Preserving Shared Calibration Uncertainty in Reusable Astrophysical Data: Query-Specific Covariance Compression with Gaia DR3

Shared calibration errors can survive the averaging of a large catalogue even when every released row retains a plausible marginal uncertainty. We formulate a query-specific alternative to discarding such dependence or distributing a full covariance matrix. For a covariance model (C = D + MM^{T}) and a declared family of fixed linear queries (A), an orthogonal projection of the calibration coordinates preserves (ACA^{T}) exactly using (\operatorname{rank}(AM)) modes. This rank is minimal among positive-semidefinite factor representations that preserve the query calibration covariance. A residual operator gives an explicit test for any later query. We evaluate the construction using positions, parallaxes and reported errors for 13,605 retained Gaia DR3 active-galactic-nucleus reference sources. The six spatial calibration modes in the experiment are specified uncertainty scenarios, not an empirical estimate of Gaia’s between-source covariance. Two retained modes reproduce the joint covariance of two registered queries to a relative residual of (5.56 \times 10^{-16}). In the stated Gaussian scenario, replacing shared dependence by row-level variances gives only 28.51% analytic coverage for a nominal 95% interval on the weighted mean. An equal-rank global covariance approximation gives 92.80% coverage for a spatial contrast, whereas the query-preserving representation retains 95% for both queries. An additional query outside the registered family exposes the limitation of the compressed representation. The result is a reproducible uncertainty-interchange method with an explicit scientific scope, rather than a new empirical calibration of the Gaia reference frame. Keywords: astrometric uncertainty; shared calibration; covariance compression; Gaia DR3; data interoperability; scientific reproducibility.