Reasoning. Stopping: at nuclear densities (>~ 2 x 10^14 g/cm^3) the gravitational stopping scale d_0 = M_0^3/pi rho <~ 0.01 cm << 10 km, so even the most boosted holes stop promptly and fall below the ~c escape velocity. Production route 1 — binaries: cosmic rays aimed at the neutron star but intercepted by its companion convert to black holes on the companion (no magnetic obstacle for the neutral product); the FCE = integral of the companion’s solid-angle fraction over the system lifetime is 2-30 Myr across known X-ray-binary classes (2-6 Myr very confident), and with even a 10% proton fraction the 14-TeV worst-case rate 5/Myr x 2 Myr FCE suffices; smaller M_min or larger proton fraction gives orders of magnitude more. Route 2 — cosmogenic neutrinos: protons above the GZK energy photo-produce pions on the CMB whose decays guarantee a neutrino flux; neutrinos evade synchrotron losses entirely, and their entire energy is available (no 1/A or parton-x penalty), with black-hole production competing only against the electroweak cross section; using a parameterization at the lower edge of worst-case (Fe-only-injection) cosmogenic-flux fits, rates are >= 4.5 x 10^3/Myr (D = 5) to 6.2 x 10^4/Myr (D = 11) at M_min = 14 TeV, y = 0.5. Interior evolution: a hole temporarily color-bound in the crust absorbs the rest of the nucleon in t_abs ~ 10^7 fm, re-neutralizes, and drifts down with average velocity sqrt(g_NS d_free/2); crust transit < 10 s x r_c[1/TeV]. In the core, subnuclear geometric accretion dM/dt = pi rho R^2 reaches r_N within a fraction of a second to a few weeks (6 ⇐ D ⇐ 11); thereafter Bondi accretion with d_0 = 7 x 10^-3 s, c_s ~ 0.1 (10^-6 of white-dwarf times) completes in ⇐ ~10 Myr even for the slowest (D = 11, 4D phase) case, ~20 yr in warped cases with R_C >= 5 Angstrom. Caveats the paper itself flags: sub-GZK composition may be heavy (though shower data indicate mixed, ~ 5, and a proton component at the GZK edge); the cosmogenic neutrino flux, while theoretically guaranteed by observed super-GZK cosmic rays plus any nonzero proton fraction, was not yet directly measured, and brane-world models with quarks and neutrinos on different branes could in principle suppress neutrino-parton gravity. Hence the bound is presented as very strong but not absolutely certain — the escape hatch requires two independent unlikely failures simultaneously.
Step 6 verdict
Verdict: approved (checked). The conclusion is properly conditionalized inside the statement (“unless cosmic rays are almost purely heavy AND the cosmogenic neutrino flux is absent or non-reactive”) - the two escape hatches are internalized, so no undercutting defeater survives. Traced: stopping (d_0 = M_0^3/pi rho <~ 0.01 cm << 10 km at nuclear density), the FCE arithmetic for binary beam dumps, the neutrino route’s freedom from 1/A and synchrotron penalties, and interior consumption ⇐ ~10 Myr << Gyr ages. Rate inputs (Auger flux, cosmogenic-flux parameterization, binary demographics) are premises priced downstream. Valid conditional on them.