Differential Polarization Calibration: A Consistency Test for Cosmic Birefringence

The cosmic microwave background birefringence angle β is exactly degenerate with a common instrumental polarization-angle offset. The Minami--Komatsu(MK) likelihood separates these quantities using Galactic foreground polarization, so its inferred detector angles merit a diagnostic that does not reuse the foreground- EB model. We develop a birefringence-blind differential estimator from antisymmetric and symmetric cross-spectra and apply it for the first time as an explicit consistency test of a foreground-assisted birefringence analysis. For a map pair, the common rotation cancels identically and the estimator measures Δα ij=α i-α j; combining all pairs in a gauge-fixed network reconstructs the observable detector-dependent calibration pattern. Applied to eight Planck NPIPE detector-set maps, the differential reconstruction agrees with the MK pattern, giving χ 2=8.18 for seven degrees of freedom (PTE=0.32), with all shared-data residuals below 1.8σ. Because both reconstructions use the same maps, this is an independent estimator and modeling route rather than an independent-data confirmation. The agreement therefore strengthens confidence in the calibration foundation of the MK-inferred β without providing an independent absolute measurement of it. A conditional common-mode reconstruction gives β=0.37 plus or minus0.12. The differential test uses existing data and can serve as a validation layer for future EB-based birefringence analyses.