Semantic Geometry for policy-constrained interpretation

TL;DR

This paper introduces a geometric framework for policy-constrained semantic interpretation that prevents hallucinated commitments, with proven optimality and empirical validation showing zero hallucinations in regulated financial data.

Contribution

The paper proposes a novel geometric approach to semantic interpretation that integrates policy constraints and guarantees no hallucinated commitments in high-stakes domains.

Findings

Zero hallucinated approvals in large-scale financial data

Framework is provably optimal in information-theoretic terms

Connects semantic interpretation with information theory and sheaf semantics

Abstract

We present a geometric framework for policy-constrained semantic interpretation that provably prevents hallucinated commitments in high-stakes domains. Semantic meaning is represented as direction on a unit sphere, evidence is modeled as sets of witness vectors, and admissible interpretations correspond to spherical convex regions. Policy constraints are introduced as explicit priors defined over the same manifold, separated from evidence geometry. Interpretation reduces to constrained optimization over admissible regions, with refusal emerging as a topologically necessary outcome under contradiction or policy exclusion. We connect this framework to information theory, Bayesian inference, and sheaf-theoretic semantics, proving that our complexity bounds are information-theoretically optimal. Empirical validation on large scale regulated financial data demonstrates zero hallucinated approvals across multiple policy regimes-the first such result at scale.