The Recursive Coherence Principle: A Formal Constraint on Scalable Intelligence, Alignment, and Reasoning Architecture

TL;DR

This paper introduces the Recursive Coherence Principle (RCP), a formal constraint ensuring semantic consistency across recursive reasoning systems, and defines the Functional Model of Intelligence (FMI) as the architecture that satisfies RCP at any scale, addressing core issues like alignment and stability.

Contribution

The paper formalizes the RCP as a foundational constraint for scalable intelligence and introduces the FMI as the unique operator satisfying RCP, providing a new structural approach to AI coherence and alignment.

Findings

RCP ensures semantic coherence across recursive reasoning layers.

FMI is the only known operator satisfying RCP at any scale.

Lack of FMI leads to coherence breakdown and AI issues like misalignment.

Abstract

Intelligence-biological, artificial, or collective-requires structural coherence across recursive reasoning processes to scale effectively. As complex systems grow, coherence becomes fragile unless a higher-order structure ensures semantic consistency. This paper introduces the Recursive Coherence Principle (RCP): a foundational constraint stating that for any reasoning system of order N, composed of systems operating over conceptual spaces of order N-1, semantic coherence is preserved only by a recursively evaluable generalization operator that spans and aligns those lower-order conceptual spaces. Crucially, this coherence enables structural alignment. Without recursive coherence, no system can reliably preserve goals, meanings, or reasoning consistency at scale. We formally define the Functional Model of Intelligence (FMI) as the only known operator capable of satisfying the RCP at any scale. The FMI is a minimal, composable architecture with internal functions (evaluation, modeling, adaptation, stability, decomposition, bridging) and external functions (storage, recall, System 1 and System 2 reasoning) vital for preserving semantic structure across inference and coordination layers. We prove that any system lacking the FMI will experience recursive coherence breakdown as it scales, arguing that common AI issues like misalignment, hallucination, and instability are symptoms of this structural coherence loss. Unlike other foundational principles, RCP uniquely captures the internal, recursive dynamics needed for coherent, alignable intelligence, modeling semantic coherence under recursion. This work significantly impacts AI alignment, advocating a shift from behavioral constraints to structural coherence, and offers a pathway for safely generalizable, robustly coherent AI at scale.