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 $β=0.37\pm0.12^\circ$. The differential test uses existing data and can serve as a validation layer for future $EB$-based birefringence analyses.