  Magnetic reconnection can power bright, rapid flares originating from the
inner magnetosphere of accreting black holes. We conduct extremely high
resolution ($5376\times2304\times2304$ cells) general-relativistic
magnetohydrodynamics simulations, capturing plasmoid-mediated reconnection in a
3D magnetically arrested disk for the first time. We show that an equatorial,
plasmoid-unstable current sheet forms in a transient, non-axisymmetric,
low-density magnetosphere within the inner few Schwarzschild radii. Magnetic
flux bundles escape from the event horizon through reconnection at the
universal plasmoid-mediated rate in this current sheet. The reconnection feeds
on the highly-magnetized plasma in the jets and heats the plasma that ends up
trapped in flux bundles to temperatures proportional to the jet's
magnetization. The escaped flux bundles can complete a full orbit as
low-density hot spots, consistent with Sgr A$^{*}$ observations by the GRAVITY
interferometer. Reconnection near the horizon produces sufficiently energetic
plasma to explain flares from accreting black holes, such as the TeV emission
observed from M87. The drop in mass accretion rate during the flare, and the
resulting low-density magnetosphere make it easier for very high energy photons
produced by reconnection-accelerated particles to escape. The extreme
resolution results in a converged plasmoid-mediated reconnection rate that
directly determines the timescales and properties of the flare.
