Structured Pseudospectra of Compact-Object Mode Matching Problems

This record contains the manuscript, REVTeX source, bibliography, reproducibility scripts, generated figures, CSV data, numerical summaries, dependency file, README, and manifest for "Structured Pseudospectra of Compact-Object Mode Matching Problems." The paper formulates compact-object mode matching as a boundary Weyl pencil, F(s; θ) = M_ext(s; θ) − M_int(s; θ), obtained by matching an exterior outgoing, radiative, or tidal response to an interior material response. Small singular values of this pencil define a matching-pencil pseudospectrum. For a simple mode, the paper derives the corresponding first-order displacement and material-sensitivity formula. The same simple-root denominator also appears in residues of driven response functions, linking spectral conditioning to tidal or source-driven excitation amplitudes. The construction distinguishes two quantities that need not coincide: the sensitivity of a mode to a chosen equation-of-state, crust, interface, or response parameter, and the conditioning of the matching equation itself. It is complementary to bulk-operator pseudospectra. The matching-pencil pseudospectrum allows unrestricted additive perturbations within the reduced response space, whereas physically admissible parameter perturbations form a narrower structured class. Two reproducible examples are included. An exactly solvable acoustic compact-object model verifies the displacement law analytically and numerically. A relativistic Gamma = 2 Tolman-Oppenheimer-Volkoff polytrope provides an axial spacetime-mode benchmark with an asymptotic outgoing exterior response. The TOV calculation uses adaptive high-accuracy integration and a Wronskian extraction at R_inf = 35 with asymptotic order N = 18. The selected root is verified under independent changes in matching radius, asymptotic order, and integration tolerance. The archive includes a single driver that regenerates both figures, all CSV files, and the numerical summaries. The scripts require NumPy, SciPy, and Matplotlib. They use explicit pseudospectral contour levels and terminate with an error if the requested contours are unresolved or the TOV convergence guard fails. This work applies the boundary-Weyl pseudospectral framework developed in "Boundary Weyl Pseudospectra and Condition Numbers of Quasinormal Modes" (doi:10.5281/zenodo.20680061) to material compact-object matching problems.