Reasoning. Two gravitational slow-down channels exist for a relativistic neutral hole: capture of partons entering impact parameter b_min*R (accretion slow-down, with quantum capture cross section sigma_c = 2^((3D-13)/(D-3)) pi R^2, b_min ~ 1.4-2.4) and elastic gravitational scattering (Coulomb slow-down, subdominant: c_sc ~ 0.5, 0.25, 0.17 for D = 5, 6, 7). Integrating the coupled momentum-loss/mass-growth equations from initial boost gamma_i (production kinematics: gamma > M/2m_p, significant production up to gamma_i ~ 3M/m_p ~ 4.5 x 10^4 at 14 TeV) gives a required stopping column density of order M_0^3/pi R^2 ~ d_0 rho: about 4.6 x 10^12 g/cm^2, versus Earth’s actual column 1.1 x 10^10 g/cm^2 — a few GeV of accretion per transit. Hence Earth (and the Sun, and ordinary stars, and the interstellar medium — the hole even escapes the galaxy) neither stops nor keeps cosmic-ray-produced neutral holes, and the classic “cosmic rays hit Earth harder than the LHC ever will” argument fails exactly in the neutral-stable case that matters. (The same physics implies typical LHC-produced holes, born faster than Earth’s 11 km/s escape velocity, mostly leave: trapping probabilities are 0.01 cm) are the only usable natural beam dumps — hence the paper’s compact-star strategy.10^-4-10^-3, and the expected number of trapped holes over the LHC lifetime falls below 1 for M > 7 TeV.) White dwarfs (d_0 ~ 1.5 km vs radii of 10^3-10^4 km) and neutron stars (d_0 <
Step 6 — validity verdict
approved / checked. Reconstruction — premises: a neutral hole interacts only gravitationally, with capture cross section ~pi R^2 (R ~ 1/M_D at TeV masses); production kinematics give boosts up to gamma_i ~ 4.5e4. Load-bearing step: required stopping column ~M_0^3/(pi R^2) ~ 4.6e12 g/cm^2 versus Earth’s actual ~1.1e10 g/cm^2, so the hole exits still relativistic and Earth/Sun survival carries no information about stable neutral holes. Independently spot-checked the core estimate: Earth column ~6.6e33 nucleons/cm^2 times pi R^2 ~ 1e-33 cm^2 gives only a handful of parton captures — a few GeV accreted against ~1e8 GeV of momentum — matching the body. The conclusion (the naive “cosmic rays hit Earth harder” argument fails exactly in the case that matters; only white dwarfs and neutron stars have d_0-scale columns) follows. This argument undercuts a safety argument; approving it records that the undercut is valid, which is what makes A-49-class compact-star bounds load-bearing. Checked.