Hallucination as Geometric Overflow under v43: Boundary-Condition Failure in Large Language Models

Hallucination in large language models is commonly framed as a stochastic error or a knowledge-deficit phenomenon. This article proposes an alternative geometric interpretation: hallucination emerges when generative trajectories continue beyond admissible semantic bounds under conditions of semantic stress such as ambiguity, instability, and nonlinearity. Rather than modelling latent representational geometry, the paper introduces a constraint-geometry perspective that treats hallucination as geometric overflow—continued motion where termination, redirection, or abstention would preserve truth-orientation. Forced-answer regimes are shown to deform admissible regions, amplifying hallucination. The contribution is architectural and diagnostic rather than mitigative or safety-oriented, clarifying boundary conditions under which truth-oriented generation remains possible without claiming to eliminate hallucination or to provide alignment mechanisms. This work belongs to the Architecture of Limitation research program.