Four fixed covariances give 25% to 93% detection power for a 3 m/s signal at 24.160 days in 24 CARMENES GJ 685 velocities

We test whether 24 public CARMENES DR1 velocities of GJ 685 can detect its reported planet signal. We fix the period at 24.160 days and fit a circular mean with free phase. For a uniform distribution of phase, a 3 m/s signal has 92.76% mean detection power with a fixed extra white-noise term of 1.46 m/s and no correlated activity. For a fixed Gaussian activity covariance with the HARPS-N median parameters, mean power is 24.63%. Power ranges from 14.15% to 35.58% with phase at a 1% false alarm threshold. Mean power reaches 90% at 6.14 m/s. The calculation is checked with 100,000 simulated velocity vectors. When the noise amplitudes are fitted, the observed likelihood-ratio statistic is 6.900. A 1,000-trial parametric bootstrap gives a conditional null tail probability of 0.0559. The survey already reported no detected signal for this target and supplied a detection map. This work adds explicit phase and covariance sensitivity, simulation calibration, and a reproducible data package. We also verify that four velocity fields in the retrieved TAP metadata have km/s labels but contain m/s values. Transfer of the HARPS-N covariance to CARMENES is an assumption. The fitted CARMENES activity amplitude is smaller. The results do not exclude the reported planet. Source code, frozen inputs, provenance, simulations, and figures are preserved.

GJ 685 · CARMENES · radial velocity · stellar activity · detection power · Gaussian process · data provenance