2026ApJ..1000..115Z

The formation channels of binary black hole (BBH) mergers detected by the LIGO/Virgo/KAGRA network remain uncertain. BBH mergers occurring inside the disks of active galactic nuclei (AGNs) may interact with surrounding gas and generate observable optical flares. We test this scenario by quantifying the spatial and temporal correlation between BBH events in GWTC-4.0 and AGN flares identified from six years of the Zwicky Transient Facility (ZTF) DR23 data. Using 80 BBH mergers selected for adequate localization, redshift reach, observing-epoch overlap, and ZTF sky coverage, we construct a likelihood for the flare-associated fraction, ${f}_{{\rm{flare}}}$, that combines each event's 3D localization with a locally estimated flare number density derived from a 3D Voronoi tessellation, while explicitly accounting for survey boundaries and incomplete catalog coverage. Adopting a postmerger time window of 200 days for potential counterparts, we infer ${f}_{{\rm{flare}}}=0.0{7}_{-0.05}^{+0.24}$ (90% confidence level). This nonzero maximum-likelihood value is driven primarily by GW190412, for which a single flare candidate (J143041.67+355703.8) is consistent in both time and spatial position. The candidate's light curve is limited to two data points during its peak, so it remains classified only as a candidate AGN flare. Excluding GW190412 yields results consistent with no association and an upper limit of ${f}_{{\rm{flare}}}\lt 0.17$ at 90% confidence level. The intrinsic properties of GW190412 and the characteristics of the candidate host AGN are broadly consistent with theoretical expectations for the AGN-disk formation channel, motivating continued, targeted electromagnetic follow-up of well-localized and highly asymmetric BBH mergers in current and upcoming time-domain surveys.