A Hemispherical Test of the Rotation Field: Difference Statistics for a Dipole Modulation of the Angle

This paper examines whether a rotation angle that differs between opposite hemispheres of the sky could be detected with patch-level uncertainties representative of published analyses, and how large a hemispherical difference would need to be before the test could see it. The calculation is performed from stated assumptions and published polarisation measurements, using the deposited script so that every quoted number can be reproduced. The headline outputs are: sigma diff deg = 0.283; significance at 0p4 = 1.4; per hemisphere err deg = 0.20. The treatment separates what the published measurements supply from what a theoretical framework must additionally provide; where a required quantity is not supplied, that absence is reported plainly as a negative result rather than replaced by an assumed value. The study is computed from stated assumptions and published inputs; it is not a new measurement. SIMULATED, NOT MEASURED in the sense that all derived quantities are calculated, not observed.