Universal Grid Mechanics (UGM):An Axiomatic, Admissibility-First Framework for Physical Reality

Universal Grid Mechanics (UGM) is an admissibility-first foundational physics framework in which physical existence is restricted to states satisfying continuity, bounded change, and local information consistency under repeated updates. Reality is modelled as a continuous persistent substrate — the grid — that admits deformation, retains history, and resists change in a bounded manner; all evolution preserves a finite admissible domain D. UGM is explicitly pre-phenomenological: no particles, fields, or spacetime geometry are assumed at the axiomatic level.

Starting from five frozen axioms and the minimal local state X = (S, M), where S is a structural deformation state and M is structural memory, this paper derives and consolidates the foundational architecture of UGM. The unique admissibility-minimizing primitive operator L6 is derived via coordination-normalized spectral anisotropy; its Taylor expansion recovers the isotropic Laplacian. From the UGM gravity Hamiltonian, the Poisson equation and the inverse-square law follow as formal limiting theorems, and the dimensionless Newton constant G = √3/4π² emerges as a geometric consequence of hexagonal coordination without gravitational data. The gravity sector retains a two-regime structure: Newtonian at low memory and MOND-like screened-Poisson behaviour at high memory.

The central new result is a global contraction theorem: admissible evolution is not merely bounded but contractive on D, guaranteeing uniqueness and asymptotic stability of the update dynamics. This upgrades UGM from a collection of admissible states to a dynamically well-posed system, justifies coarse-graining, and strengthens the structural exclusion of General Relativity. The Admissible Path Interpretation replaces globally monotone-memory language with the precisely correct pathwise non-negativity of realized increments, derived from admissibility and branch selection. A causal memory-kernel formulation connects structural memory accumulation to the kinematic discriminator and provides a structural pathway toward the radial acceleration relation, with the characteristic acceleration scale a* ≈ 1.2 × 10⁻¹⁰ m s⁻² treated as an emergent memory–kinematic scale rather than a primitive constant.

This record includes the Gap Accounting companion document (ugm_gap_accounting) which provides a complete verified status table of every claimed result in the UGM corpus as of V02.10a, a dependency tree, submission readiness assessment, and a prioritized next-steps list.