{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WAYD3CIUUKVDQOG63FFRDGI7FK","short_pith_number":"pith:WAYD3CIU","schema_version":"1.0","canonical_sha256":"b0303d8914a2aa3838ded94b11991f2a82eb12e81f83b0e6580c607e039725ef","source":{"kind":"arxiv","id":"1801.04840","version":1},"attestation_state":"computed","paper":{"title":"Pressure Reconstruction for Weak Solutions of the Two-Phase Incompressible Navier--Stokes Equations with Surface Tension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christiane Kraus, Helmut Abels, Johannes Daube","submitted_at":"2018-01-15T15:12:06Z","abstract_excerpt":"For the two-phase incompressible Navier--Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify our definition and, under reasonable regularity assumptions, we reconstruct the pressure function from the weak formulation."},"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":"1801.04840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T15:12:06Z","cross_cats_sorted":[],"title_canon_sha256":"8245b656d5597aabf4d882e0d676400e573239f6cb70e6104de3b515f116d839","abstract_canon_sha256":"a8b0b325de4901252a9ac01f42b4d6b2f6d4ac34f42fad3e3ed09e2f791cab99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:03.072680Z","signature_b64":"e/gPVjBX4FST/7DfuTwNFCXVJMUoPSx408MgEGmAaRcuiQI4usuSzUt6BDuA5KJhEXEDJfKQZ9wUeBZUW/eDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0303d8914a2aa3838ded94b11991f2a82eb12e81f83b0e6580c607e039725ef","last_reissued_at":"2026-05-18T00:26:03.071963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:03.071963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pressure Reconstruction for Weak Solutions of the Two-Phase Incompressible Navier--Stokes Equations with Surface Tension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christiane Kraus, Helmut Abels, Johannes Daube","submitted_at":"2018-01-15T15:12:06Z","abstract_excerpt":"For the two-phase incompressible Navier--Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify our definition and, under reasonable regularity assumptions, we reconstruct the pressure function from the weak formulation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04840","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":"1801.04840","created_at":"2026-05-18T00:26:03.072084+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.04840v1","created_at":"2026-05-18T00:26:03.072084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04840","created_at":"2026-05-18T00:26:03.072084+00:00"},{"alias_kind":"pith_short_12","alias_value":"WAYD3CIUUKVD","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"WAYD3CIUUKVDQOG6","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"WAYD3CIU","created_at":"2026-05-18T12:32:59.047623+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/WAYD3CIUUKVDQOG63FFRDGI7FK","json":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK.json","graph_json":"https://pith.science/api/pith-number/WAYD3CIUUKVDQOG63FFRDGI7FK/graph.json","events_json":"https://pith.science/api/pith-number/WAYD3CIUUKVDQOG63FFRDGI7FK/events.json","paper":"https://pith.science/paper/WAYD3CIU"},"agent_actions":{"view_html":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK","download_json":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK.json","view_paper":"https://pith.science/paper/WAYD3CIU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.04840&json=true","fetch_graph":"https://pith.science/api/pith-number/WAYD3CIUUKVDQOG63FFRDGI7FK/graph.json","fetch_events":"https://pith.science/api/pith-number/WAYD3CIUUKVDQOG63FFRDGI7FK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/action/storage_attestation","attest_author":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/action/author_attestation","sign_citation":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/action/citation_signature","submit_replication":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/action/replication_record"}},"created_at":"2026-05-18T00:26:03.072084+00:00","updated_at":"2026-05-18T00:26:03.072084+00:00"}