A Minimal Axiomatic Foundation for Probability-Space Physics

This work presents a minimal axiomatic foundation underlying the Probability-Space framework, developed independently of physical assumptions. Beginning from an initially complete logical axiom set, the framework is systematically compressed to a minimal core of four axioms governing information, realization, accessibility, and selection. From this minimal core, the paper derives unavoidable logical consequences including temporal asymmetry, unobservable futures, sequential realization, accessibility boundaries, and the necessity of asymmetry for change. By introducing probability as a quantitative representation of accessibility, it is shown that boundaries and gradients necessarily produce physical response. Energy, curvature, and acceleration emerge as manifestations of constrained realization rather than as primitive assumptions. No physical quantities—such as spacetime, force, energy, or constants—are assumed at the axiomatic level. Physical structure appears only as a downstream consequence of logical constraints once realization is permitted. This paper serves as a foundational companion to the previously published Probability-Space physical theory (Zenodo DOI: 10.5281/zenodo.17794870), establishing the logical necessity of the structures employed in that work while remaining empirically agnostic.