Reality-Constrained Artificial Intelligence (RCAI): A Purely Information-Theoretic Framework for Hallucination Reduction via Logit Projection

Large Language Models (LLMs) generate text by sampling from probability distributions over high-dimensional vocabularies. While highly capable, such systems may produce outputs that violate factual, logical, structural, or domain-specific constraints. Existing approaches—including fine-tuning, Reinforcement Learning from Human Feedback (RLHF), Retrieval Augmented Generation (RAG), and post-hoc verification—reduce but do not eliminate invalid generations during decoding. This paper introduces Reality-Constrained Artificial Intelligence (RCAI), a constrained-decoding framework that enforces explicit invariants at inference time through projection of model logits onto a dynamically validated admissible token set. We formalize the notion of a Truth Subspace, define a Constraint Projection Operator acting directly in logit space, and prove that any token excluded by the active constraint system has zero sampling probability under RCAI decoding. For practical deployment, we introduce approximate constraint manifolds constructed from formal logic systems, knowledge graphs, retrieval modules, and semantic entailment validators. We derive error bounds relating residual hallucination probability to the false-positive mass of the approximate constraint system. RCAI is model-agnostic and can be integrated with existing autoregressive architectures without retraining.