{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OXABTCQNSWA4OYVB5EMSVMKGOS","short_pith_number":"pith:OXABTCQN","schema_version":"1.0","canonical_sha256":"75c0198a0d9581c762a1e9192ab14674bdb77e86a56850e30472443c6ebf13eb","source":{"kind":"arxiv","id":"1905.03187","version":1},"attestation_state":"computed","paper":{"title":"Path-following methods for calculating linear surface wave dispersion relations on vertical shear flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Peter Maxwell, Simen {\\AA} Ellingsen","submitted_at":"2019-05-05T04:02:40Z","abstract_excerpt":"The path-following scheme in [Loisel and Maxwell, SIAM J. Matrix Anal. Appl., 39-4 (2018), pp. 1726-1749] is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current. This is equivalent to solving the Rayleigh instability equation with linearised free-surface boundary condition for each sought point on the curve. Taking advantage of the analyticity of the dispersion relation, a path-following or continuation approach is adopted. The problem is discretized using a collocation scheme, parametrised along either a radial or angu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.03187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-05T04:02:40Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"2310a9c10f8c38c0cfffcd720a402d87dacc40eda7b6c293f0170a5965201e1c","abstract_canon_sha256":"d4a6a02a4e8bde21f7116d2be299bc0e672cd53474a5da81994cfd618ae12379"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:42.623796Z","signature_b64":"2kCWvYr8X5z4uQ3vmo7sarJAJElNo68RS8cY4yplkTRHmQX0ibDAOJZN9+raG7FkAfChuf6NvGflWk4jRQi+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75c0198a0d9581c762a1e9192ab14674bdb77e86a56850e30472443c6ebf13eb","last_reissued_at":"2026-05-17T23:46:42.623169Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:42.623169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Path-following methods for calculating linear surface wave dispersion relations on vertical shear flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Peter Maxwell, Simen {\\AA} Ellingsen","submitted_at":"2019-05-05T04:02:40Z","abstract_excerpt":"The path-following scheme in [Loisel and Maxwell, SIAM J. Matrix Anal. Appl., 39-4 (2018), pp. 1726-1749] is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current. This is equivalent to solving the Rayleigh instability equation with linearised free-surface boundary condition for each sought point on the curve. Taking advantage of the analyticity of the dispersion relation, a path-following or continuation approach is adopted. The problem is discretized using a collocation scheme, parametrised along either a radial or angu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03187","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.03187","created_at":"2026-05-17T23:46:42.623270+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.03187v1","created_at":"2026-05-17T23:46:42.623270+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03187","created_at":"2026-05-17T23:46:42.623270+00:00"},{"alias_kind":"pith_short_12","alias_value":"OXABTCQNSWA4","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"OXABTCQNSWA4OYVB","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"OXABTCQN","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS","json":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS.json","graph_json":"https://pith.science/api/pith-number/OXABTCQNSWA4OYVB5EMSVMKGOS/graph.json","events_json":"https://pith.science/api/pith-number/OXABTCQNSWA4OYVB5EMSVMKGOS/events.json","paper":"https://pith.science/paper/OXABTCQN"},"agent_actions":{"view_html":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS","download_json":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS.json","view_paper":"https://pith.science/paper/OXABTCQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.03187&json=true","fetch_graph":"https://pith.science/api/pith-number/OXABTCQNSWA4OYVB5EMSVMKGOS/graph.json","fetch_events":"https://pith.science/api/pith-number/OXABTCQNSWA4OYVB5EMSVMKGOS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS/action/storage_attestation","attest_author":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS/action/author_attestation","sign_citation":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS/action/citation_signature","submit_replication":"https://pith.science/pith/OXABTCQNSWA4OYVB5EMSVMKGOS/action/replication_record"}},"created_at":"2026-05-17T23:46:42.623270+00:00","updated_at":"2026-05-17T23:46:42.623270+00:00"}