## 1. Data

We take TESS full-frame light curves for M dwarfs below 0.35 solar masses within 100 pc. We remove stars with a brighter neighbour inside two TESS pixels, since a blended neighbour can supply the period. Rotation periods come from a Lomb-Scargle periodogram with a false-alarm threshold of 0.1 per cent.

## 2. Saturation

Plotting activity against Rossby number, the relation is flat below a Rossby number of 0.09 and falls as a power law with index 2.1 above it. We fit a broken power law with the break as a free parameter and report the posterior median.

## 3. Discussion

The saturation point is lower than earlier estimates for partly convective stars. Removing blends moved the break, which suggests that earlier samples mixed periods from neighbours into the fully convective population.