Reasoning (as reconstructable from the abstract; the detailed numerics are in the paywalled body). Hawking’s result gives each mode an occupation Gamma_slm(omega) / (e^(2pi*omega/kappa) -/+ 1); the physical emission rate therefore hinges on the greybody factors Gamma — the probability that a quantum of given spin s, angular momentum l,m and frequency omega tunnels through the potential barrier around the hole. Page computes these numerically by integrating the Teukolsky-Press perturbation equations for neutrino (s=1/2), photon (s=1) and graviton (s=2) fields, then sums the power over species and modes. Higher spin suppresses low-frequency transmission, which is why gravitons carry only 2% while neutrinos dominate. The M^-2 power law integrates to lifetime proportional to M^3; adding massive-species channels as the temperature rises past their rest masses shortens the final stages and sets the initial-mass threshold for evaporation within the age of the universe at (5 +/- 1) x 10^14 g. This is the calculation the ~10^-27 s figure for a (higher-dimensional, TeV-scale) LHC hole descends from; it is pure theory resting on the Hawking formalism, with no empirical input.
Step 6 — validity verdict
approved / trusted. Reconstruction: Hawking’s mode occupation Gamma_slm(omega)/(e^(2pi*omega/kappa) -/+ 1) makes the physical power hinge entirely on the greybody factors; Page integrates the Teukolsky-Press perturbation equations numerically for s = 1/2, 1, 2, sums over modes and species, and obtains 2e-4 hbar c^6 G^-2 M^-2 split 81/17/2; the M^-2 law integrates to the M^3 lifetime and, with massive channels added as temperature rises, the (5 +/- 1)e14 g threshold. The structural inferences are traced and correct: higher spin suppresses low-frequency transmission (ordering neutrinos > photons > gravitons), and M^-2 → M^3 is elementary. The load-bearing content — the numerical greybody integration fixing the coefficients — is a specialist numerical-GR computation behind a paywalled text; retracing is infeasible at reasonable cost, so trusted. Credibility: independently recomputed with consistent results by later authors (Elster 1983; MacGibbon & Webber 1990, extending to QCD channels), agrees with known analytic low-frequency limits, no published refutation.