This paper establishes a complete universality classification for defect concatenation systems based on purely algebraic and structural principles, without recourse to geometry, probability, or renormalization methods. A shell-based framework with ordered boundary concatenation induces a defect map into a group, and global scaling behavior is shown to depend only on the algebraic nature of this defect group and its cancellation structure. Finite groups lead to termination at finite scale, while infinite abelian groups produce a universal logarithmic scaling regime characterized by a rigid exponent. In the non–abelian case, either termination persists or a strict deviation from the abelian exponent arises due to noncommuting accumulation effects. The classification theorem demonstrates that all admissible large-scale behaviors fall into a small number of universality classes determined by group structure alone. Critical exponents are derived from ordered concatenation and cancellation constraints rather than analytic or spatial mechanisms. The results provide a fully intrinsic characterization of scaling regimes within defect-driven systems.
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