{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6GLC7KUC74ZPAY7PAOZ7CBSACF","short_pith_number":"pith:6GLC7KUC","canonical_record":{"source":{"id":"0908.3332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-08-23T19:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"2376c26fa3681b1a95e3feec04695ee3e5d51b082716d80b22dcb36c4c07e3dc","abstract_canon_sha256":"89649fae08f8fcd9e42e6faab539b43f84ca7397ef491ffb2bbdaa2862014b00"},"schema_version":"1.0"},"canonical_sha256":"f1962faa82ff32f063ef03b3f10640115700890d872e7591efeb8aa69522d8da","source":{"kind":"arxiv","id":"0908.3332","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3332","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3332v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3332","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"6GLC7KUC74ZP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6GLC7KUC74ZPAY7P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6GLC7KUC","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6GLC7KUC74ZPAY7PAOZ7CBSACF","target":"record","payload":{"canonical_record":{"source":{"id":"0908.3332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-08-23T19:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"2376c26fa3681b1a95e3feec04695ee3e5d51b082716d80b22dcb36c4c07e3dc","abstract_canon_sha256":"89649fae08f8fcd9e42e6faab539b43f84ca7397ef491ffb2bbdaa2862014b00"},"schema_version":"1.0"},"canonical_sha256":"f1962faa82ff32f063ef03b3f10640115700890d872e7591efeb8aa69522d8da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:51.378449Z","signature_b64":"8JDSFc6s9Qy+xyj4aPFBqwrEtOmimNLqDFXnU17AfgxPLbijwqfoiSEsxdc1+Ry9t2jGIMSNXxDs64dr36FaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1962faa82ff32f063ef03b3f10640115700890d872e7591efeb8aa69522d8da","last_reissued_at":"2026-05-18T00:54:51.377993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:51.377993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.3332","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":"2026-05-18T00:54:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EvxFLtUGyVR7B+8IXiuwf37VTSuPULO3qrvyaLYtBU8jZmitlUpsQPcBTRTYaab8CrQSa3HshYa235kDkPxFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:57:13.782470Z"},"content_sha256":"ba6f06d5b4652a94a17334ab89210768e64676e49ec75b58440249fad9a69a30","schema_version":"1.0","event_id":"sha256:ba6f06d5b4652a94a17334ab89210768e64676e49ec75b58440249fad9a69a30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6GLC7KUC74ZPAY7PAOZ7CBSACF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic solutions for the two-phase Navier-Stokes equations with surface tension and gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gieri Simonett, Jan Pruess","submitted_at":"2009-08-23T19:59:09Z","abstract_excerpt":"We consider the motion of two superposed immiscible, viscous, incompressible, capillary fluids that are separated by a sharp interface which needs to be determined as part of the problem. Allowing for gravity to act on the fluids, we prove local well-posedness of the problem. In particular, we obtain well-posedness for the case where the heavy fluid lies on top of the light one, that is, for the case where the Rayleigh-Taylor instability is present. Additionally we show that solutions become real analytic instantaneously."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3332","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":"2026-05-18T00:54:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HygR6g+cGGOl/F8isg/wzyu1TuJqdciCJaCMt2eSBYdBOs90h+ilJfxZ5o8J5lTnjZEjDfgICKwv+f2ZO0+zAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:57:13.783135Z"},"content_sha256":"586303bc45dee158f351f8aa24458e3771a3eca12906f73cf84cec475ac5a144","schema_version":"1.0","event_id":"sha256:586303bc45dee158f351f8aa24458e3771a3eca12906f73cf84cec475ac5a144"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GLC7KUC74ZPAY7PAOZ7CBSACF/bundle.json","state_url":"https://pith.science/pith/6GLC7KUC74ZPAY7PAOZ7CBSACF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GLC7KUC74ZPAY7PAOZ7CBSACF/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":"2026-06-11T03:57:13Z","links":{"resolver":"https://pith.science/pith/6GLC7KUC74ZPAY7PAOZ7CBSACF","bundle":"https://pith.science/pith/6GLC7KUC74ZPAY7PAOZ7CBSACF/bundle.json","state":"https://pith.science/pith/6GLC7KUC74ZPAY7PAOZ7CBSACF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GLC7KUC74ZPAY7PAOZ7CBSACF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6GLC7KUC74ZPAY7PAOZ7CBSACF","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":"89649fae08f8fcd9e42e6faab539b43f84ca7397ef491ffb2bbdaa2862014b00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-08-23T19:59:09Z","title_canon_sha256":"2376c26fa3681b1a95e3feec04695ee3e5d51b082716d80b22dcb36c4c07e3dc"},"schema_version":"1.0","source":{"id":"0908.3332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3332","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3332v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3332","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"6GLC7KUC74ZP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6GLC7KUC74ZPAY7P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6GLC7KUC","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:586303bc45dee158f351f8aa24458e3771a3eca12906f73cf84cec475ac5a144","target":"graph","created_at":"2026-05-18T00:54:51Z","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":"We consider the motion of two superposed immiscible, viscous, incompressible, capillary fluids that are separated by a sharp interface which needs to be determined as part of the problem. Allowing for gravity to act on the fluids, we prove local well-posedness of the problem. In particular, we obtain well-posedness for the case where the heavy fluid lies on top of the light one, that is, for the case where the Rayleigh-Taylor instability is present. Additionally we show that solutions become real analytic instantaneously.","authors_text":"Gieri Simonett, Jan Pruess","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-08-23T19:59:09Z","title":"Analytic solutions for the two-phase Navier-Stokes equations with surface tension and gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3332","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:ba6f06d5b4652a94a17334ab89210768e64676e49ec75b58440249fad9a69a30","target":"record","created_at":"2026-05-18T00:54:51Z","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":"89649fae08f8fcd9e42e6faab539b43f84ca7397ef491ffb2bbdaa2862014b00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-08-23T19:59:09Z","title_canon_sha256":"2376c26fa3681b1a95e3feec04695ee3e5d51b082716d80b22dcb36c4c07e3dc"},"schema_version":"1.0","source":{"id":"0908.3332","kind":"arxiv","version":1}},"canonical_sha256":"f1962faa82ff32f063ef03b3f10640115700890d872e7591efeb8aa69522d8da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1962faa82ff32f063ef03b3f10640115700890d872e7591efeb8aa69522d8da","first_computed_at":"2026-05-18T00:54:51.377993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:51.377993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8JDSFc6s9Qy+xyj4aPFBqwrEtOmimNLqDFXnU17AfgxPLbijwqfoiSEsxdc1+Ry9t2jGIMSNXxDs64dr36FaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:51.378449Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.3332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba6f06d5b4652a94a17334ab89210768e64676e49ec75b58440249fad9a69a30","sha256:586303bc45dee158f351f8aa24458e3771a3eca12906f73cf84cec475ac5a144"],"state_sha256":"48078dac86ea262378bff166124bcc64c3e8393b9fff4913992c7141a14f282b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VtAZxivRkSbmrsBpbMcua7uFeXe017lKrewvxPt+ORgNEStObGN4aWYB36FLSqDRGygBUM8M2NXcTu+bKf0PAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:57:13.786805Z","bundle_sha256":"912bfe192539975b2af67bcdc336ff62a96c80eb124a932da6ceda2116c1f13e"}}