Axiomatic Criterion Atlas (ACA): Persistent Geometry-Based Semantic Navigation

Abstract (English) Large Language Models (LLMs) can maintain locally coherent language while progressively destabilizing the semantic orientation that originally constrained their reasoning process. Existing mitigation approaches rely heavily on probabilistic continuation, prompt engineering, or post-generation filtering, which often fail to distinguish between mere contextual coherence and the preservation of epistemic criterion. This work introduces the Axiomatic Criterion Atlas (ACA) Runtime: a geometry-based criterion supervision framework that models semantic reasoning as navigable evolution within a structured contextual topology. Rather than reconstructing the criterion through repeated natural language prompts, ACA externalizes it into a persistent geometric infrastructure composed of invariant orientation and contextual semantic fields. Experimental results demonstrate that semantically coherent trajectories can progressively lose epistemic orientation under rhetorical pressure, a vulnerability ACA mitigates through topology-aware runtime supervision. A comparative benchmark reveals that replacing prompt-heavy criterion preservation with ACA’s deterministic semantic orientation yields a runtime token reduction of 70.26%. These results suggest that reliable generative reasoning depends on preserving navigability through persistent semantic topology, proposing a fundamental transition from prompt-engineered control toward a reusable geometric criterion infrastructure. Resumen (Español) Los Grandes Modelos de Lenguaje (LLMs) pueden mantener una coherencia contextual mientras desestabilizan progresivamente la orientación semántica que originalmente limitaba su proceso de razonamiento. Este trabajo introduce el Axiomatic Criterion Atlas (ACA) Runtime, una arquitectura de supervisión basada en geometría que modela el razonamiento semántico como una evolución navegable dentro de una topología contextual estructurada. En lugar de reconstruir el criterio de los modelos mediante el uso continuo de prompts masivos, ACA lo externaliza hacia una infraestructura geométrica persistente. Los resultados experimentales demuestran formalmente que la coherencia contextual no equivale a la integridad epistémica. Al aplicar esta arquitectura, las pruebas de rendimiento muestran una reducción del 70.26% en el uso de tokens en tiempo de ejecución, proponiendo una transición fundamental del control basado en prompt engineering hacia una infraestructura de criterio geométrico reutilizable. Key Findings / Hallazgos Principales: Formal separation of Contextual Coherence and Epistemic Integrity ($\text{Contextual Coherence} \neq \text{Epistemic Integrity}$). Introduction of Criterion Drift detection through directional invariants in embedding spaces. A measured 70.26% reduction in operational token overhead compared to traditional prompt-heavy alignment strategies.