Topological Resonance in Discrete Hexagonal Lattices: Resolving Half-Integer Quantization and Thermal Stabilization

Abstract This paper formalizes the transition from classical integer-bound constraints to scaled half-integer representations within a discrete hexagonal lattice framework. By drawing parallels from the historical resolution of the anomalous Zeeman effect, we establish a robust topological model governed by invariant residue manifolds. The integration of dual-track routing and a Mod 9 invariant successfully mitigates thermal runaway at high-frequency operational thresholds, offering a scalable architecture for non-dissipative energy management in complex lattice systems.