Under independent Gaussian errors, free parallax modes through degree 8 leave a 0.93% formal dipole error reduction for 253,953 Gaia-CRF3 sources

Quasar parallaxes can help reduce proper-motion errors. Unknown parallax calibration can also change the fitted motion field. We measure how much formal dipole precision remains when smooth residual parallax means are free. We use 253,953 public Gaia-CRF3 sources with five-parameter solutions and a fixed random-index selection. We fit the full per-source parallax and motion covariance. The primary motion model has an electric dipole and a rigid rotation. With the Z5 parallax mean fixed, the geometric dipole standard error is 2.17% lower than in a motion-only fit. With 81 scalar parallax modes through degree 8 free, the reduction is 0.93%. The directional variance ratios are 0.976925 to 0.984835. Degree-8 controls give reductions of 0.84% to 1.06%. A fixed-mean conditional fit transfers an imposed +10 microarcsecond parallax offset into a dipole change of (+1.736, +0.888, +0.373) microarcseconds per year. Direct full-covariance fits and 2,000 Gaussian simulations check the calculation. The conditional correction and its calibration sensitivity are known. This work adds a joint nuisance-parameter benchmark for a specified public sample. The result assumes independent Gaussian catalogue errors. It does not establish empirical coverage or a new acceleration detection. The package contains code, aggregate normal systems, all fits, figures, source queries and hashes, and reproduction instructions. Raw Gaia data can be retrieved from ESA under their source license.

Gaia-CRF3 · quasar proper motion · solar acceleration · parallax calibration · conditional covariance · nuisance parameters · reproducible astronomy