Reasoning. Electromagnetic energy loss is a long-range process independent of the particle’s internal microphysics, so a charged black hole’s stopping power equals a muon’s at equal Lorentz gamma. Bethe-Bloch regime (gamma < 10^3): ~2 MeV cm^2/g, i.e. ~11 MeV/cm at mean Earth density; above gamma ~ 10^3, pair production, bremsstrahlung and nuclear dissociation grow linearly, ~60 MeV/cm at gamma ~ 10^4. Production kinematics force the hole’s momentum above M^2/2m_p ~ 10^8 GeV (for M = 14 TeV), giving a slow-down distance to gamma ~ 10^3 of order M/(6 keV) cm — over 10^4 km at 14 TeV, more than Earth’s radius, with the remaining slow-down at ~1 GeV/m taking a comparable distance; a careful estimate still leaves Earth stopping unit-charge holes up to ~7 TeV. For heavier holes the Sun suffices: core density ~150 g/cm^3 over ~1.4 x 10^5 km stops well beyond 100 TeV. Magnetic monopoles stop ~100x more easily (magnetic charge >= 1/alpha times e). Any accreted extra charge only strengthens stopping. Given the ~10^22/A above-LHC-energy collisions over Earth’s history, many such objects would have stopped and accreted in Earth and Sun; their multi-Gyr health closes the charged branch — which is why the paper’s remaining work targets the neutral branch only.
Step 6 — validity verdict
approved / checked. Reconstruction — premises: (i) electromagnetic stopping depends only on charge and gamma, not internal microphysics, so a charged hole stops like a heavy muon; (ii) the stopping ranges: Earth column stops unit-charge holes up to ~7 TeV, the solar core (~150 g/cm^3 over 1.4e5 km, column ~2e12 g/cm^2) well beyond 100 TeV; (iii) ~1e22/A above-LHC-energy cosmic-ray collisions over Earth’s history imply many produced holes stopped and accreted, if stable charged holes exist at these masses; (iv) Earth and Sun persist after ~4.5 Gyr. Modus tollens closes the charged branch. The load-bearing hidden premise — the hole retains its charge while slowing — is the branch definition itself; a hole that neutralizes exits to the neutral branch, which the argument explicitly hands to the compact-star analysis (A-46 ff.), so the defeater “it might shed charge” changes the branch, not the validity. The range arithmetic is order-of-magnitude traceable (~2 MeV cm^2/g against the available columns). Checked.