Bootstrapping black holes at low impact parameter

We study the low-impact-parameter bootstrap for gravitational effective field theories (EFTs) using the stringy dispersion relation (SDR). After incorporating eikonal spectral support, we ask where the residual spectrum is supported in partial-wave space. On finite grids, the extremal spectra are far from featureless: a cap-saturated low-impact band tracking an order-one Giddings-Porto rotating black-hole scale appears across a substantial part of the allowed EFT boundary being examined, accompanied by a separate Regge-like high-spin ridge. A broad region between this black-hole-band and the eikonal input layer is available to the optimizer but remains largely empty. The gap is available but expensive; the black-hole-scale band is capped and useful. Thus the pole-subtracted bootstrap acts as a microscope for the small-impact-parameter completion of gravity: it resolves organized black-hole-scale and Regge-like structures rather than a featureless residual continuum.