Universal Grid Mechanics (UGM): A Five-Axiom Admissibility Foundation for the Physical Continuum — UGM02 Version V3.2b, Typed-Admissibility and Source-Ownership Edition

Abstract

Universal Grid Mechanics begins with a basic question: what must be true before a state or change can count as physically real? UGM02 answers through five axioms. Admissible states exist; reality is carried by a persistent physical continuum; physical state is distinct from mathematical representation and observation; independently realized evolution preserves admissibility; and continuation-relevant retained state must be present, bounded, finite in distinguishable capacity, and declared before a test is inspected. This paper combines mathematical completeness with direct, reader-facing language. It defines the complete present state, distinguishes declared-state equality from continuation equality, separates candidate updates from independently realized updates, and keeps finite updates primary. A general pre-phenomenological update expression is retained as an imported open structural template rather than promoted as a completed constraint or universal equation of observables. The paper develops retained-state regimes, the complete observation chain, prediction certification, an imported observation-closure construction, time and spacetime bridges, structural eigenmodes, evidence calibration, and explicit failure conditions. The framework does not begin with particles, forces, constants, a metric, or an inventory of phenomena. It constrains what later sector theories may consistently describe and what must be specified before an empirical claim is promoted. Zenodo recommends using the Description field for the abstract and permits additional descriptions for notes or technical information. This record (DOI: 10.5281/zenodo.19151677) consolidates the UGM axiomatic paper version chain from V02.10a onward. The original UGM v1.0 record is 10.5281/zenodo.18529620. This is the revised final version. (DOI: 10.5281/zenodo.21563573). v03.2b