AI Completionism: A Structural Validation Framework for LLM Outputs using Typed B-Graph Rewriting Systems (TGRS)

AI Completionism: A Structural Validation Framework for LLM Outputs using Typed B-Graph Rewriting Systems (TGRS) Y. Okada Mathematical Completionism Research Institute, Japan Abstract We propose AI Completionism, a structural validation framework for detecting and mitigating ontology-level structural hallucinations in Large Language Model (LLM) outputs. Hallucinations are characterized as violations of typed semantic constraints within a Typed B-Graph Rewriting System (TGRS). Hereafter, we refer to the Typed B-Graph Rewriting System as TGRS throughout this paper. The framework models LLM reasoning trajectories as finite compositions of typed graph morphisms and verifies semantic admissibility relative to a domain ontology and constraint system. We further introduce Asymmetric Divergence Pair (ADP) analysis for identifying unsafe reasoning branches that violate semantic consistency. Under finite structural reduction assumptions, structurally detectable hallucinations can be identified and eliminated through finite admissibility verification. This transforms a subclass of hallucination mitigation from a probabilistic generation problem into a decidable structural verification problem.