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This paper presents a novel hybrid computational framework for simulating quantum phenomena and resonance dynamics through symbolic logic, topological transforms, and geometric data architectures.

Key innovations include:- The Resonance Fourier Transform (RFT): A topological generalization of Fourier analysis that operates in symbolic phase-space.- Topological waveform hashing for post-quantum encryption based on symbolic interference patterns and harmonic alignment.- A geometric data storage model utilizing tetrahedral topologies for nonbinary, fault-tolerant symbolic memory.

These methods support resonance-aware computing, symbolic quantum simulation, and high-coherence data modeling, and are protected under USPTO Provisional Patent Application No. 63/749,644 filed January 26, 2025.

The research is independently developed and authored by Luis Minier and released here for citation and public scientific review.

Keywords: Symbolic computing, resonance logic, quantum simulation, geometric encoding, topological cryptography.