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Gyrochronology allows the derivation of ages for cool main sequence stars based on their observed rotation periods and masses, or a suitable proxy thereof. It is increasingly well-explored for FGK stars, but requires further measurements for older ages and K-M-type stars. We study the nearby, 3 Gyr-old open cluster Ruprecht 147 to compare it with the previously-studied, but far more distant, NGC 6819 cluster, and especially to measure cooler stars than was previously possible there. We constructed an inclusive list of 102 cluster members from prior work, including Gaia DR2, and for which light curves were also obtained during Campaign 7 of the Kepler/K2 space mission. [...] Periodic signals are found for 32 stars, 21 of which are considered to be both highly reliable and to represent single, or effectively single, Ru147 stars. These stars cover the spectral types from late-F to mid-M stars, and they have periods ranging from 6d-32d, allowing for a comparison of Ruprecht 147 to both of the other open clusters and to models of rotational spindown. The derived rotation periods connect reasonably to, overlap with, and extend to lower masses the known rotation period distribution of the 2.5 Gyr-old cluster NGC 6819. The data confirm that cool stars lie on a single surface in rotation period-mass-age space, and they simultaneously challenge its commonly assumed shape. The shape at the low mass region of the color-period diagram at the age of Ru147 favors a recently-proposed model, which requires a third mass-dependent timescale in addition to the two timescales required by a former model, suggesting that a third physical process is required to model rotating stars effectively.