Abstract Large language models frequently preserve local linguistic coherence while progressively losing the semantic orientation that initially constrained their reasoning trajectory. Existing mitigation strategies—such as repeated prompt engineering, retrieval augmentation, self-evaluation, and post-generation filtering—often reconstruct criterion linguistically at each step, increasing contextual overhead while remaining vulnerable to long-horizon semantic drift. This work presents the Axiomatic Criterion Atlas (ACA) v0.3 together with its companion methodology for artifact construction. ACA is a geometry-based framework for persistent semantic orientation in generative systems. It externalizes criterion into reproducible geometric artifacts composed of semantic fields, directional invariants, triaxial projections, artifact metadata, validation structures, and runtime-facing manifests. Its Triaxial Criterion Projection (F–C–P) models semantic orientation across Foundation, Context, and Principle, allowing derived operational fields—such as scientific inquiry, security training, phishing attack detection, and fictional teaching—to emerge from stable configurations rather than from fixed primitive labels. The central empirical finding is that criterion is better observed in semantic trajectories than in isolated classifications. A statement may remain locally coherent and contextually compatible while gradually inverting the invariant structure that gives its field epistemic value. ACA therefore separates contextual coherence from epistemic integrity, formalizing criterion drift as directional loss of invariant orientation within otherwise coherent semantic space. Validation across 100 individual cases, 6 trajectory cases, and 36 diagnostic cases yielded 85.71% axis accuracy, 6/6 trajectory matches, and 90.16% diagnostic tag recall. A runtime benchmark further showed a 70.26% reduction in criterion-preservation token overhead compared with prompt-heavy alignment strategies. The companion methodology addresses the upstream question on which such runtime preservation depends: which semantic structures deserve to become persistent ACA artifacts? It introduces an artifact ontology distinguishing non-contingent artifacts, contingent contextual artifacts, derived operational artifacts, diagnostic projections, and runtime policy states. It further formalizes attractor selection, invariant justification, pole construction, boundary testing, artifact promotion, and reproducibility requirements. Under this methodology, semantic artifacts are not arbitrary prompt-derived categories; they are promoted only when they demonstrate geometric stability, relational coherence, boundary clarity, criterion relevance, trajectory utility, invariant compatibility, reproducibility, and runtime compatibility. ACA does not claim universal truth verification, consciousness, moral certainty, or replacement of human judgment. Its narrower contribution is a reproducible geometric and methodological infrastructure for operational criterion preservation in generative systems. Reliable long-horizon reasoning, we argue, depends not only on probabilistic continuation or contextual similarity, but on preserving the orientation of meaning as context, objectives, and semantic trajectories evolve. Keywords: semantic orientation, criterion preservation, geometric artifacts, attractor selection, invariant justification, triaxial projection, semantic drift, artifact promotion, AI alignment, generative systems
Rosati Beristain Ernesto (Wed,) studied this question.