A Gaussian interval test rejects the quoted Gaia DR3 errors for 18 eclipsing binaries with fixed eclipse limits

An earlier SCI study found excess scatter in the Gaia DR3 orbit inclinations of 18 eclipsing binaries. Its fit assumed a uniform distribution of true cos(i) values within each eclipse limit. We test the same data without a distribution for the true values. We assume independent scalar Gaussian errors and treat the quoted linear errors and the wider eclipse limits as fixed. We use the squared distance from each measured value to its allowed interval. The largest tail probability occurs when every true value is at an interval endpoint. Direct convolution gives p between 0.0076855 and 0.0076969. One million simulations give p = 0.007691. Thus the quoted-error model fails at the 0.05 level without a uniform inclination distribution. Inverting the test gives a one-sided 95% lower limit of about 1.15 on a common error multiplier. Every test that removes one star gives p < 0.045. Removing the two nearly circular orbits gives p about 0.0099. The alternative Kepler-16 orbit gives p about 0.0178. Increasing every eclipse limit by about 36% removes the rejection. A fresh Gaia download matches all 20 inherited orbit rows exactly. We reproduce the earlier uniform-orientation fit at a multiplier of 1.917. The new result is conditional on the scalar Gaussian model, independence, and valid eclipse limits. Local covariance draws show departures from linear Gaussian propagation. We infer no universal Gaia correction. The package gives the proof, code, input data, provenance, figures, numerical checks, and reproduction instructions.

Gaia DR3 · eclipsing binaries · orbital inclination · uncertainty calibration · Gaussian means · constrained inference · reproducible astronomy