What question did this study set out to answer?

The aim is to establish a multi-scale resolution of the Fractional Quantum Hall Effect and topological insulation using geometric principles.

June 5, 2026Open Access

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

Key Points

The aim is to establish a multi-scale resolution of the Fractional Quantum Hall Effect and topological insulation using geometric principles.
Utilized integer-based framework within Z/256Z for analysis.
Replaced quantum wave mechanics with rigid geometry of Hexagonal Close-Packed structure.
Employed finite-difference state-tracking to analyze edge-state robustness.
Demonstrated emergence of fractional conductance states based on geometric ratios of locked neighbor contacts.
Found that edge-state robustness is inherent to the spatial crystal structure.

Abstract

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

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