{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TNAM74HDMUN6WBYFGSSMSVFKST","short_pith_number":"pith:TNAM74HD","canonical_record":{"source":{"id":"2507.13330","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-07-17T17:48:19Z","cross_cats_sorted":["physics.bio-ph","physics.flu-dyn","q-bio.TO"],"title_canon_sha256":"dbf59e9f6d3d0d0a58e8da6a584dd71147b1f5f0ca646b941524d5cc3d9935cd","abstract_canon_sha256":"24c321a0d75ee339da107b1087f8cb90c7bfc4e4318da2b2884a6e70528d5299"},"schema_version":"1.0"},"canonical_sha256":"9b40cff0e3651beb070534a4c954aa94e94fc7edad499fa66374bc9dba7953c2","source":{"kind":"arxiv","id":"2507.13330","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13330","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13330v1","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13330","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"pith_short_12","alias_value":"TNAM74HDMUN6","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"pith_short_16","alias_value":"TNAM74HDMUN6WBYF","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"pith_short_8","alias_value":"TNAM74HD","created_at":"2026-07-05T11:38:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TNAM74HDMUN6WBYFGSSMSVFKST","target":"record","payload":{"canonical_record":{"source":{"id":"2507.13330","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-07-17T17:48:19Z","cross_cats_sorted":["physics.bio-ph","physics.flu-dyn","q-bio.TO"],"title_canon_sha256":"dbf59e9f6d3d0d0a58e8da6a584dd71147b1f5f0ca646b941524d5cc3d9935cd","abstract_canon_sha256":"24c321a0d75ee339da107b1087f8cb90c7bfc4e4318da2b2884a6e70528d5299"},"schema_version":"1.0"},"canonical_sha256":"9b40cff0e3651beb070534a4c954aa94e94fc7edad499fa66374bc9dba7953c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:59.257046Z","signature_b64":"9vmafgcJptvACUDt4JWL1Nfvnqs+cP3d1IOwKuQ4dt9U2pK3lx+q7WYXY9nCJQ0ZyOaySZWiUIdUf4/xk6GGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b40cff0e3651beb070534a4c954aa94e94fc7edad499fa66374bc9dba7953c2","last_reissued_at":"2026-07-05T11:38:59.256313Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:59.256313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.13330","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":"2026-07-05T11:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwvfNI/AMMkFLJBR7BU8ZihwUuMYRuAU035cmPNNAOyVBdEi0g+939/IZrzBxboA+e+kdzFo8dc858pxV+IFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:24:35.915042Z"},"content_sha256":"02c8052438e852a63e3eaefbe66e9a510c2bc3f60bea5229a73210124c644035","schema_version":"1.0","event_id":"sha256:02c8052438e852a63e3eaefbe66e9a510c2bc3f60bea5229a73210124c644035"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TNAM74HDMUN6WBYFGSSMSVFKST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A hierarchy of blood vessel models, Part II: 3D-3D to 3D-1D and 1D","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["physics.bio-ph","physics.flu-dyn","q-bio.TO"],"primary_cat":"math.AP","authors_text":"Laurel Ohm, Sarah Strikwerda","submitted_at":"2025-07-17T17:48:19Z","abstract_excerpt":"We propose and analyze a hierarchy of three models of blood perfusion through a tissue surrounding a thin arteriole or venule. Our goal is to rigorously link 3D-3D Darcy--Stokes, 3D-1D Darcy--Poiseuille, and 1D Green's function methods commonly used to model this process. Here in Part II, we consider the most detailed level, a 3D-3D Darcy-Stokes system coupled across the permeable vessel surface by mass conservation and pressure/stress balance conditions. We derive a convergence result between the 3D-3D model and both the 3D-1D Darcy--Poiseuille model and 1D Green's function model proposed in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13330","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.13330/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4VlRVpLhefijLCqexQzatg451HETnNwQ3KBk/G6Z8bYWie8l5VXluhcxDo2CXRzyEwrzQVUuXwpKRd2QYV96AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:24:35.915997Z"},"content_sha256":"8c5067b511dbc32814f95e41eb900d33d75ac423cf500eb255aa3fb4005fd4a1","schema_version":"1.0","event_id":"sha256:8c5067b511dbc32814f95e41eb900d33d75ac423cf500eb255aa3fb4005fd4a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNAM74HDMUN6WBYFGSSMSVFKST/bundle.json","state_url":"https://pith.science/pith/TNAM74HDMUN6WBYFGSSMSVFKST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNAM74HDMUN6WBYFGSSMSVFKST/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":"2026-08-14T12:24:35Z","links":{"resolver":"https://pith.science/pith/TNAM74HDMUN6WBYFGSSMSVFKST","bundle":"https://pith.science/pith/TNAM74HDMUN6WBYFGSSMSVFKST/bundle.json","state":"https://pith.science/pith/TNAM74HDMUN6WBYFGSSMSVFKST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNAM74HDMUN6WBYFGSSMSVFKST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TNAM74HDMUN6WBYFGSSMSVFKST","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":"24c321a0d75ee339da107b1087f8cb90c7bfc4e4318da2b2884a6e70528d5299","cross_cats_sorted":["physics.bio-ph","physics.flu-dyn","q-bio.TO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-07-17T17:48:19Z","title_canon_sha256":"dbf59e9f6d3d0d0a58e8da6a584dd71147b1f5f0ca646b941524d5cc3d9935cd"},"schema_version":"1.0","source":{"id":"2507.13330","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13330","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13330v1","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13330","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"pith_short_12","alias_value":"TNAM74HDMUN6","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"pith_short_16","alias_value":"TNAM74HDMUN6WBYF","created_at":"2026-07-05T11:38:59Z"},{"alias_kind":"pith_short_8","alias_value":"TNAM74HD","created_at":"2026-07-05T11:38:59Z"}],"graph_snapshots":[{"event_id":"sha256:8c5067b511dbc32814f95e41eb900d33d75ac423cf500eb255aa3fb4005fd4a1","target":"graph","created_at":"2026-07-05T11:38:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.13330/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose and analyze a hierarchy of three models of blood perfusion through a tissue surrounding a thin arteriole or venule. Our goal is to rigorously link 3D-3D Darcy--Stokes, 3D-1D Darcy--Poiseuille, and 1D Green's function methods commonly used to model this process. Here in Part II, we consider the most detailed level, a 3D-3D Darcy-Stokes system coupled across the permeable vessel surface by mass conservation and pressure/stress balance conditions. We derive a convergence result between the 3D-3D model and both the 3D-1D Darcy--Poiseuille model and 1D Green's function model proposed in ","authors_text":"Laurel Ohm, Sarah Strikwerda","cross_cats":["physics.bio-ph","physics.flu-dyn","q-bio.TO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-07-17T17:48:19Z","title":"A hierarchy of blood vessel models, Part II: 3D-3D to 3D-1D and 1D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13330","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":"sha256:02c8052438e852a63e3eaefbe66e9a510c2bc3f60bea5229a73210124c644035","target":"record","created_at":"2026-07-05T11:38:59Z","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":"24c321a0d75ee339da107b1087f8cb90c7bfc4e4318da2b2884a6e70528d5299","cross_cats_sorted":["physics.bio-ph","physics.flu-dyn","q-bio.TO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-07-17T17:48:19Z","title_canon_sha256":"dbf59e9f6d3d0d0a58e8da6a584dd71147b1f5f0ca646b941524d5cc3d9935cd"},"schema_version":"1.0","source":{"id":"2507.13330","kind":"arxiv","version":1}},"canonical_sha256":"9b40cff0e3651beb070534a4c954aa94e94fc7edad499fa66374bc9dba7953c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b40cff0e3651beb070534a4c954aa94e94fc7edad499fa66374bc9dba7953c2","first_computed_at":"2026-07-05T11:38:59.256313Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:59.256313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9vmafgcJptvACUDt4JWL1Nfvnqs+cP3d1IOwKuQ4dt9U2pK3lx+q7WYXY9nCJQ0ZyOaySZWiUIdUf4/xk6GGDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:59.257046Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13330","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02c8052438e852a63e3eaefbe66e9a510c2bc3f60bea5229a73210124c644035","sha256:8c5067b511dbc32814f95e41eb900d33d75ac423cf500eb255aa3fb4005fd4a1"],"state_sha256":"fa34a832dc7883cf316c5ba5fabc2b900a466d3aeffe949d7890a1c4c2bcc545"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+dttbshRJTJFivtbIHbCg4sMowcPWeFvfnAfpgyJB95jA/SAflpDFeVewl00WlflOVm4veeqh0E4kFOTG0QuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T12:24:35.922471Z","bundle_sha256":"898a38e3122373ccf26ce8baabaeec0bebdca435dc6f3c2906236148a0f3498f"}}