State-Expanding Systems: A Constraint-Limited Theory of Novelty Growth
Year: 2026
Type: preprint
Abstract: This paper introduces a constraint-limited model of combinatorial growth that examines how feasibility scales with increasing system dimensionality. The framework analyzes the balance between expanding possibility spaces and constraint structures that prune feasible configurations. The model shows that when feasible configurations grow as c^n within a combinatorial space of size 2^n, the feasible fraction collapses for constant c < 2. Sustained novelty generation therefore requires c(n) to approach the combinatorial base, producing a narrow “complexity corridor” between regimes of trivial repetition and combinatorial sparsity. The paper derives the analytic structure of this corridor and explores it through numerical simulations and visualizations. The results suggest a possible structural explanation for why complex systems may emerge only within a narrow range where combinatorial expansion and constraint relaxation operate at comparable scales. The manuscript includes the full mathematical derivation, simulation results, and discussion of implications for complex systems.
Author: Costolo, Michael
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7133648592