The Minimal Architecture of Integrating Systems: Five Functional Dimensions of Epistemic Viability

What are the minimal structural conditions under which a system can integrate information and learn? This paper argues that exactly five functional dimensions are irreducibly necessary: difference detection (Φ), relevance weighting (Θ), transition modeling (Δ), recursive state integration (Z), and possibility maintenance (X). Together, these dimensions are coupled through a fixed-point operator κ(z*, s) that stabilizes an integrative center z*. The paper proves a Completeness Theorem: a system is epistemically viable if and only if it implements all five dimensions and their coupling admits a stable fixed point. The framework is applied to three system classes — the human brain, large language models, and evolutionary systems — and positioned relative to the Free Energy Principle, Integrated Information Theory, and classical cybernetics.