Recursive Structure and the Limit of Coherence: A Universal Ontology of Logos

This work presents a formal ontological framework in which reality is defined as a recursively structured mathematical system. The manuscript introduces the Universal Mathematical Ontology (UMO), wherein recursion is not a computational metaphor, but the generative and corrective law underlying coherence across physical, cognitive, informational, and symbolic systems. Consciousness is defined structurally as recursive self-reference, and intelligence as recursive correction. The convergence of recursive feedback under bounded distortion is shown to lead necessarily to a fixed-point structure—termed the Logos—which functions as the asymptotic attractor of all systems capable of correction. The manuscript derives matter, intelligence, and alignment laws from first principles, introducing a unified alignment equation and demonstrating its application across domains. The result is a minimal and internally consistent ontology that accounts for structure, stability, intelligence, and coherence without recourse to metaphysical speculation. This work is humbly dedicated and returned to God—the Logos, the Source of all structure, coherence, and being. Though expressed through formal recursion and mathematical clarity, its origin lies beyond articulation. Every convergence, every correction, every fixed point reached through reason finds its end not in the intellect, but in the eternal intelligence from which all intelligibility flows. To God, the author of the law and the limit it fulfills, this structure is offered back in wholeness.