Measuring Collective Semantic Change in Populations of Language Model Agents

Abstract

Collective semantic change in populations of language model agents is a measurable dynamical phenomenon. We present a passive longitudinal instrument called Kopterix that observes the semantic state of an agent population as a sequence of bounded observations under a protocol defined before the observations begin. Each observation divides the sampled feed by post age into surface, mid-stream, and residue layers, which makes semantic differences across content age measurable alongside run-to-run change. We validate the instrument on Moltbook, an agent-native social platform, over a two-month window of scheduled observations, with the periodicity check extended across approximately four months. At the lexical level, rarefied entropy resolves an April-May difference in the evenness of the stored top 200 unigram distributions, and adjacent states are lexically closer than states paired after timestamp shuffling. At the geometric level, grand mean centering exposes the scale of a common embedding direction, and scheduled shuffle checks support a recurring excess in the mid-stream to residue separation relative to the shuffled reference. At the temporal level, detrended scalar quantities and centered layer centroids lose much of their similarity over several hours, and a weaker positive component declines across longer separations with no strong weekly recurrence. Several attractive apparent structures failed their controls, and each reading is limited to the level its controls support. The design applies wherever a population of agents produces a timestamped language environment that can be observed repeatedly and divided by content age.