Ontic Zero and the Resolution of Foundational Underdetermination in Physics A Meta-Axiomatic Framework

Ontic Zero and the Resolution of Foundational Underdetermination in Physics A Meta-Axiomatic Framework Author: Jose Jorge Leon Gavonel Date: December 30, 2025, Status: for formal review (Philosophy of Physics category) Abstract Modern physics operates across two distinct structural regimes: ordinal structures, encoding order and hierarchy without magnitude, and cardinal structures, encoding metric extension, continuity, and infinite dimensionality. While these regimes coexist formally within mathematics, their coupling in physics is pragmatic rather than ontologically grounded. This underdetermination manifests in persistent boundary pathologies such as singularities, divergences, fine-tuning, and unbounded infinities. This paper introduces Ontic Zero, a meta-axiomatic framework that establishes ordinal differentiation as ontically primary and cardinal extension as conditionally admissible. Rather than rejecting continua or infinite dimensional formalisms, Ontic Zero provides explicit criteria governing their ontological legitimacy. Minimal asymmetry (δ) is shown to be a transcendental necessity for any extension, while Gödelian incompleteness is reframed as a structural feature of extensional regimes. Ontic Zero does not replace physical theories or generate new empirical predictions; instead, it functions as a foundational constraint system that explains why existing theories succeed where they do and fail at their boundaries.