Replication Package for "Critical Absorption Exponents for Black-Hole Inverse-Quality-Factor Continuity"

This record contains the replication package for the manuscript “Critical Absorption Exponents for Black-Hole Inverse-Quality-Factor Continuity”. \frac{\log|\rho_{\rm eff}|^{-1}}{2L\Omega_{\rm BH}}\left[1+O(L^{-1})\right].]Black-hole inverse-Q continuity therefore requires the invariant critical condition[\frac{\log|\rho_{\rm eff}|^{-1}}{2L}\to\Gamma_{\rm BH}.]In the Schwarzschild coordinate gap (\eta=(R-2M)/(2M)), this condition becomes[|\rho_{\rm eff}|\sim\eta^{p_},\qquadp_=4M\Gamma_{\rm BH}.]For the Schwarzschild (\ell=2) fundamental comparator, the package uses (M\Gamma_{\rm BH}\simeq0.08896232), giving (p_*\simeq0.35584928). The archive includes the LaTeX manuscript source, generated PDF, numerical scripts, CSV output tables, and figures required to reproduce the Regge–Wheeler scattering/membrane benchmark and the finite-interval direct-root branch-selection red-team check. The benchmark demonstrates the asymptotic distinction between reflective, subcritical, and critical absorption laws. Reflective and subcritical laws retain residual inverse-Q mismatch, while the critical law removes the residual up to the expected finite-(L) correction. The finite-interval Regge–Wheeler/membrane direct-root calculation is included as a branch-selection diagnostic and red-team check. It verifies that the same membrane law can be posed as a finite-interval radial eigenproblem and illustrates that nearest-real-frequency root selection and cavity-targeted root selection are distinct. It is not used as evidence for the asymptotic exponent.