The origin of merging binary black holes detected through gravitational waves remains a fundamental question in astrophysics. While stellar evolution imposes an upper mass limit of $\sim 50M_{\odot }$ for black holes, some observed mergers—most notably GW190521—involve significantly more massive components, suggesting alternative formation channels. Here we investigate the maximum masses attainable by black hole mergers within active galactic nucleus (AGN) disks. Using a comprehensive semianalytic model incorporating 27 binary and environmental parameters, we explore the role of AGN disk conditions in shaping the upper end of the black hole mass spectrum. We find that an AGN disk lifetime is the dominant factor, with high-mass mergers ($\gtrsim 200M_{\odot }$) only possible if disks persist for $\gtrsim 40\mathrm{Myr}$. The joint electromagnetic observation of an AGN-assisted merger could therefore lead to a direct measurement of the age of an AGN disk.

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• Gravitational waves
• Astronomical black holes
• Galactic nuclei & quasars