Holographic covering and the fortuity of black holes

We propose a classification of BPS states in holographic CFTs into monotone and fortuitous, based on their behaviors in the large $N$ limit. Intuitively, monotone BPS states form infinite sequences with increasing rank $N$, while fortuitous ones exist within finite ranges of consecutive ranks. A precise definition is formulated using supercharge cohomology. We conjecture that under the AdS/CFT correspondence, monotone BPS states are dual to smooth horizonless geometries, and fortuitous ones are responsible for typical black hole microstates and give dominant contributions to the entropy. We present supporting evidence for our conjectures in the $\mathcal{N}=4$ SYM and symmetric product orbifolds.