Wave-Particle Duality as Computation-Data Ontological Correspondence

We establish that quantum mechanical wave-particle duality is the manifestation of a more fundamental computation-data ontological correspondence. Building on the Zeckendorf-k-bonacci tensor (ZkT) framework developed in our previous work,we demonstrate that: (1) wave behavior corresponds to temporal computation processes within recursive algorithmic networks; (2) particle behavior represents discrete data crystallization in frequency domain through Fourier transforms; (3) quantum measurement emerges as computation-data collapse in finite observers; (4) Heisenberg uncertainty principle derives purely from Fourier analysis constraints; (5) information conservation through Parseval’s theorem ensures ontological equivalencebetween computational and data representations. We provide rigorous mathematical proofs connecting k-bonacci recursions to quantum phenomena and present testable experimental predictions. This framework resolves the conceptual paradox of wave-particle duality by revealing it as inevitable consequence of recursive information processing systems, establishing quantum mechanics as a special case of computational ontology rather than fundamental physics.