Spectral Logic Gates: A Path-Based Paradigm for Structure-Aware Computing

We present a spectral logic system that performs computation on path structures with complex-valued amplitudes, leveraging spectral in- terference, entropy-driven feedback, and programmable interfaces. Un- like traditional Boolean or quantum logic, our system operates directly on path dictionaries, enabling dynamic structural reasoning. We de- fine logic gates (AND, CNOT, NOT, CONV, RECOVERY), introduce Fourier-based cluster detection, and demonstrate collapse detection and recovery through entropy modulation. A category-theoretic framework models paths as morphisms, supporting future type systems. Experiments on DAGs with 100 to 10,000 paths validate the system’s stability and ef- ficiency, positioning it as a novel paradigm for neuromorphic computing, photonic circuits, and AI reasoning.