Stable Semantic Phases under Coarse-Graining of Observation Geometries

Abstract

This preprint studies semantic stability under coarse-graining of observation geometries on Ahlfors-type metric-measure spaces. It defines stable semantic phases across resolutions and proves coarse-graining results that preserve effective dimension, local regularity, and threshold structure within controlled bounds.

Keywords

• large language models
• observation geometries
• semantic phase transitions
• multi-scale semantics
• coarse-graining
• stable semantic phases
• ahlfors-regular metric spaces
• poisson–boolean percolation
• random geometric graphs
• sharp threshold phenomena
• renormalisation-type parameter maps

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