{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:22ER4SMMR22C5HACF2QNCYLMTQ","short_pith_number":"pith:22ER4SMM","canonical_record":{"source":{"id":"1405.4115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-05-16T10:14:46Z","cross_cats_sorted":[],"title_canon_sha256":"83793cf6c57136f601bc3043f158f9c427e0328bda4477cf19c70d5426973f15","abstract_canon_sha256":"22b1b77c2317e696a100ffbce3c637756c85d61ea9be1e3eb699278e26dcf7fc"},"schema_version":"1.0"},"canonical_sha256":"d6891e498c8eb42e9c022ea0d1616c9c3a53dc3818716b360c0824f92217f91f","source":{"kind":"arxiv","id":"1405.4115","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4115","created_at":"2026-05-18T02:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4115v1","created_at":"2026-05-18T02:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4115","created_at":"2026-05-18T02:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"22ER4SMMR22C","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"22ER4SMMR22C5HAC","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"22ER4SMM","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:22ER4SMMR22C5HACF2QNCYLMTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-05-16T10:14:46Z","cross_cats_sorted":[],"title_canon_sha256":"83793cf6c57136f601bc3043f158f9c427e0328bda4477cf19c70d5426973f15","abstract_canon_sha256":"22b1b77c2317e696a100ffbce3c637756c85d61ea9be1e3eb699278e26dcf7fc"},"schema_version":"1.0"},"canonical_sha256":"d6891e498c8eb42e9c022ea0d1616c9c3a53dc3818716b360c0824f92217f91f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:38.457885Z","signature_b64":"T/ZoMTNQ3oe1XQjFtS8af25CpwPM07PYQVLdqDom7sPXX9T208vIkekDw20Z0oaIFdK8tdeMy8FdFpXkALWZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6891e498c8eb42e9c022ea0d1616c9c3a53dc3818716b360c0824f92217f91f","last_reissued_at":"2026-05-18T02:40:38.457108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:38.457108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4115","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":"2026-05-18T02:40:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whN1HmV/fDu9KJr2mcH4GMgQccHd/wl371qdGZp3jdsgYxaaH+yYTpPfzSyGzvgJxKG6Ivjsg8QRZK3mPZi4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:14:37.436834Z"},"content_sha256":"212c23d5f9ddf91f9cb9f9030cd1993191bafaee76afddf3c7d524e52e50a0aa","schema_version":"1.0","event_id":"sha256:212c23d5f9ddf91f9cb9f9030cd1993191bafaee76afddf3c7d524e52e50a0aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:22ER4SMMR22C5HACF2QNCYLMTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Flow of Newtonian and power law fluids in elastic tubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Taha Sochi","submitted_at":"2014-05-16T10:14:46Z","abstract_excerpt":"We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4115","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":"2026-05-18T02:40:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TmYWNIEvhfBPYdSdQO8gINuQomVr2hM1gaO/QwnSiAX74tczcfYmgcVLbdbyErNnlHq+7Q1dkQIKWbtZVglQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:14:37.437488Z"},"content_sha256":"2c15129c34fe2cb6d45ddf3623f7af5f87fe2bf78d3e44c786131f4383cac00d","schema_version":"1.0","event_id":"sha256:2c15129c34fe2cb6d45ddf3623f7af5f87fe2bf78d3e44c786131f4383cac00d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22ER4SMMR22C5HACF2QNCYLMTQ/bundle.json","state_url":"https://pith.science/pith/22ER4SMMR22C5HACF2QNCYLMTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22ER4SMMR22C5HACF2QNCYLMTQ/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":"2026-06-06T22:14:37Z","links":{"resolver":"https://pith.science/pith/22ER4SMMR22C5HACF2QNCYLMTQ","bundle":"https://pith.science/pith/22ER4SMMR22C5HACF2QNCYLMTQ/bundle.json","state":"https://pith.science/pith/22ER4SMMR22C5HACF2QNCYLMTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22ER4SMMR22C5HACF2QNCYLMTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:22ER4SMMR22C5HACF2QNCYLMTQ","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":"22b1b77c2317e696a100ffbce3c637756c85d61ea9be1e3eb699278e26dcf7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-05-16T10:14:46Z","title_canon_sha256":"83793cf6c57136f601bc3043f158f9c427e0328bda4477cf19c70d5426973f15"},"schema_version":"1.0","source":{"id":"1405.4115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4115","created_at":"2026-05-18T02:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4115v1","created_at":"2026-05-18T02:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4115","created_at":"2026-05-18T02:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"22ER4SMMR22C","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"22ER4SMMR22C5HAC","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"22ER4SMM","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:2c15129c34fe2cb6d45ddf3623f7af5f87fe2bf78d3e44c786131f4383cac00d","target":"graph","created_at":"2026-05-18T02:40:38Z","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 derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting case","authors_text":"Taha Sochi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-05-16T10:14:46Z","title":"The Flow of Newtonian and power law fluids in elastic tubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4115","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":"sha256:212c23d5f9ddf91f9cb9f9030cd1993191bafaee76afddf3c7d524e52e50a0aa","target":"record","created_at":"2026-05-18T02:40:38Z","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":"22b1b77c2317e696a100ffbce3c637756c85d61ea9be1e3eb699278e26dcf7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-05-16T10:14:46Z","title_canon_sha256":"83793cf6c57136f601bc3043f158f9c427e0328bda4477cf19c70d5426973f15"},"schema_version":"1.0","source":{"id":"1405.4115","kind":"arxiv","version":1}},"canonical_sha256":"d6891e498c8eb42e9c022ea0d1616c9c3a53dc3818716b360c0824f92217f91f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6891e498c8eb42e9c022ea0d1616c9c3a53dc3818716b360c0824f92217f91f","first_computed_at":"2026-05-18T02:40:38.457108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:38.457108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T/ZoMTNQ3oe1XQjFtS8af25CpwPM07PYQVLdqDom7sPXX9T208vIkekDw20Z0oaIFdK8tdeMy8FdFpXkALWZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:38.457885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:212c23d5f9ddf91f9cb9f9030cd1993191bafaee76afddf3c7d524e52e50a0aa","sha256:2c15129c34fe2cb6d45ddf3623f7af5f87fe2bf78d3e44c786131f4383cac00d"],"state_sha256":"a9aabbaefb9636d5cd9c066e0f00040690b4cffa169616ca7b5bbf6e1ceee719"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcIG1PIPNYpPGYs2CZZXYTCpIorYCtegurBVthP6Px9prNXEE0Knyd+uVkBOmaZmhhU3uSmsL1WVqCEk/W0eAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:14:37.441686Z","bundle_sha256":"8141c258f948020ab781d60097ee2f987b64d6c872683f4636946df6c02a16f5"}}