Anisotropic Birefringence: Patch-to-Patch Variance Around a Uniform Angle and What It Adds to the Mean

This paper examines what a direction-dependent rotation field would add on top of a uniform angle, how large its patch-to-patch scatter would be for representative published power levels, and why the variance is a separate observable from the mean. 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: rms at 0p05 = 0.224; rms at 0p10 = 0.316; mean deg = 0.30; patch scatter over mean pct = 75. 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.