Reasoning
- The exclusion’s load-bearing step is that white dwarfs stop cosmic-ray-produced mBHs (G-M section 5), so that the stars’ survival bounds mBH danger. That stopping demonstration is computed semiclassically.
- G-M’s own restriction M_min > 3 M_5 (text after their eq. E.2) marks where the semiclassical treatment is reliable; Giddings had earlier written that for masses of order the fundamental Planck scale ‘there is no control over quantum gravity effects which are likely to invalidate the semiclassical picture’. Reliability of prediction is not a production bound: mBHs below M_min can still be produced - we just cannot predict their behaviour.
- Sensitivity: for theories with 2 extra dimensions, the safety-critical black holes cease to be excluded if their scattering cross section falls short of the semiclassical value by merely a factor ~10 (G-M fig. 2). Hence sub-M_min mBHs with modestly reduced cross sections would traverse white dwarfs, and the exclusion of dangerous black holes ‘remains not definite’.
Step 6 verdict
Verdict: approved (checked). Reconstruction: (P1) G-M’s white-dwarf stopping demonstration is computed semiclassically; (P2) G-M restrict semiclassical reliability to M > M_min = 3 M_5; (P3) production below M_min still occurs - the reliability-of-prediction vs production-bound distinction is correct; (P4) for n=2 a mere ~10x cross-section shortfall already voids the stopping exclusion (G-M fig. 2 sensitivity). (C) the astrophysical exclusion is not definite for the sub-M_min population. The conclusion is deliberately weak (“might”, “remains not definite”) and follows from the premises. Coherence probe of the implicit asymmetry: cosmic-ray-produced holes traverse the star while still light and relativistic (quantum regime), whereas LHC holes are produced slow and could grow into the semiclassical regime - so reduced quantum-regime stopping and Earth danger are not self-contradictory. Whether sub-M_min cross sections actually fall short is premise territory (steps 7-8). Valid.