The Semantic Grounding Floor: A Structural Limit on Autonomous AI Reliability

This paper establishes a structural limit on the semantic reliability of autonomous AI systems operating under fixed grounding boundaries. It demonstrates that persistent semantic errors (“hallucinations”) are not merely consequences of insufficient model scale, data, or optimization, but arise from a fundamental constraint on internal semantic certification. The analysis introduces Semantic Horizon Mass (α_D), a deployment-dependent, measure-theoretic quantity representing the fraction of real-world inputs whose semantic correctness cannot be certified using admissible evidence available at inference time. Under an explicit justification norm, the paper derives the Semantic Grounding Floor Law, a constitutive constraint establishing that for any such system, semantic divergence is lower-bounded by α_D unless assertions are deferred. This yields a non-eliminable error–deferral tradeoff governing reliability-critical autonomy. From this constraint, the paper derives a composite scaling law that separates statistically reducible error from an irreducible semantic floor. While increased model capacity reduces learnable error, semantic divergence persists whenever systems continue to assert beyond their grounding boundary. This explains why confidence calibration, ensemble methods, extended internal reasoning, or self-verification cannot eliminate certain classes of semantic failure under fixed grounding assumptions. The paper further translates these limits into engineering practice. It presents externally auditable procedures for estimating semantic horizon mass from deployment logs, formal grounding and certification schemas, and reliability scorecards suitable for safety assurance and regulation. Semantic failures are reframed not as model defects, but as boundary-induced reliability exposure arising from finite certification budgets. The framework establishes a principled foundation for AI reliability engineering, positioning autonomy as a function of grounding boundaries, controlled deferral, and external certification rather than internal intelligence or scale alone.