The General Theory of Irreversible Distinguishability IV: Stability, Dimensional Selection, and Structural Closure

This paper derives structural stability conditions governing admissible spacetimedimensionality, gauge symmetry, and internal degrees of freedom under irreversibleloss. Building on the refinement-based emergence of spacetime (Paper II) and gaugestructure (Paper III), we introduce stability axioms requiring persistence under localperturbations. These axioms exclude non-compact gauge groups, infinite-rank symmetries, non-integer dimensions, and excessive combined spatial–internal complexity.Spacetime dimensionality and gauge structure are shown to be jointly constrained byloss-induced stability, yielding a finite admissible window of coupled structures. Allcontinuous structural freedom is exhausted at this level, forcing remaining admissiblestructure to be discrete. This establishes a formal transition from fundamental physical structure to chemistry, where stable composite persistence becomes the dominantorganizing principle. No physical postulates, phenomenology, or empirical inputs areassumed.