-theoretic architecture that unifies particle geometry, quantized observables, and quantum non-locality within a classical electrodynamic setting. By modeling fundamental entities as non-radiating topological Hopf fiber bundle () solitons embedded in a complex vacuum impedance tensor field , we demonstrate that fundamental particle properties—such as rest mass scaling, spin angular momentum, electric charge, and magnetic moment structures—can be naturally framed as emergent phenomenological geometric scaling features and topological invariants rather than ad hoc inputs. We show that evanescent near-field boundary conditions enforce zero Poynting vector divergence (), preventing radiative collapse without requiring point-particle renormalization. Furthermore, quantum transitions and the fine-structure constant are mapped to a discrete, continued-fraction expansion of (), framing energy levels as phase-locked resonant states across a complex impedance staircase. To establish rigorous empirical falsifiability, We propose three discriminative experimental protocols executable within current laboratory capabilities (10^-3 ~ 10^-4 rad): (I) Wide-range Pancharatnam-Berry phase sweeps using a spatial light modulator (SLM) on SPDC entangled photon pairs to verify the macroscopic 8π topological periodicity and 4π sign inversion predicted by S^3 -> S^2 topological winding; (II) Low-order continued-fraction RF/optical driving (e.g., 22/7) on trapped 171Yb+ ions to induce orders-of-magnitude coherence protection via complex-impedance matching at targeted resonance ratios; and (III) High-precision precession sweeps on cryogenic HfF+ molecular ions under strong electric field modulation to detect differential slope anomalies (saddle points), confirming the phase-locking response of the topological core. We invite experimental collaborations across ultrafast optics, trapped-ion cavity QED, and precision measurement laboratories to validate these predictions and explore active topological entanglement engineering.