Gartner's Omega Algebra: A Unified Framework for Quantum Mechanics, General Relativity, and Cosmology

This archive presents Gartner's Omega Algebra (GOA), a typed algebraic system specified by 18 axioms (13 kinematic + 5 dynamic) designed to maintain computational and logical integrity beyond points of physical singularity. The framework provides a unified description where quantum mechanics, general relativity, and cosmology emerge from a shared algebraic substrate. Included are machine-checked formalizations in Coq, a high-performance C execution engine, and empirical validation deriving 34 fundamental physical constants—including the fine-structure constant ($\alpha$) to 0.284 ppb accuracy—with zero free parameters.