The Mathematical Foundations of Constrained Object Hierarchies-A Universal Framework for World Modeling, General Intelligence and Agentic Systems

Constrained Object Hierarchies (COH) offer a unified theoretical foundation for artificial general intelligence (AGI), rooted in neuroscience principles and developed with full mathematical rigor. This paper presents the complete formalization of COH theory, showing how intelligence emerges from hierarchically composed structures governed by adaptive optimization constraints. We introduce precise definitions, establish core properties of soundness and completeness, and situate COH within established mathematical frameworks including category theory, dynamical systems, and information theory. Building on this foundation, we prove three central theorems that demonstrate COH’s practical significance for AGI: guaranteeing high‑fidelity world modeling, preventing jagged or non-smooth intelligence behaviors, and enabling the construction of coherent agentic systems. These results provide quantitative bounds on representational accuracy, generalization performance, and decision-making complexity. Collectively, the findings show that COH delivers a mathematically rigorous, interpretable, and scalable basis for modeling intelligent systems across six heterogeneous domains, while preserving the flexibility required for general intelligence and ensuring explicit guarantees for safety and transparency.