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Context. TOI-732 is an M dwarf hosting two transiting planets that are located on the two opposite sides of the radius valley. Inferring a reliable demographics for this type of systems is key to understanding their formation and evolution mechanisms. Aims. By doubling the number of available space-based observations and increasing the number of radial velocity (RV) measurements, we aim at refining the parameters of TOI-732 b and c. We also use the results to study the slope of the radius valley and the density valley for a well-characterised sample of M-dwarf exoplanets. Methods. We performed a global Markov chain Monte Carlo analysis by jointly modelling ground-based light curves and CHEOPS and TESS observations, along with RV time series both taken from the literature and obtained with the MAROON-X spectrograph. The slopes of the M-dwarf valleys were quantified via a support vector machine (SVM) procedure. Results. TOI-732b is an ultrashort-period planet (P= 0.76837931_-0.00000042^+0.0000039days) with a radiusR_b= 1.325_-0.058^+0.057R_⊕, a massM_b= 2.46 ± 0.19M_⊕, and thus a mean densityρ_b= 5.8_-0.8^+1.0g cm^-3, while the outer planet atP= 12.252284 ± 0.000013 days hasR_c= 2.39_-0.11^+0.10R_⊕,M_c= 8.04_-0.48^+0.50M_⊕, and thusρ_c= 3.24_-0.43^+0.55g cm^-3. Even with respect to the most recently reported values, this work yields uncertainties on the transit depths and on the RV semi-amplitudes that are smaller up to a factor of ~1.6 and ~2.4 for TOI-732 b and c, respectively. Our calculations for the interior structure and the location of the planets in the mass-radius diagram lead us to classify TOI-732 b as a super-Earth and TOI-732 c as a mini-Neptune. Following the SVM approach, we quantified d logR_p,valley/ d logP= -0.065_-0.013^+0.024, which is flatter than for Sun-like stars. In line with former analyses, we note that the radius valley for M-dwarf planets is more densely populated, and we further quantify the slope of the density valley as d log ρ^_valley/ d logP= -0.02_-0.04^+0.12. Conclusions. Compared to FGK stars, the weaker dependence of the position of the radius valley on the orbital period might indicate that the formation shapes the radius valley around M dwarfs more strongly than the evolution mechanisms. 

Planets with radii between that of the Earth and Neptune (hereafter referred to as `sub-Neptunes') are found in close-in orbits around more than half of all Sun-like stars1,2. However, their composition, formation and evolution remain poorly understood3. The study of multiplanetary systems offers an opportunity to investigate the outcomes of planet formation and evolution while controlling for initial conditions and environment. Those in resonance (with their orbital periods related by a ratio of small integers) are particularly valuable because they imply a system architecture practically unchanged since its birth. Here we present the observations of six transiting planets around the bright nearby star HD 110067. We find that the planets follow a chain of resonant orbits. A dynamical study of the innermost planet triplet allowed the prediction and later confirmation of the orbits of the rest of the planets in the system. The six planets are found to be sub-Neptunes with radii ranging from 1.94R⊕ to 2.85R⊕. Three of the planets have measured masses, yielding low bulk densities that suggest the presence of large hydrogen-dominated atmospheres.