Reasoning. The relativistic phase (boost gamma_i up to ~3M_i/m_p ~ 4.5 x 10^4) is governed by parton capture within b_min*R plus gravitational Coulomb scattering; the required column density (5.25) scales as (M_D/M_0)^3 (gamma_i M_i/M_D)^((D-5)/(D-3)) M_0^3 with M_0^3 = 4.6 x 10^12 g/cm^2. The nonrelativistic phase (from p ~ M down to below the escape velocity v_WD ~ 0.02) proceeds by sub-nuclear “bag-model” accretion of nucleons (checked in Appendix D: captured mass per nucleon crossing < m_p, capture radius stays under 1 fm); its column density (5.32) is of the same order. Parameter robustness: the stopping distance is maximized at c_ac,M = c_ac,p (perfect accretion) and small c_sc; varying c_ac,p from 1 to 1/4 changes the bound < 25% provided c_sc > (0.12, 0.07) for D = 6, 7 — and the actual quantum-scattering estimates give c_sc = (0.25, 0.17); the final numbers take the worst case (c_sc = 0, c_ac,p = 1, M_D = M_i/3). Comparison against realistic density profiles (Shen models; column densities 13/21/38 x 10^15 g/cm^2 for 1.0/1.1/1.2 Msun, ~10% systematic from temperature and composition) yields the stopping verdicts; off-zenith incidence reduces available column (Fig. 1 right), which is priced into the production-rate acceptances (10%, 10%, 2% of flux kept for D = 5, 6, 7). Note the D = 7 gap is harmless: D = 7 holes above ~6 TeV already have Earth-accretion times > 20 Gyr, and the sub-6-TeV ones stop in a solar-mass star.
Step 6 — validity verdict
approved / trusted. Reconstruction: the column density required to stop a 7-14 TeV neutral hole — relativistic parton-capture-plus-scattering phase (Eq. 5.25, scaling as (M_D/M_0)^3 gamma_i^((D-5)/(D-3))) followed by nonrelativistic bag-model nucleon accretion (Eq. 5.32, same order) — is compared with available white-dwarf diameters (13/21/38 e15 g/cm^2 for 1.0/1.1/1.2 Msun, +/-10% systematic): D = 5, 6 stop in a solar-mass star, D = 7 needs >~1.1 Msun, D >= 8 generally exceeds WD stopping power and is handed to neutron stars. The comparison logic, worst-case parameter bookkeeping (c_sc = 0, c_ac,p = 1, M_D = M_i/3; <25% sensitivity across the allowed range), off-zenith acceptance haircuts, and the closure of the D = 7 gap via A-47’s >20 Gyr Earth times are traced and internally consistent. Why trusted: the load-bearing numbers come from integrating the coupled slow-down/mass-growth equations through realistic WD profiles (section 5, Appendices C-D) — a specialist computation not retraceable here. Credibility: same internally cross-checked formalism as A-47, adopted by LSAG, no published refutation.