Convergence Without Identity: Structural Similarity and Recurrence Under Constraint in the Paton System

Systems composed of similar underlying material and operating under shared constraints can converge toward highly similar configurations. However, exact identity between independently formed systems is structurally prohibited due to differences in formation timing, microstate arrangement, and interaction history. This paper formalises convergence without identity as a structural condition within the Paton System and demonstrates that constraint-consistent environments produce recurring forms across scale. Similarity is therefore continuous and governed by admissibility, while recurrence emerges from constraint replication rather than duplication. The result is a unified constraint principle: systems may approach extreme similarity, but identity remains structurally excluded, while recurrence remains inevitable across domains.