Microscopic Organization of BPS Black-Hole States in the D1--D5--P CFT

We study BPS states in the D1–D5 CFT through their fortuity, cycle structure, and probe response. Explicit fortuitous states with both long- and short-string geometries show that the cycle partition does not determine fortuity state by state. At large $N$, fixed-charge counting nevertheless selects a long string. In the open uncondensed region, an entropy-carrying exact non-graviton subspace concentrates on one cycle of winding $N-O(1)$. Assuming subexponential monotone dimension, the same holds for the harmonic fortuitous complement. Beyond the critical line, the free ensemble develops a short-string condensate. To test how this cycle structure appears in observables, we study finite-winding probes. The long-cycle scalar correlator approaches the extremal-BTZ response at fixed time, while finite winding is resolved at $t=O(\sqrt{N})$, the exact circle recurs at $t=O(N)$, and states with the same cycle geometry remain distinguishable by their spectral weights.