{"paper":{"title":"A generalized linear matrix method for normal modes in collisionless stellar disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Evgeny V. Polyachenko, Ilia G. Shukhman","submitted_at":"2026-06-30T11:35:25Z","abstract_excerpt":"We generalize the linear matrix method for computing normal modes in collisionless stellar disks to distribution functions with sharp edges at zero angular momentum ($L=0$). The generalization adds boundary-integral terms to the matrix equation without increasing its size. We validate the method by computing $m=2$ modes for two Kuzmin--Toomre disk models (Miyamoto $n_{\\rm M}=3$ and Kalnajs $m_{\\rm K}=6$ families) and comparing the eigenvalues with those obtained from an independent nonlinear matrix method based on logarithmic-spiral expansions. A systematic convergence study over grid resoluti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31523","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.31523/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}