Triadic Phase–Memory Embedding for Regime Detection in LHC Collider Time Series

We present a data-driven and fully reproducible method for detecting operational regimes in Large Hadron Collider (LHC) time series using a triadic phase–memory embedding. Public CMS Open Data luminosity records are analyzed at the level of luminosity sections. By combining instantaneous phase, phase velocity, and inter-channel coupling measures, the method identifies three characteristic regimes corresponding to injection/ramp, stable beams, and degradation or end-of-fill. No modification of Standard Model dynamics is assumed; the approach is purely methodological and intended for interpretable change-point and regime analysis.