{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JEZCXTH5E3KUJL5JCBITNGGDZH","short_pith_number":"pith:JEZCXTH5","schema_version":"1.0","canonical_sha256":"49322bccfd26d544afa910513698c3c9cffa7fac0dd4eff0c4394d9cab4d888f","source":{"kind":"arxiv","id":"1310.2787","version":1},"attestation_state":"computed","paper":{"title":"On the Leray-Hopf Extension Condition for the Steady-State Navier-Stokes Problem in Multiply-Connected Bounded Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni P. Galdi","submitted_at":"2013-10-10T12:24:09Z","abstract_excerpt":"Employing the approach of A. Takeshita [Pacific J. Math., Vol. 157 (1993), 151--158], we give an elementary proof of the invalidity of the Leray-Hopf Extension Condition for certain multiply connected bounded domains of R^n, n=2,3, whenever the flow through the different components of the boundary is non-zero. Our proof is alternative to and, to an extent, more direct than the recent one proposed by J.G. Heywood [J. Math. Fluid Mech. Vol. 13 (2011), 449--457]."},"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":"1310.2787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-10T12:24:09Z","cross_cats_sorted":[],"title_canon_sha256":"e80972ac6ed96307768216fe739acfd56fc81695bdc3a710dd5d34fd39b90857","abstract_canon_sha256":"bd8a10a6745d6ae949de07f0ef3f476466b71df9077591ff5adf97ebb4e14df9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:46.697289Z","signature_b64":"9eJ2vmU99Q1qfoflTGEKzsR5r6IcqaDiZluBhXiRt7n8dpqFKWNNhkTonDLlMB6E2DgoQ698YOoGeoe5gB6zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49322bccfd26d544afa910513698c3c9cffa7fac0dd4eff0c4394d9cab4d888f","last_reissued_at":"2026-05-18T03:10:46.696406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:46.696406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Leray-Hopf Extension Condition for the Steady-State Navier-Stokes Problem in Multiply-Connected Bounded Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni P. Galdi","submitted_at":"2013-10-10T12:24:09Z","abstract_excerpt":"Employing the approach of A. Takeshita [Pacific J. Math., Vol. 157 (1993), 151--158], we give an elementary proof of the invalidity of the Leray-Hopf Extension Condition for certain multiply connected bounded domains of R^n, n=2,3, whenever the flow through the different components of the boundary is non-zero. Our proof is alternative to and, to an extent, more direct than the recent one proposed by J.G. Heywood [J. Math. Fluid Mech. Vol. 13 (2011), 449--457]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2787","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":"1310.2787","created_at":"2026-05-18T03:10:46.696515+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2787v1","created_at":"2026-05-18T03:10:46.696515+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2787","created_at":"2026-05-18T03:10:46.696515+00:00"},{"alias_kind":"pith_short_12","alias_value":"JEZCXTH5E3KU","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JEZCXTH5E3KUJL5J","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JEZCXTH5","created_at":"2026-05-18T12:27:49.015174+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/JEZCXTH5E3KUJL5JCBITNGGDZH","json":"https://pith.science/pith/JEZCXTH5E3KUJL5JCBITNGGDZH.json","graph_json":"https://pith.science/api/pith-number/JEZCXTH5E3KUJL5JCBITNGGDZH/graph.json","events_json":"https://pith.science/api/pith-number/JEZCXTH5E3KUJL5JCBITNGGDZH/events.json","paper":"https://pith.science/paper/JEZCXTH5"},"agent_actions":{"view_html":"https://pith.science/pith/JEZCXTH5E3KUJL5JCBITNGGDZH","download_json":"https://pith.science/pith/JEZCXTH5E3KUJL5JCBITNGGDZH.json","view_paper":"https://pith.science/paper/JEZCXTH5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2787&json=true","fetch_graph":"https://pith.science/api/pith-number/JEZCXTH5E3KUJL5JCBITNGGDZH/graph.json","fetch_events":"https://pith.science/api/pith-number/JEZCXTH5E3KUJL5JCBITNGGDZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JEZCXTH5E3KUJL5JCBITNGGDZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JEZCXTH5E3KUJL5JCBITNGGDZH/action/storage_attestation","attest_author":"https://pith.science/pith/JEZCXTH5E3KUJL5JCBITNGGDZH/action/author_attestation","sign_citation":"https://pith.science/pith/JEZCXTH5E3KUJL5JCBITNGGDZH/action/citation_signature","submit_replication":"https://pith.science/pith/JEZCXTH5E3KUJL5JCBITNGGDZH/action/replication_record"}},"created_at":"2026-05-18T03:10:46.696515+00:00","updated_at":"2026-05-18T03:10:46.696515+00:00"}