Abstract

The Retro-Harmonic Equation (RHE) introduces a novel mathematical framework for phase coherence, integrating non-ergodic spectral constraints with Floquet systems, quantum resonance, and biological oscillatory dynamics. By incorporating prime-indexed spectral corrections, this work reveals a fundamental selection mechanism in phase evolution—where coherence emerges dynamically through structured deviations from uniform periodicity. This principle governs quantum stability, neural oscillations, and AI learning architectures, bridging deep connections between number theory, spectral physics, and cognition. This paper explores the experimental implications of RHE across three domains: Quantum Systems – Stability enhancements in superconducting qubits via prime-indexed Floquet spectral structures. Neuroscience – A novel framework for EEG phase coherence analysis, predicting prime-indexed neural resonance. Artificial Intelligence – Prime-indexed constraints on recurrent neural networks for enhanced temporal stability and adversarial robustness Fundamentally, RHE suggests that coherence is not merely emergent but actively sculpted by structured spectral constraints, allowing a redefinition of free will as the capacity to modulate coherence within an evolving spectral lattice of time. This work builds upon the Retro-Harmonic Equation (RHE) framework, extending it into Floquet systems and prime-indexed resonance structures. The experimental feasibility of RHE-based constraints is discussed in quantum weak measurement protocols, EEG phase coherence experiments, and AI spectral learning architectures.