The compact multiple system HIP 41431.

The nearby (50 pc) K7V dwarf HIP~41431 (EPIC 212096658) is a compact 3-tier hierarchy. Three K7V stars with similar masses, from 0.61 to 0.63 solar, make a triple-lined spectroscopic system where the inner binary with a period of 2.9 days is eclipsing, and the outer companion on a 59-day orbit exerts strong dynamical influence revealed by the eclipse time variation in the {\em Kepler} photometry. Moreover, the centre-of-mass of the triple system moves on a 3.9-year orbit, modulating the proper motion. The mass of the 4-th star is 0.35 solar. The Kepler and ground-based photometry and radial velocities from four different spectrographs are used to adjust the spectro-photodynamical model that accounts for dynamical interaction. The mutual inclination between the two inner orbits is 2\fdg16$\pm$0\fdg11, while the outer orbit is inclined to their common plane by 21\degr$\pm$16\degr. The inner orbit precesses under the influence of both outer orbits, causing observable variation of the eclipse depth. Moreover, the phase of the inner binary is strongly modulated with a 59-day period and its line of apsides precesses. The middle orbit with eccentricity $e=0.28$ also precesses, causing the observed variation of its radial velocity curve. Masses and other parameters of stars in this unique hierarchy are determined. This system is dynamically stable and likely old.