Directly confronts the objection that Hawking’s derivation implicitly assumes standard low-energy physics holds for field modes of arbitrarily short (trans-Planckian) wavelength at the horizon. Shows that introducing an explicit short-distance (Planck-scale) cutoff via a “free-fall” frame prescription still reproduces the standard Hawking thermal spectrum — an influential argument that the derivation is more robust to trans-Planckian physics than critics feared, though the assumption needed (dispersion relation regularity in the free-fall frame) remains a physical hypothesis about unknown short-distance physics, not a proof. relevance_note: the primary technical treatment of whether Hawking radiation survives once trans-Planckian/short-distance physics is taken seriously — cited by both defenders and critics of Premise A.