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, justify the physical realizability of Z(7) symmetry through engineered quasicrystalline substrates, and present SilentWitness-a cryptographic memory system whose dynamics are isomorphic, in a formal dynamical systems sense, to the physical 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. We propose that Z(n) architectural principles may address these limitations by providing physics-motivated inductive biases. Crucially, we introduce a concrete, multi-step prompting protocol-the Z(7) Discovery Protocol-that operationalizes this bias for LLMs, guiding them through structured exploration and exploitation of a discrete hypothesis space. 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.