PFUSRC‑174: PFUSRC Ontological Frequency Theory Based on a Foundational Reconstruction of the Fourier Transform

Abstract

Classical physics and mathematics define frequency as the number of periodic oscillations per unit time within the spacetime dimension, relying on the Fourier transform to achieve the transformation between the time domain and the frequency domain. This has become a core tool of modern signal processing, wave mechanics, and quantum observation. However, traditional frequency theory rests solely upon three‑dimensional spacetime projection appearances. It cannot distinguish the ontological difference between internally generated spontaneous frequencies and externally driven perturbation frequencies within a system, nor can it explain the deep roots of the time–frequency duality paradox and the uncertainty of quantum observation, giving rise to a scientific fissure of “engineering utility with ontological distortion.” Relying on the PFUSRC 11‑dimensional triple coaxial 45° bicone topological unified system and the seven‑layer ontological flow framework (L1–L7), this paper carries out a foundational reconstruction of the classical frequency system: frequency is elevated from a motion parameter of spacetime appearance to the ontological flow‑variable rate of higher‑dimensional topological closed‑loop revolution. The paper strictly distinguishes the topological origins, steady‑state mechanisms, and persistence logics of ontological spontaneous frequencies and external perturbation frequencies, and demonstrates the spurious validity of humanity’s three‑dimensional external observation system. It is ultimately demonstrated that the Fourier transform and quantum measurement are both low‑dimensional external fitting tools possessing only engineering application value and lacking genuine explanatory power over cosmic ontological reality. A universal ontological frequency axiomatic system is thereby established, one that precedes spacetime and is rooted in topological structure.