Semantic Brownian Motion in Large Language Models: Failure Geometries Under Structured Absence

This publication presents an empirical behavioral study of large language models (LLMs) when confronted with a structured absence: a plausible but non-existent Unicode emoji (“the seahorse emoji”). Using an identical prompt sequence across multiple locally hosted models with differing training objectives, the study documents systematic patterns of representational drift, substitution, and narrative escalation rather than stable recognition of non-existence. These behaviors are analyzed using the descriptive framework of semantic Brownian motion, which characterizes semantic diffusion in the absence of a strong attractor toward a correct resolution. The results demonstrate that failure modes are architecture-sensitive and reproducible, reflecting training incentives rather than random hallucination. The accompanying terminal logs are provided as primary empirical evidence supporting the analysis.