Diagnosing the rho-region inter-experiment mode in LO-HVP windows: A CMD-3-aligned covariance test and optimised future-window design.

This record contains version 6 of a covariance mode diagnostic of the e+e- -> pi+pi- input to muon g-2 leading order hadronic vacuum polarization (LO-HVP) Euclidean window comparisons. The manuscript isolates a CMD-3 aligned, between-experiment mode, in the shared (ID,FULL) window plane, localizes much of the variance to the rho region, adds a sensitivity optimised smooth window scan, reports a leave-one-branch-out optimization control, and provides a bounded required connection profile for 'CMD-3 to rest' comparisons. The release includes the manuscript PDF and LaTeX source, figure files, processed data products, public input data snapshots, a fixed mode preregistration for future KNTW style combinations, a one page CMD-3 convention/ covariance query note, citation metadata, README, and checksums. The work is diagnostic. It does not determine which experiment is correct, does not supersede the primary experimental publications or HEPData records, and does not provide a complete Standard-Model update. Upstream experimental tables retain their original record status and terms; author created manuscript text, figures, processed outputs, and notes are released under CC-BY-4.0. Project record: 10.17605/OSF.IO/CKJBU Prereg: 10.17605/OSF.IO/3CXFW