  The Gaia mission is delivering exquisite astrometric data for 1.47 billion
sources, which are revolutionizing many fields in astronomy. For a small
fraction of these sources the astrometric solutions are poor, and the reported
values and uncertainties may not apply. For many analyses it is important to
recognize and excise these spurious results, commonly done by means of quality
flags in the Gaia catalog. Here we devise and apply a path to separating 'good'
from 'bad' astrometric solutions that is an order-of-magnitude cleaner than any
single flag: we achieve a purity of 99.7% and a completeness of 97.6% as
validated on our test data. We devise an extensive sample of manifestly bad
astrometric solutions: sources whose inferred parallax is 'negative' at >= 4.5
sigma; and a corresponding sample of presumably good solutions: the sources in
HEALPix patches of the sky that do not contain extremely negative parallaxes.
We then train a neural net that uses 14 pertinent Gaia catalog entries to
discriminate these two samples, captured in a single 'astrometric fidelity'
parameter. An extensive and diverse set of verification tests show that our
approach to assessing astrometric fidelity works very cleanly also in the
regime where no negative parallaxes are involved; its main limitations are in
the very low S/N regime. Our astrometric fidelities for all EDR3 can be queried
via the Virtual Observatory. In the spirit of open science, we make our code
and training/validation data public, so that our results can be easily
reproduced.
