A Foundational Framework for Natural Philosophy: Singularity, Duality, and Triality

Abstract

This paper proposes the Singularity-Duality-Triality (S-D-T) framework as a falsifiable, heuristic model for predicting the emergence of stable, complex systems. Departing from purely descriptive metaphysics, we ground the model in physically consequential patterns and advance a series of testable hypotheses. We first present structural and process-based evidence from topological physics—specifically the Z8 classification of topological superconductors, the existence of anyons, and the AdS/CFT correspondence—as the primary motivation for the model’s construction. The framework’s explanatory utility is then demonstrated through its application to the Standard Model, from which we derive two key claims: that the inherent instabilities of Grand Unified Theories are a predicted consequence of unmediated duality, and that the three generations of matter form a complete S-D-T system whose triadic closure is the necessary condition for CP violation and baryogenesis—a principled explanation for an empirical fact the Standard Model itself treats as a brute datum. The model’s viability as a scientific theory is established by defining clear prohibitive claims that meet the Popperian criterion of refutability, while directly confronting the principal vulnerability of any cross-domain heuristic: the risk of unfalsifiable post-hoc pattern-fitting. We argue that the S-D-T heuristic qualifies as a ‘real pattern’ in the sense of Ontic Structural Realism by providing a framework for information compression that yields predictive leverage. The S-D-T framework is offered not as a final metaphysics, but as a working scientific model to be tested, refined, or refuted by future empirical work.

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