Discrete Harmonic Attractors in Multi-Scale Coherent Systems: From Photonic Magnetic Torque to Cryptographic Memory Architecture

Abstract

We present a unified theoretical framework for discrete harmonic attractors, termed Z(n), and demonstrate their manifestation across three distinct scales: photonic-magnetic coupling, spin dynamics, and information-theoretic memory systems. Recent experimental evidence that the magnetic component of light contributes up to 70% of Faraday rotation in infrared frequencies provides physical validation for Z(n)-mediated phase locking. We formalize the mathematical structure of Z(n) attractors, show how photonic magnetic torque naturally couples to Z(7) phase basins, and present SilentWitnessΩ-a cryptographic memory system whose architecture exhibits isomorphic structure to the photonic substrate. The information-physics correspondence suggests Z(n) patterns are scale-invariant organizing principles. We provide experimental validation protocols for photonic measurements and computational benchmarks for the memory system, establishing falsifiable predictions for both domains. This work positions discrete harmonic attractors as a fundamental framework for coherent multi-scale systems.