The paper aims to improve the census of open clusters (OCs) by distinguishing between bound and unbound clusters using their masses, radii, and dynamics. The authors derived corrected photometric masses for 6956 clusters and used these masses to compute the Jacobi radii, which are used to identify bound and unbound clusters. They found that only 5647 (79%) of the clusters are compatible with bound OCs, with only 11% within 250 pc. The study also derived a completeness-corrected age and mass function for the OC census, estimating that the Milky Way contains approximately 1.3 × 10^5 open clusters, with only about 4% currently known. The cluster mass measurements are the largest to date and are used to infer the mass-dependent completeness limit of the OC census, showing that it is complete within 1.8 kpc for objects heavier than 230 M⊙. The moving groups in the sample show different trends in their size as a function of age and mass, suggesting they are unbound and undergoing different dynamical processes. The paper concludes by demonstrating the effectiveness of Jacobi radii in distinguishing between bound and unbound star clusters and publishes an updated star cluster catalogue with improved classifications.The paper aims to improve the census of open clusters (OCs) by distinguishing between bound and unbound clusters using their masses, radii, and dynamics. The authors derived corrected photometric masses for 6956 clusters and used these masses to compute the Jacobi radii, which are used to identify bound and unbound clusters. They found that only 5647 (79%) of the clusters are compatible with bound OCs, with only 11% within 250 pc. The study also derived a completeness-corrected age and mass function for the OC census, estimating that the Milky Way contains approximately 1.3 × 10^5 open clusters, with only about 4% currently known. The cluster mass measurements are the largest to date and are used to infer the mass-dependent completeness limit of the OC census, showing that it is complete within 1.8 kpc for objects heavier than 230 M⊙. The moving groups in the sample show different trends in their size as a function of age and mass, suggesting they are unbound and undergoing different dynamical processes. The paper concludes by demonstrating the effectiveness of Jacobi radii in distinguishing between bound and unbound star clusters and publishes an updated star cluster catalogue with improved classifications.