This record contains the manuscript, LaTeX source, bibliography, figure-generation script, generated figures, CSV data, and summary files for "Boundary Weyl Pseudospectra and Condition Numbers of Quasinormal Modes." The paper develops a structured pseudospectral diagnostic for black-hole and anti-de Sitter quasinormal modes. Rather than perturbing the full bulk evolution operator, it studies sensitivity to perturbations of the boundary response. Given a Weyl, or Dirichlet-to-Neumann, function M(s) for the radial or bulk boundary-value problem and a boundary law B(s), the quasinormal spectrum is encoded by the boundary pencil F(s) = M(s) − B(s). Specializing nonlinear-eigenvalue pseudospectrum and condition-number methods to this pencil, the manuscript defines the boundary pseudospectrum through the small singular values of F(s) and derives the first-order simple-pole displacement formula and the associated boundary condition number for boundary-law perturbations. Small values of the denominator ⟨ℓ, F′(s*)r⟩ signal boundary-driven ill-conditioning, while its vanishing marks a non-simple zero of the boundary pencil, including an exceptional point or other higher-order zero. The same denominator appears in the residue of the boundary-induced component of the source-driven bulk response; its reciprocal, weighted by the adjoint-channel source overlap, controls the boundary-induced amplitude with which a localized source excites the corresponding ringdown mode. Using the adjoint-pair Kreĭn resolvent formula with the Dirichlet-type reference extension, the boundary pseudospectrum is related to the boundary-induced, Schur-complement component of the bulk resolvent. The construction is complementary to bulk-operator pseudospectra and to explicit Robin or double-trace spectral-flow analyses. The distinction is demonstrated on an exactly computable finite-dimensional model. The archive includes one deterministic figure-and-data-generation script requiring only NumPy and Matplotlib. The script reproduces both figures, the convergence-table values, all CSV data, and the numerical summary file. It includes hard-fail checks that the requested local contour levels lie within the sampled range and that the local grid reaches the |ζ| = 10⁻³ level. Figure 1 tests the displacement law on a finite-worldtube Schwarzschild–AdS₄ scalar pencil, with a broad-domain view and a root-centered logarithmic-radial resolution of the pseudospectral contours |ζ| = 1, 10⁻¹, 10⁻², 10⁻³ compared with the first-order prediction; the associated checks include convergence under step doubling and horizon-offset reduction, a complex boundary perturbation, and a frequency-dependent memory-channel perturbation. Figure 2 exhibits a boundary exceptional point in a controlled rational pencil that is the exact Schur complement of a 3×3 non-normal generator, with the inverse-square-root divergence of the boundary condition number, two quasinormal modes evaluated at the same boundary parameter coalescing at the exceptional point, and a comparison between the bulk and boundary pseudospectra of the same system. This work is a companion to "Causal Passive Boundary Impedances for AdS Black-Hole Terminals: Gauge-Admissible Laws, Worldtube Exchange, and Quasinormal-Mode Stability" (doi:10.5281/zenodo.21225984; submitted to Physical Review D).
Russell Moore (Fri,) studied this question.