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Schwarzschild spectral ladders on the negative imaginary axis: Endpoint nonselection, branch-cut phase, and Jost classification
Compactified spectral discretisations may yield stable negative-imaginary-axis (NIA) eigenvalue ladders, but finite-matrix convergence does not establish quasinormal poles. For axial Schwarzschild perturbations, ingoing--outgoing factorisation leaves an unwanted horizon solution behaving as $t^{4α}$
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