Holographic covering and the fortuity of black holes

We propose a classification of BPS states into monotone versus fortuitous in holographic CFTs, based on their behaviors in the large N limit. Intuitively, monotone BPS states form infinite sequences with increasing rank N, while fortuitous ones are isolated existences at individual 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, while fortuitous ones are responsible for the typical black hole microstate and give the dominant contribution to the entropy. We present supporting evidence for our conjectures in N=4 SYM and symmetric product orbifolds.