Parity-Sensitive Cosmology III: A Sparse-Sample Scalar Test for Global Jet Alignment

Understanding the large-scale distribution of spin directions in extragalactic sources requires careful treatment of projection effects intrinsic to observations made from a single vantage point in curved spacetime. While the intrinsic spin axis of radio jets (or galaxies) is defined in the source frame, observations provide only a 2D projection onto the sky plane, often modulated by Doppler boosting or resolution-limited morphology. To perform any meaningful statistical test of isotropy or parity symmetry on cosmological scales, spin vectors must be consistently mapped into the observer’s frame in three dimensions, accounting for inclination, projection, and the spherical geometry of the sky.