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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.<\/jats:p>\n<jats:p><jats:italic>Aims<\/jats:italic>. 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.<\/jats:p>\n<jats:p><jats:italic>Methods<\/jats:italic>. 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.<\/jats:p>\n<jats:p><jats:italic>Results<\/jats:italic>. TOI-732b is an ultrashort-period planet (<jats:italic>P<\/jats:italic> = 0.76837931<jats:sub>-0.00000042<\/jats:sub><jats:sup>+0.0000039<\/jats:sup> days) with a radius <jats:italic>R<\/jats:italic><jats:sub>b<\/jats:sub> = 1.325<jats:sub>-0.058<\/jats:sub><jats:sup>+0.057<\/jats:sup><jats:italic>R<\/jats:italic><jats:sub>\u2295<\/jats:sub>, a mass <jats:italic>M<\/jats:italic><jats:sub>b<\/jats:sub> = 2.46 \u00b1 0.19 <jats:italic>M<\/jats:italic><jats:sub>\u2295<\/jats:sub>, and thus a mean density <jats:italic>\u03c1<\/jats:italic><jats:sub>b<\/jats:sub> = 5.8<jats:sub>-0.8<\/jats:sub><jats:sup>+1.0<\/jats:sup> g cm<jats:sup>-3<\/jats:sup>, while the outer planet at <jats:italic>P<\/jats:italic> = 12.252284 \u00b1 0.000013 days has <jats:italic>R<\/jats:italic><jats:sub>c<\/jats:sub>  = 2.39<jats:sub>-0.11<\/jats:sub><jats:sup>+0.10<\/jats:sup><jats:italic>R<\/jats:italic><jats:sub>\u2295<\/jats:sub>, <jats:italic>M<\/jats:italic><jats:sub>c<\/jats:sub> = 8.04<jats:sub>-0.48<\/jats:sub><jats:sup>+0.50<\/jats:sup><jats:italic>M<\/jats:italic><jats:sub>\u2295<\/jats:sub>, and thus <jats:italic>\u03c1<\/jats:italic><jats:sub>c<\/jats:sub> = 3.24<jats:sub>-0.43<\/jats:sub><jats:sup>+0.55<\/jats:sup> g cm<jats:sup>-3<\/jats:sup>. 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 log <jats:italic>R<\/jats:italic><jats:sub>p,valley<\/jats:sub> \/ d log<jats:italic>P<\/jats:italic> = -0.065<jats:sub>-0.013<\/jats:sub><jats:sup>+0.024<\/jats:sup>, 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 \u03c1^<jats:sub>valley<\/jats:sub> \/ d log <jats:italic>P<\/jats:italic> = -0.02<jats:sub>-0.04<\/jats:sub><jats:sup>+0.12<\/jats:sup>.<\/jats:p>\n<jats:p><jats:italic>Conclusions<\/jats:italic>. 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.<\/jats:p>","DOI":"10.1051\/0004-6361\/202348180","type":"journal-article","created":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T19:45:06Z","timestamp":1701287106000},"page":"A66","source":"Crossref","is-referenced-by-count":32,"title":["Characterising TOI-732 b and c: New insights into the M-dwarf radius and density valley"],"prefix":"10.1051","volume":"682","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1916-5935","authenticated-orcid":false,"given":"A.","family":"Bonfanti","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2404-2427","authenticated-orcid":false,"given":"M.","family":"Brady","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8749-1962","authenticated-orcid":false,"given":"T. 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