The Mathematical Foundations of Constrained Object Hierarchies: A Theory of General Intelligence

Constrained Object Hierarchies (COH) present a comprehensive theoretical framework for artificial general intelligence (AGI) grounded in neuroscience principles. This paper develops the complete mathematical foundation of COH theory, demonstrating how intelligence emerges from hierarchical compositional structures constrained by adaptive optimization principles. We provide formal definitions, prove theorems regarding the theory's soundness and completeness, and establish connections with established mathematical frameworks including category theory, dynamical systems, and information theory. The paper shows that COH provides a mathematically rigorous basis for modeling intelligent systems across domains while maintaining the flexibility required for general intelligence.