{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QVAZJ5NK2PPCTAMVRWY7W7VIQD","short_pith_number":"pith:QVAZJ5NK","schema_version":"1.0","canonical_sha256":"854194f5aad3de2981958db1fb7ea880ce05fac6072d3ab39e51ca1f9fa6a547","source":{"kind":"arxiv","id":"1606.02114","version":2},"attestation_state":"computed","paper":{"title":"Completeness of Inertial Modes of an Incompressible Non-Viscous Fluid in a Corotating Ellipsoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP","astro-ph.SR"],"primary_cat":"physics.flu-dyn","authors_text":"George Backus, Michel Rieutord","submitted_at":"2016-06-07T12:17:59Z","abstract_excerpt":"Inertial modes are the eigenmodes of contained rotating fluids restored by the Coriolis force. When the fluid is incompressible, inviscid and contained in a rigid container, these modes satisfy Poincar\\'e's equation that has the peculiarity of being hyperbolic with boundary conditions. Inertial modes are therefore solutions of an ill-posed boundary-value problem. In this paper we investigate the mathematical side of this problem. We first show that the Poincar\\'e problem can be formulated in the Hilbert space of square-integrable functions, with no hypothesis on the continuity or the different"},"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":"1606.02114","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-06-07T12:17:59Z","cross_cats_sorted":["astro-ph.EP","astro-ph.SR"],"title_canon_sha256":"98703a88563411b1270d6e26a1ed128626cf13c2ce77b129ebc9b96ad844a733","abstract_canon_sha256":"c8f6e66f84ca47fc9f1141040af9e86c47f567ad5fb05c40d0fa7b5870d23c16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:55.567142Z","signature_b64":"IaaW4lokJwhTRp2xtnJ9j+wTrPObsgKAP/vVUswsSVuOZuvUMNS0S1ZlDPE3dA6uN/ebxAQ/pPIhChYB+5iTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"854194f5aad3de2981958db1fb7ea880ce05fac6072d3ab39e51ca1f9fa6a547","last_reissued_at":"2026-05-18T00:42:55.566463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:55.566463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Completeness of Inertial Modes of an Incompressible Non-Viscous Fluid in a Corotating Ellipsoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP","astro-ph.SR"],"primary_cat":"physics.flu-dyn","authors_text":"George Backus, Michel Rieutord","submitted_at":"2016-06-07T12:17:59Z","abstract_excerpt":"Inertial modes are the eigenmodes of contained rotating fluids restored by the Coriolis force. When the fluid is incompressible, inviscid and contained in a rigid container, these modes satisfy Poincar\\'e's equation that has the peculiarity of being hyperbolic with boundary conditions. Inertial modes are therefore solutions of an ill-posed boundary-value problem. In this paper we investigate the mathematical side of this problem. We first show that the Poincar\\'e problem can be formulated in the Hilbert space of square-integrable functions, with no hypothesis on the continuity or the different"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02114","kind":"arxiv","version":2},"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":"1606.02114","created_at":"2026-05-18T00:42:55.566573+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.02114v2","created_at":"2026-05-18T00:42:55.566573+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02114","created_at":"2026-05-18T00:42:55.566573+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVAZJ5NK2PPC","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVAZJ5NK2PPCTAMV","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVAZJ5NK","created_at":"2026-05-18T12:30:41.710351+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/QVAZJ5NK2PPCTAMVRWY7W7VIQD","json":"https://pith.science/pith/QVAZJ5NK2PPCTAMVRWY7W7VIQD.json","graph_json":"https://pith.science/api/pith-number/QVAZJ5NK2PPCTAMVRWY7W7VIQD/graph.json","events_json":"https://pith.science/api/pith-number/QVAZJ5NK2PPCTAMVRWY7W7VIQD/events.json","paper":"https://pith.science/paper/QVAZJ5NK"},"agent_actions":{"view_html":"https://pith.science/pith/QVAZJ5NK2PPCTAMVRWY7W7VIQD","download_json":"https://pith.science/pith/QVAZJ5NK2PPCTAMVRWY7W7VIQD.json","view_paper":"https://pith.science/paper/QVAZJ5NK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.02114&json=true","fetch_graph":"https://pith.science/api/pith-number/QVAZJ5NK2PPCTAMVRWY7W7VIQD/graph.json","fetch_events":"https://pith.science/api/pith-number/QVAZJ5NK2PPCTAMVRWY7W7VIQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVAZJ5NK2PPCTAMVRWY7W7VIQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVAZJ5NK2PPCTAMVRWY7W7VIQD/action/storage_attestation","attest_author":"https://pith.science/pith/QVAZJ5NK2PPCTAMVRWY7W7VIQD/action/author_attestation","sign_citation":"https://pith.science/pith/QVAZJ5NK2PPCTAMVRWY7W7VIQD/action/citation_signature","submit_replication":"https://pith.science/pith/QVAZJ5NK2PPCTAMVRWY7W7VIQD/action/replication_record"}},"created_at":"2026-05-18T00:42:55.566573+00:00","updated_at":"2026-05-18T00:42:55.566573+00:00"}