Operator Identification in Charged Lepton-Flavor Violation: Global EFT Analysis with RG Evolution, Polarization Observables, and Bayesian Model Discrimination at Future Colliders

Charged lepton-flavor violation is a null-test frontier of the Standard Model and a direct probe of physics beyond it. We present a global effective field theory (EFT) analysis across FCC-ee, ILC, CLIC, HL-LHC, HE-LHC, and muon colliders at 3 and 10 TeV, with operator identification as the primary target rather than exclusion reach alone. The analysis combines low-energy constraints, collider differential observables, and Dalitz-level $\mu\to 3e$ information in a common profile-likelihood framework. Key hadron-collider and muon-collider signal/background samples are generated at event level and propagated through Delphes detector simulation, while clean $e^+e^-$ benchmark channels are modeled with CDR-calibrated parametric response. We include one-loop renormalization-group (RG) running and operator mixing between UV matching and measurement scales, finding 10--30\% shifts in selected operator-correlation entries when comparing tree-level and RG-evolved coefficient mappings at multi-TeV matching scales. Polarization asymmetries are used to separate $c_{H\ell}$ and $c_{He}$ directions, and UV discrimination is quantified with Bayes factors for benchmark leptoquark and heavy-neutral-lepton hypotheses. The full code chain for event generation, detector response, inference, and figure reproduction is provided.