Quadratic run fits to 112 Barnard's Star epochs give a 0.356 m/s channel difference at 4.1244 days

We test whether the simultaneous blue and red velocities of Barnard's Star contain the same signals at four reported planet periods. We use all 112 paired epochs in Table 4 of Basant et al. (2025). We subtract the red velocity from the blue velocity. We fit a separate quadratic trend for each of nine observing runs, with sine and cosine terms at all four fixed periods. The difference term at 4.1244 days has an amplitude of 0.356 m/s. An independent Gaussian error model gives F(2,78) = 6.466 and p = 0.00252. An approximate run wild-bootstrap check gives 4 exceedances in 512 sign patterns. Its four-period Holm value is 0.03125. Few informative runs limit this check. Removal of any one run gives amplitudes from 0.321 to 0.403 m/s. A Huber fit gives 0.282 m/s. A coherent unit signal at 71 or 142 days leaks little into this term under the tested model. This exploratory result is conditional on fit choices made after data inspection. It does not give a full false alarm probability for the research process. The physical cause is not identified, and the result does not show that planet c is absent. The package includes source table data, independent PDF checks, provenance, code, fit tables, and figures.

Barnard's Star · MAROON-X · radial velocity · wavelength dependence · channel difference · stellar activity · reproducible research