With 2 m/s extra Gaussian noise, Gliese 12 velocities give 95% bounds below 1.73 m/s for one circular signal at 34, 39, or 58 days

We test sensitivity to one added circular signal in the public HARPS-N, ESPRESSO, and CARMENES velocities of Gliese 12. The main sample has 192 measurements. We fit separate instrument offsets and H-alpha slopes, with a signed amplitude at the fixed transit clock of planet b. We assume independent Gaussian errors with quoted variance plus (2 m/s)^2. At fixed periods of 34, 39, and 58 days, conservative 95% upper amplitude bounds are 1.724, 1.418, and 1.603 m/s. A separate power calculation gives sufficient amplitudes of 1.706, 1.697, and 1.743 m/s for at least 95% detection power at every phase. This calculation uses a conservative 1% false alarm threshold across 1099 frequencies from 5 to 100 days. The largest main-model residual peak is at 31.398 days, with a chi-square decrease of 29.887. Its analytic upper bound on the global null p value is 0.000356 under that fixed model. The score falls below the conservative threshold when a specified 30-day covariance is added with the same total diagonal variance. Activity terms also change the peak and sensitivity. We report all nine planned models and a denser grid check. Full GLS fits, injections, Gaussian simulations, and a fresh-directory repeat check the calculation. The bounds apply to one circular signal at each fixed period under the stated model. They do not exclude the full published multi-signal models or establish a new planet. The package preserves the source data, provenance, row selections, information matrices, results, figures, code, and reproduction instructions.

Gliese 12 · radial velocities · detection sensitivity · amplitude bounds · orbital phase · stellar activity · fixed Gaussian covariance · reproducible data