This paper develops a purely structural theory of universality based on ordered shell accumulation and algebraic defect concatenation, without invoking metrics, fields, or renormalization. A window system with shell–additive boundary paths induces a defect map into a group, and large–scale behavior is shown to depend solely on the algebraic type of this defect group and its cancellation capacity. Finite groups enforce termination at finite scale, while infinite abelian groups yield a rigid logarithmic scaling law with exponent two. In contrast, non–abelian groups either produce termination or induce a strict increase in the logarithmic exponent governed by noncommuting supply. This establishes universality classes as algebraic invariants rather than geometric or dimensional properties. Critical exponents emerge from ordered accumulation and cancellation structure, not from analytic or spatial considerations. The framework provides a complete classification of admissible scaling regimes under minimal structural assumptions.
Anonymous (Tue,) studied this question.