{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WAYD3CIUUKVDQOG63FFRDGI7FK","short_pith_number":"pith:WAYD3CIU","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"},"canonical_sha256":"b0303d8914a2aa3838ded94b11991f2a82eb12e81f83b0e6580c607e039725ef","source":{"kind":"arxiv","id":"1801.04840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04840","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04840v1","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04840","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"WAYD3CIUUKVD","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WAYD3CIUUKVDQOG6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WAYD3CIU","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WAYD3CIUUKVDQOG63FFRDGI7FK","target":"record","payload":{"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"},"canonical_sha256":"b0303d8914a2aa3838ded94b11991f2a82eb12e81f83b0e6580c607e039725ef","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"},"source_kind":"arxiv","source_id":"1801.04840","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZbkzow8AMcihm8PgoIukTZa/jtuQ3SOHuJ0AVgSTZ4TjF55hjjOV6uHaEd3qVRxhS9W3Fiq1BwSLyTQJAv1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:39:59.212420Z"},"content_sha256":"ad4ad00e9e633b2678ed1f05ddff0b16bcacf290a8cc5630fb3bfc61938fa50c","schema_version":"1.0","event_id":"sha256:ad4ad00e9e633b2678ed1f05ddff0b16bcacf290a8cc5630fb3bfc61938fa50c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WAYD3CIUUKVDQOG63FFRDGI7FK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38GL0DVmGfuNlxWsT7Yci88CZd+JYJvEU+rBgRspNoulxjBWtyUYu5RXgocZW9JS1RD91AMIPh2ETlyizjO3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:39:59.212795Z"},"content_sha256":"70cd16d3796fcf22fcb33f696b063fa905f67a9f577dea19b4d9a9b0041ddaf7","schema_version":"1.0","event_id":"sha256:70cd16d3796fcf22fcb33f696b063fa905f67a9f577dea19b4d9a9b0041ddaf7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/bundle.json","state_url":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T12:39:59Z","links":{"resolver":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK","bundle":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/bundle.json","state":"https://pith.science/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WAYD3CIUUKVDQOG63FFRDGI7FK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WAYD3CIUUKVDQOG63FFRDGI7FK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a8b0b325de4901252a9ac01f42b4d6b2f6d4ac34f42fad3e3ed09e2f791cab99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T15:12:06Z","title_canon_sha256":"8245b656d5597aabf4d882e0d676400e573239f6cb70e6104de3b515f116d839"},"schema_version":"1.0","source":{"id":"1801.04840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04840","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04840v1","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04840","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"WAYD3CIUUKVD","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WAYD3CIUUKVDQOG6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WAYD3CIU","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:70cd16d3796fcf22fcb33f696b063fa905f67a9f577dea19b4d9a9b0041ddaf7","target":"graph","created_at":"2026-05-18T00:26:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Christiane Kraus, Helmut Abels, Johannes Daube","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T15:12:06Z","title":"Pressure Reconstruction for Weak Solutions of the Two-Phase Incompressible Navier--Stokes Equations with Surface Tension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04840","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ad4ad00e9e633b2678ed1f05ddff0b16bcacf290a8cc5630fb3bfc61938fa50c","target":"record","created_at":"2026-05-18T00:26:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a8b0b325de4901252a9ac01f42b4d6b2f6d4ac34f42fad3e3ed09e2f791cab99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T15:12:06Z","title_canon_sha256":"8245b656d5597aabf4d882e0d676400e573239f6cb70e6104de3b515f116d839"},"schema_version":"1.0","source":{"id":"1801.04840","kind":"arxiv","version":1}},"canonical_sha256":"b0303d8914a2aa3838ded94b11991f2a82eb12e81f83b0e6580c607e039725ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0303d8914a2aa3838ded94b11991f2a82eb12e81f83b0e6580c607e039725ef","first_computed_at":"2026-05-18T00:26:03.071963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:03.071963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e/gPVjBX4FST/7DfuTwNFCXVJMUoPSx408MgEGmAaRcuiQI4usuSzUt6BDuA5KJhEXEDJfKQZ9wUeBZUW/eDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:03.072680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad4ad00e9e633b2678ed1f05ddff0b16bcacf290a8cc5630fb3bfc61938fa50c","sha256:70cd16d3796fcf22fcb33f696b063fa905f67a9f577dea19b4d9a9b0041ddaf7"],"state_sha256":"9250f93eb96c9f82b93743bd887d70bc775e121507da4049694f0a82f0d9f8f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a++oGnl5vRaV90GBUtnWGwCQDdopjmnaA0fzT9VzXv+1ADXfyO4eUllienKjBt/z6JrR959qCEKSM0powzqlDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:39:59.215202Z","bundle_sha256":"a96db9dab6423f409cd6b78c51550ab42b195056c85a12590ab02fb210130446"}}