Hilbert's Sixth Problem Revisited Through Viscous Time Theory Axiomatizing Physics by Axiomatizing Admissibility, Coherence, and Recoverability

Hilbert’s Sixth Problem asks for an axiomatization of physics, especially the probabilistic foundations of mechanics and the passage from microscopic dynamics to macroscopic laws. Despite foundational progress in probability theory and statistical mechanics, a persistent conceptual gap remains: probability appears as a primitive or as an epistemic tool, rather than as a quantity derived from the structure of physical evolution itself. This paper proposes a Viscous Time Theory (VTT) reformulation of Hilbert 6: physics is axiomatized by admissibility (what transformations can occur while preserving identity), coherence (the measurable structure of informational organization), and recoverability (which collapses are irreversible independent of observer perspective). We present a minimal axiomatic system in which (i) time emerges as informational viscosity, (ii) probability emerges as an induced measure over admissible trajectories, and (iii) the micro→macro transition becomes a geometric scaling limit of coherence fields rather than an ad hoc coarse-graining step. We do not claim a completed proof of Hilbert 6 in the classical sense. Instead, we provide a coherent, falsifiable program that reframes the target: the objective is not “derive probability from mechanics,” but “derive probability from the geometry of admissible informational evolution,” with classical mechanics and statistical mechanics emerging as distinct regime limits.