Supplementary Addendum: Unified Chronoscalar Scaling Across Quantum Hall Systems, Graphene, Nematic FQHE, and Planetary Aurorae, with Machian Direction and Drift-Dynamics Derivation

Abstract

This Supplementary Addendum provides complete observational, mathematical, and crossdomain support for the chronoscalar scaling law developed in the main text. It compiles empirical data from ultra-clean quantum Hall experiments, graphene transport, nematic fractional QHE, and planetary auroral asymmetries, and demonstrates that each domain independently exhibits anomalies scaling with the same chronoscalar quantity ϵCFT = |∇T|Leff , where ∇T is the permanent Machian gradient of the chronoscalar field. We further derive the chronoscalar modification to magnetospheric MHD drift, demonstrate the mechanism for Mach-locked auroral asymmetries, and show agreement with Earth, Jupiter, and Saturn. This addendum is self-contained and uses notation compatible with the main PRL manuscript.

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