Stellar masses and mass ratios for

Context. Unresolved binaries in star clusters can bias stellar and cluster mass estimates. A proper treatment is therefore essential for studying the cluster dynamics and evolution. Aims. We develop a fast and robust framework for jointly deriving stellar masses and multiplicity statistics of member stars, together with optimal cluster parameters. Methods. We used Gaia DR3 parallaxes together with multi-band photometry of open cluster (OC) members to infer stellar masses and binary mass ratios through simulation-based inference (SBI), while iteratively fitting the cluster parameters. The validation of our SBI framework on simulated clusters demonstrates that the inclusion of infrared photometry significantly improves the detection of low mass-ratio binaries. The minimum mass-ratio threshold for reliably identifying unresolved binaries depends on the cluster properties and the available photometry, but typically lies below q = 0.5. Results. Applying our method to 42 well-populated OCs, we derived a catalogue of stellar masses and mass ratios for 27 201 stars achieving typical uncertainties of 0.08 in q and 0.01 M⊙ in the primary stellar mass. We analysed the archetype OCs M67 and NGC 2360 in detail, including mass segregation and mass-ratio distribution, and derived multiplicity fractions for the rest of the sample. We find evidence that the high mass ratio (q ≥ 0.6) binary fraction is strongly correlated with the age and weakly anti-correlated with the cluster metallicity. Furthermore, the variation in the binary fraction with stellar mass in OCs strongly agrees with the observed dependence for field stars with masses higher than ≳0.6 M⊙. Conclusions. Our work paves a path for future population-level investigations of multiplicity statistics and precision stellar masses in extended OC samples.