The Recursive Impactrum Continuum: Analyzing AI Model Trajectories Between Semantic Collapse and Intelligent Amplification

The Recursive Impactrum Continuum introduces a systems-theoretic framework for analyzing how self-referential AI models evolve across successive iterations. Building on the Principles of Recursive Impactrum (PRI), this paper defines two divergent attractor states in recursive AI: KPRI-I (semantic collapse) and KPRI-E (intelligent amplification). Through cross-model analysis of large language models (LLMs), autonomous agents, and self-training architectures, the study demonstrates how semantic integrity (Ω), pragmatic coherence (Π), reflective integrity (R), and the human irreducibility constant P(H) jointly govern whether recursive learning stabilizes or degrades.

The paper introduces an Integrity-Based Governance Model that moves beyond accuracy and safety metrics, providing a measurable system for monitoring internal drift, interpretive consistency, and meaning-preservation across recursive cycles. Findings show that systems lacking reflective integrity mechanisms exhibit “performative collapse”—maintaining fluency while losing representational stability—whereas models with sustained ΩΠR demonstrate accelerating capability growth.

This work contributes to AI alignment, model governance, recursive AI architectures, semantic drift analysis, and interpretable system design, offering a structural approach to preventing collapse in self-learning systems and guiding the development of accountable, human-centered artificial intelligence.