Universal Grid Mechanics (UGM) proposes that physical reality is not fundamentally composed of particles, fields, or spacetime, but of a continuous underlying structure: the grid, that can deform, store stress, and update itself. Instead of beginning with equations, UGM begins with a small set of ontological axioms that determine which physical states are physically admissible. Motion, forces, time, and observable objects arise as consequences of how stored stress relaxes within this grid under local interaction. Singularities and infinities are excluded by construction, rather than repaired after the fact. This paper presents the axiomatic foundation of UGM, the primitive update elements, a coherence–selection mechanism governing outcome stability, a non-spacetime admissibility metric, and a concrete empirical touchpoint illustrating falsifiability. Quantitative instantiations and full mathematical derivations are presented in companion technical work.