Dynamic Phase Resonances in Hexagonal Close-Packed Media: Fractional Quantum Hall Topology and Geometric Charge Localization (Part VI)

This paper establishes an integer-based multi-scale resolution of the Fractional Quantum Hall Effect (FQHE) and topological insulation phenomena, replacing quantum wave mechanics with the rigid geometry of the Hexagonal Close-Packed (3HCP) matrix. Operating within the ring of integers modulo 256 (Z/256Z), the author demonstrates that fractional conductance states (1/3, 2/5, 3/7) emerge as geometric ratios of locked neighbor contacts within the 12-fold coordination shell. The study replaces abstract wave-function models with exact finite-difference state-tracking, proving that edge-state robustness is a hardware-level feature of the spatial crystal. Creative Commons Attribution Non Commercial No Derivatives 4.0 International