The Constitutive Coupling Architecture: A Category-Theoretic, Modal-Logical, and Free-Energy Framework for Synthetic Intelligence in Haugeland's Sense

Artificial intelligence research has long distinguished systems that simulate intelligent behavior from systems that synthesize it from first principles. John Haugeland labeled the second project Synthetic Intelligence, but the distinction has never received a unified, mathematically rigorous treatment. Symbolic AI, deep learning, large language models, and the standard Free Energy Principle each capture partial aspects of intelligence while leaving its constitutive, intentional, and modal dimensions unaddressed.This paper introduces the Constitutive Coupling Architecture (CCA), a framework combining three formalisms: an enriched categorical adjunction F ⊣ G modeling agent–environment coupling; a modal logic extended with an intentionality operator I_orig capturing Brentano's aboutness; and a Constitutive Free Energy (CFE) generalizing standard variational free energy with a categorical coupling term. The three combine into one object certified by a coherence operator, Ψ: a system is synthetically intelligent, in this precise sense, exactly when Ψ = 1.We prove seven theorems: soundness and weak completeness of the modal logic; irreducibility of any Ψ-coherent system to purely symbolic or purely statistical architectures; convergence of the free-energy dynamics to a stable fixed point, with conditional uniqueness; and, under a stated capacity hypothesis, non-satisfaction of the coherence certificate by standard large language models, including under continuous fine-tuning. This last result concerns a specific formal property, not behavioral competence, a scope discussed at the end of the paper. The treatment is self-contained; algorithmic instantiation and empirical validation are left to future work.