Semantic Geometry and Hallucination Behavior in Large Language Models

This work presents a quantitative and reproducible evaluation frameworkfor hallucination behavior in large language models (LLMs),grounded in a geometric interpretation of semantic convergence. Rather than treating hallucination as a sporadic internal failure,we analyze it as a systematic behavioral phenomenon that emergesunder specific prompting regimes.In particular, we focus on the interaction betweenprompt ambiguity, response constraints, and model-specific stability. Using controlled synthetic tasks (Task B),we evaluate multiple LLMs under two regimes:an abstain-allowed setting and a forced-response setting.This design enables explicit separation betweenmodel uncertainty, abstention behavior, and erroneous confident outputs. The evaluation introduces a set of quantitative metrics, including:- accuracy under ambiguity,- unknown (abstention) rate and correctness,- hallucination frequency (incorrect confident responses),- forced-unknown violation rate. Across repeated trials with fixed random seeds,we demonstrate that hallucination patterns arestable, model-dependent, and highly reproducible.These results indicate that hallucination is not random noise,but a structured outcome of the interaction betweeninput conditions and internal model dynamics. Conceptually, this analysis is consistent with the Protiform framework(fluctuation → convergence → structure),in which hallucination corresponds to a breakdown of semantic convergenceunder ill-posed or over-constrained inputs.However, the present release emphasizes empirical behaviorand reproducible evaluation, rather than proposing a new training algorithm. This release includes:- the full manuscript (PDF),- supplementary figures,- a complete evaluation dataset (JSONL),- reproducible Python evaluation and aggregation scripts,- documented execution environments and command histories. Together, these materials provide an open benchmarkfor studying hallucination as a behavioral and geometric stability problem,and serve as a foundation for future work onrobust reasoning and stable semantics in LLMs.Reproducible evaluation code and datasets are available on GitHub:(copy & paste the URL below):https://github.com/hideyuki49/llm-hallucination-geometry