{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SL6VHVVLESUSMQXFR2TP2Y64X6","short_pith_number":"pith:SL6VHVVL","canonical_record":{"source":{"id":"1308.6629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-30T00:02:10Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"0230d14fa45ccbe529f8b47556b9401b003d6d1ff43cbd21f300d59a8718b1cc","abstract_canon_sha256":"3360d34113d4b122b47664d6091c0342517c4b5390877e95ba0410402beef8bc"},"schema_version":"1.0"},"canonical_sha256":"92fd53d6ab24a92642e58ea6fd63dcbfbff644ed194742db8da56131c1e83cdc","source":{"kind":"arxiv","id":"1308.6629","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6629","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6629v1","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6629","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"SL6VHVVLESUS","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SL6VHVVLESUSMQXF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SL6VHVVL","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SL6VHVVLESUSMQXFR2TP2Y64X6","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-30T00:02:10Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"0230d14fa45ccbe529f8b47556b9401b003d6d1ff43cbd21f300d59a8718b1cc","abstract_canon_sha256":"3360d34113d4b122b47664d6091c0342517c4b5390877e95ba0410402beef8bc"},"schema_version":"1.0"},"canonical_sha256":"92fd53d6ab24a92642e58ea6fd63dcbfbff644ed194742db8da56131c1e83cdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:38.602152Z","signature_b64":"FcRYbHxpP/x/urpYMK/pXeh39sMMwFtcW8CICk9fXZmtIDwFdBlIYY37tJukkmoi6RxFRZQW9LOCT39flqKHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92fd53d6ab24a92642e58ea6fd63dcbfbff644ed194742db8da56131c1e83cdc","last_reissued_at":"2026-05-18T03:14:38.601659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:38.601659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6629","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":"2026-05-18T03:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5e8RvbipNjWe3nZCOHd9yixsufYPjWfFYtvjv/MAE+k4FaFYuMcCPyWWtAaQz5HHLom9C9G2dtnYmtJJYsJODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:09:54.871405Z"},"content_sha256":"fe84898877256adddfe0e6b44e7436342e31e800ba17dfa9f29c2ecbd895b111","schema_version":"1.0","event_id":"sha256:fe84898877256adddfe0e6b44e7436342e31e800ba17dfa9f29c2ecbd895b111"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SL6VHVVLESUSMQXFR2TP2Y64X6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A volume-of-fluid formulation for the study of co-flowing fluids governed by the Hele-Shaw equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Shahriar Afkhami, Yuriko Renardy","submitted_at":"2013-08-30T00:02:10Z","abstract_excerpt":"We present a computational framework to address the flow of two immiscible viscous liquids which co-flow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions based on the shallow depth of the domain are used to reduce the governing equations to one of Hele-Shaw type. The distinctive feature of the numerical method is the accurate modeling of the capillary effects. A continuum approach coupled with a volume-of-fluid formulation for computing the interface motion and for modeling the interfacial tension in Hele-Shaw flows is fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6629","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":"2026-05-18T03:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gfXWjiZjepfb9H1yyAwOprisA+N606FO413TXyFeBOdMVreHKpf8N5N+fR5aeI9wf1we9HSdSYI60Mq8ptb5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:09:54.872111Z"},"content_sha256":"84faafb830b75de13592e5327fd2af024e16e713fb7a3ee5d3f909d83643f7b9","schema_version":"1.0","event_id":"sha256:84faafb830b75de13592e5327fd2af024e16e713fb7a3ee5d3f909d83643f7b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SL6VHVVLESUSMQXFR2TP2Y64X6/bundle.json","state_url":"https://pith.science/pith/SL6VHVVLESUSMQXFR2TP2Y64X6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SL6VHVVLESUSMQXFR2TP2Y64X6/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":"2026-06-11T21:09:54Z","links":{"resolver":"https://pith.science/pith/SL6VHVVLESUSMQXFR2TP2Y64X6","bundle":"https://pith.science/pith/SL6VHVVLESUSMQXFR2TP2Y64X6/bundle.json","state":"https://pith.science/pith/SL6VHVVLESUSMQXFR2TP2Y64X6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SL6VHVVLESUSMQXFR2TP2Y64X6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SL6VHVVLESUSMQXFR2TP2Y64X6","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":"3360d34113d4b122b47664d6091c0342517c4b5390877e95ba0410402beef8bc","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-30T00:02:10Z","title_canon_sha256":"0230d14fa45ccbe529f8b47556b9401b003d6d1ff43cbd21f300d59a8718b1cc"},"schema_version":"1.0","source":{"id":"1308.6629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6629","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6629v1","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6629","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"SL6VHVVLESUS","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SL6VHVVLESUSMQXF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SL6VHVVL","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:84faafb830b75de13592e5327fd2af024e16e713fb7a3ee5d3f909d83643f7b9","target":"graph","created_at":"2026-05-18T03:14:38Z","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 present a computational framework to address the flow of two immiscible viscous liquids which co-flow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions based on the shallow depth of the domain are used to reduce the governing equations to one of Hele-Shaw type. The distinctive feature of the numerical method is the accurate modeling of the capillary effects. A continuum approach coupled with a volume-of-fluid formulation for computing the interface motion and for modeling the interfacial tension in Hele-Shaw flows is fo","authors_text":"Shahriar Afkhami, Yuriko Renardy","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-30T00:02:10Z","title":"A volume-of-fluid formulation for the study of co-flowing fluids governed by the Hele-Shaw equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6629","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:fe84898877256adddfe0e6b44e7436342e31e800ba17dfa9f29c2ecbd895b111","target":"record","created_at":"2026-05-18T03:14:38Z","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":"3360d34113d4b122b47664d6091c0342517c4b5390877e95ba0410402beef8bc","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-30T00:02:10Z","title_canon_sha256":"0230d14fa45ccbe529f8b47556b9401b003d6d1ff43cbd21f300d59a8718b1cc"},"schema_version":"1.0","source":{"id":"1308.6629","kind":"arxiv","version":1}},"canonical_sha256":"92fd53d6ab24a92642e58ea6fd63dcbfbff644ed194742db8da56131c1e83cdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92fd53d6ab24a92642e58ea6fd63dcbfbff644ed194742db8da56131c1e83cdc","first_computed_at":"2026-05-18T03:14:38.601659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:38.601659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FcRYbHxpP/x/urpYMK/pXeh39sMMwFtcW8CICk9fXZmtIDwFdBlIYY37tJukkmoi6RxFRZQW9LOCT39flqKHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:38.602152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe84898877256adddfe0e6b44e7436342e31e800ba17dfa9f29c2ecbd895b111","sha256:84faafb830b75de13592e5327fd2af024e16e713fb7a3ee5d3f909d83643f7b9"],"state_sha256":"548585edd81ff78e4d46fc0b0f003d154e9c45b1cb8fb81c6908619a835361d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"56iCwn/ahHNxAMZ2zASHeQLdZFXU92JUNMSXD4PBHmUcKlh9449f0N4AcPv0vMjbuaPNx3f+CP1xJoZdRgRpCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:09:54.876002Z","bundle_sha256":"ae06e90bc7149c6a94fa193776a67affcc04bcd62c03c9e5051c4c4351efa396"}}