Probing Multi-Agent Coordination with Multivariate Multifractal Detrended Fluctuation Analysis

Understanding how information access shapes language-model team interactions requires diagnostics that capture semantic variation across scales. We introduce a semantic-trajectory diagnostic that applies a multivariate generalization of multifractal detrended fluctuation analysis to message embeddings, quantifying how accumulated variation changes with message window length under different weightings of small and large residual fluctuations. We test its sensitivity to information access by comparing shared and restricted access to prior exchanges in 100 matched pairs of four-agent realizations across four repeated task templates. Four structured reordering controls probe the contribution of message order. Shared history is associated with broader fluctuation-scaling spectra, with the largest differences at orders emphasizing smaller residual fluctuations. This contrast persists across alternative ordering controls and stricter fit requirements, and its direction is consistent across five encoders. These results demonstrate that the diagnostic detects differences in multiscale semantic structure associated with team information access in a consistent direction and that it generalizes across embedding models and robustness checks. By combining a multiscale semantic measure with a controlled history-access comparison, this work provides a methodological foundation for studying language-model team interactions and for identifying semantic failures.