Oscillation and Polarity as the Generative Basis of Mathematical Structure and Physical Law

This paper proposes a generative framework in which two minimal primitives—oscillation and polarity—may jointly underlie the emergence of mathematical structure and physical law. Polarity, treated as a two-state involutive distinction, is examined as a potential basis for generating core mathematical elements such as distinction, relation, order, number, and algebraic structure. Oscillation, interpreted as the temporal expression of polarity, is considered as a possible source of the frequency-based formulations that appear across major areas of physics. A historical survey of foundational equations suggests that many either take the form of wave equations or admit frequency-mode solutions, spanning classical mechanics [1–3, 15], electromagnetism [4, 17], quantum theory [5–9, 13, 16, 18], relativity [10, 11, 21], and quantum field theory [12, 19, 20]. In addition, previously reported vibration-plate experiments are revisited here through the lens of this framework, with their geometric outcomes interpreted in terms of frequency-dependent structure. Within this proposed approach, polarity provides a structural basis for mathematics, oscillation provides a dynamical basis for physics, and frequency serves as a connecting layer between the two. The aim of this work is to explore whether these minimal primitives can offer a coherent and testable generative foundation without presupposing existing mathematical or physical formalisms.