New AI framework reframes hallucination as unsupported canonicalization

A new formal paper by Hai Hai Fu, posted on arXiv (2608.07476) on April 27, 2026, presents a unified framework for “determinization” in structure theories—mathematical systems defined as triples T = (Σ, A, I) of signature, axioms, and inference policy. The work distinguishes three levels of canonicalization: closure stabilization (per-seed convergence), global completion (seed-independent convergence), and full determinization (a unique admissible interpretation). It also classifies non-determinism into epistemic plurality (Type E) and structural plurality (Type S), with a refined Type S-strong subclass defined by the absence of common upper bounds.

The paper proposes two canonicalization mechanisms: operator-based completion and selector-based construction. It proves that pure inference-based completion reduces to a saturated closure operator under positive, non-retractive rules with an additional soundness condition. For Type E theories, closure stabilization is established, but full determinization depends on a global confluence property that remains open. For Type S-strong theories, determinization is achieved via canonical selection. The author further shows that multi-level canonicalization forms a structurally non-commutative system via staged operators, and provides a conditional classification theorem reducing intrinsic mechanisms to closure or selection. Notably, the framework is applied to LLM-assisted reasoning, where hallucination is interpreted as unsupported canonicalization—a perspective that could inform future robustness techniques for AI systems.