Reasoning. Cross section: sigma ~ pi R^2(sqrt(s-hat))/4, black hole formed only for b < 0.5 R with inelasticity y (fraction of parton CM energy trapped); conservatively y = M_min/14 TeV — the smallest value still compatible with producing mass M_min at the LHC (larger y only raises cosmic-ray rates), and M_min = 3 M_D (lower than the usual 5 M_D threshold, again lowering rates only through larger allowed M_D). Convolution: CTEQ6M PDFs at scale 1/R; bulk of production at parton x <~ 0.6 where PDFs are known to <10%; Auger spectrum (linearly interpolated, up to 2 x 10^20 eV) with sigma_NN = 100 mb; for mass-A primaries only E/A per nucleon. Magnetic screening (Appendix G): synchrotron loss in the star’s dipole field caps the surface-reaching energy at E_max = 3.6 x 10^18 eV (5000 km / R_0)(10^6 G / B_p)^2 for protons at theta = pi/2, so fields <~ few x 10^5 G pass the needed ~10^18-10^20 eV flux — and such low-field massive white dwarfs are observed. Robustness checks in the paper: a hypothesized 20% Auger energy-scale overestimate roughly halves rates; pure-Fe composition (inconsistent with shower-depth data showing mixed composition, ~ 5, and with a >~10% proton fraction indicated near the GZK energy) still yields thousands of holes per few thousand years in the main cases; the interstellar-medium channel (production probability ~1.4 x 10^-4 en route) provides ~1/Myr even for pure Fe onto white dwarfs of ANY magnetic field — enough to doom a 120-Myr-old Sirius B in the dangerous scenarios. Stopping-acceptance reductions (10%/10%/2% for D = 5/6/7) are already included in the >5000-per-10-Myr statement.
Step 6 verdict
Verdict: approved (checked). Reconstruction: measured Auger flux x trapped-surface geometric cross section x PDF convolution x magnetic-screening cap, with every disputable choice (y = M_min/14 TeV, M_min = 3 M_D, pure-Fe composition, stopping-geometry acceptance) pushed in the rate-lowering direction, so the accumulated-hole counts are lower bounds and “production is never the bottleneck” follows. Load-bearing step: the direction-of-conservatism plus orders-of-magnitude margin. Traced with an independent order-of-magnitude cross-check: flux above 1e19 eV ~ 1/km^2/yr on a pi(5400 km)^2 disc gives ~1e8 primaries/yr; per-impact BH probability 1e-8..1e-10 (sigma_BH ~ pb-nb vs sigma_NN ~ 100 mb) yields 1-100/yr, matching the quoted per-Myr ranges. Hidden premise surfaced: trapped-surface production estimates remain valid at these parton energies - a premise priced downstream, not an inference gap. No undercutting defeater survives conditional on the premises.