Sub-Limit Dynamics: Boundary Interaction as the Structural Determinant in Finitely Constrained Generative Systems

Two independent lines of investigation have produced structurally parallel results. In the arithmetic setting, the morphological vocabulary of positional expansions of unit fractions consists of exactly six forms, with completeness governed by a criterion on the joint factorization of b and b−1. In the trajectory setting, boundary-constrained walks on de Bruijn graphs produce exactly seven dynamic regimes collapsing to three terminal outcomes, with feasibility determined by the interaction between accumulated history and residual action space. Both settings exhibit the same phenomena: finite vocabulary, early saturation, an efficiency paradox in which internal optimization is antagonistic to structural…