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The search for and the characterization of ultra-compact dual active galactic nuclei (AGN) are among the hottest topics of current extragalactic astrophysics. These systems involve two accreting massive black holes (MBHs) embedded within the same host galaxy, with relative projected separations from a few hundred pc down to a few pc. They are central to understanding hierarchical galaxy formation, black hole growth and demographics, and accretion─feedback coupling in the most extreme interaction phases. Even more compellingly, such tight pairs are the most direct precursors of gravitationally bound binary MBHs (sub-pc scale separation), which are among the loudest emitters of gravitational waves (GWs) in the low-frequency ranges. SHARP will deliver the first statistical census and physical characterization of ultra-compact dual AGN up to cosmic distances, finally bridging the observational gap between kpc-scale pairs and sub-pc GW-emitting binaries, and enabling a breakthrough understanding of MBH growth, feedback and co-evolution across cosmic time.

Stellar multiplicity is key in dynamical evolution of open clusters (OCs) and processes of stellar formation and evolution. Since most stars form in multiple systems, investigating how environmental properties affect their occurrence is crucial. We aim to investigate how binary fraction and mass ratios change across different OC environments. Using a sample of 773 OCs, we identified binary systems and estimated binary fractions, obtaining values in the ranges 0.10-0.85 overall and 0.06-0.79 for high mass-ratio systems. No strong dependence on age or evolutionary stage is found, while an anticorrelation between metallicity and the binary fraction is identified. However, young and old clusters exhibit distinct mass-ratio distributions. We also find that the probability of a star being the primary component increases with stellar mass. In contrast, the probability of a star belonging to a binary system increases with mass for masses below 1 solar mass, and remains between 60% and 70% for high masses. Binary systems are preferentially located in the inner regions of clusters compared to single stars, and the mean mass ratio decreases with increasing distance from the cluster center. These results suggest that the binary fraction appears to be set at early times and remains largely unaffected by cluster dynamical evolution. The concentration of binaries in the inner regions of clusters likely reduces their susceptibility to dynamical escape.