Reasoning. Subatomic phase: a slow hole captures a nucleus only when its D-dimensional gravity beats the electromagnetic restoring force K*d binding the nucleus to its site (K ~ 14 eV/Angstrom^2, from dipole estimates and Debye temperatures 300-600 K); this defines the capture radius R_EM = [(D-1)^(D-1) k_D M m / ((D-2)^(D-2) K M_D^(D-2))]^(1/(D-1)), well above the Schwarzschild radius. Integrating dM/dt = pi rho v R_EM^2 at escape velocity with mean Earth density (both conservative: real holes slow as they accrete and see higher central density but lower speed) gives growth-to-1-Angstrom times: negligible for D = 6, 7; but for D >= 8 the force law turns 4D at R_C (5-6 R_D, with R_D < 1 Angstrom), and the 4D phase takes t = 9.9 x 10^18/chi s ~ 3 x 10^11 yr — the weakness of 4D gravity is the bottleneck. Macroscopic phase: once R_EM > a ~ 1 Angstrom (mass 10^11 g in 4D), treat Earth’s interior as an inviscid compressible fluid (neglecting cohesion — again conservative) and apply Bondi accretion generalized to D dimensions: dM/dt = pi lambda_D c_s R_B^2 rho with R_B = ((D-3)/4c_s^2)^(1/(D-3)) R and 4 ⇐ lambda_4 ⇐ 18. With d_0 c_s = 1.33 x 10^-4 s (Birch’s law, tested for Fe to Earth-core densities), the 4D radius-doubling time from R_B ~ a is 1.2 x 10^12/lambda_4 yr. D = 7 (R_D > a) combines D-dimensional and 4D Bondi phases into 6.4-94 Gyr for M_D = 1-5 TeV. Cross-check: a captured minimum-mass (10^15 g) primordial black hole would consume Earth in > 47 Myr — consistent with no PBH having been captured, and calibrating the formalism. Radiative (Eddington) feedback is argued NOT to slow this further (spherical BH accretion is radiatively inefficient), so the bound does not lean on it.
Step 6 — validity verdict
approved / trusted. Reconstruction: trapped-hole growth is computed in two phases — subatomic capture only when D-dimensional gravity beats the electromagnetic restoring force (capture radius R_EM), then D-dimensional/4D Bondi accretion — under uniformly growth-maximizing choices (escape velocity with mean density, fluid Earth without cohesion, no Eddington throttling claimed as help); the resulting times (~3e11 yr for the D>=8 4D phase, ~1.2e12/lambda_4 yr for 4D Bondi, 6.4-94 Gyr for D=7) all vastly exceed the Sun’s 5 Gyr remainder, giving the conclusion for R_C < 200 Angstrom. The logical frame — conservative lower bounds on accretion time exceeding the solar lifetime imply irrelevance — is traced and valid. Why trusted: the load-bearing numeric content (R_EM formula, D-dimensional Bondi generalization, phase-matching integrations across ~20 pages of section 4 and Appendix A) is a specialist derivation not retraceable at reasonable cost. Credibility: the internal calibration against a captured 1e15 g primordial hole (>=47 Myr to consume Earth, consistent with standard results) checks the formalism; adopted by the LSAG review; no published quantitative refutation.