Unified Framework for Resonant and Geometric Memory Architectures in Advanced AI and Quantum Systems

This research compendium presents five original memory system architectures developed by Hilmir F. Halldórsson, each proposing a radically new approach to memory encoding, coherence, and retrieval. Rooted in geometry, entropy, resonance, and physics-inspired modeling, these systems offer novel paradigms for AI memory, quantum computing, and neuromorphic simulation. The five systems include: Vesica Memory Core (VMC) – A chaos-modulated, geometry-locked memory system based on planar overlap and scalar resonance. Tensor-Resonant Geometry – A physics-based model using spacetime curvature, dark matter optics, and neutrino fields for ultra-coherent memory. Resonant-Entropic VMC – An entropic and resonance-driven system with multilevel stochastic feedback and dynamic curvature adaptation. Geometric Resonant Memory Units (GRMUs) – Curvature-based attractor memory encoding phase and coherence in geometric manifolds. Unified GRMU–VMC Framework – A full-stack integration merging geometry and entropy to form a dynamic and simulation-ready memory engine. Each system is accompanied by mathematical formalisms, pseudocode, and implementation pathways for both software and hardware design. Taken together, they define a unified, future-ready architecture for emotionally-aware, dynamically stable, and physically interpretable memory.