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 SilentWitness-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. Recent evaluations reveal systematic limitations in large language models (LLMs) for scientific discovery tasks, including diminishing returns from scaling, shared failure modes across frontier models, and disconnection between question-level and project-level performance. We propose that Z(n) architectural principles-particularly discrete phase-space structuring and information-physics duality-may address these limitations by providing physics-motivated inductive biases for hypothesis space exploration. We establish experimental protocols for both photonic validation and computational benchmarks, and propose SDE-style scenario-grounded evaluation of Z(n)-augmented discovery systems as critical future work.