reasoning - Quantize a free field on the classical spacetime of a collapsing body; the Bogoliubov transformation between in-modes (past null infinity) and out-modes (future null infinity) acquires, from the exponential red-shift near the forming horizon, mixing coefficients whose ratio is exactly a Boltzmann factor — yielding a steady late-time flux, thermal at T = hbar c^3/(8 pi G M k_B), independent of collapse details. Energy conservation then gives dM/dt ~ -1/M^2 (Stefan-Boltzmann over horizon area ~ M^2 at T^4 ~ M^-4), so lifetime ~ M^3: a solar-mass hole outlives the universe, while a TeV-mass hole decays in far under 10^-25 s. Robustness: re-derived independently via Euclidean path-integral and tunneling methods; broad theorist consensus. Load-bearing caveat: the derivation is semiclassical (fixed background, no backreaction, trans-Planckian mode extrapolation) and is least controlled precisely in the near-Planck/TeV regime relevant to hypothetical LHC black holes.
Verdict (step 6)
approved / trusted. The downstream chain is checked: given a thermal flux at T ~ 1/M, Stefan-Boltzmann over horizon area ~M^2 at T^4 ~ M^-4 gives dM/dt ~ -1/M^2 and lifetime ~ M^3, hence <<10^-25 s at TeV mass — elementary and traced. The load-bearing step — the Bogoliubov-coefficient derivation of exactly thermal late-time flux from the exponential horizon red-shift — is a specialist multi-page QFT-in-curved-spacetime calculation not traceable at reasonable cost here, so trusted: independently re-derived by Euclidean path-integral and tunneling methods, ~50 years without a published refutation of the semiclassical result. The statement’s own caveat (semiclassical control is weakest in the near-Planck/TeV regime) correctly marks where premise truth gets priced in step 7.