{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IGHMOGB2OQRX5KNIHR5FC6HTPM","short_pith_number":"pith:IGHMOGB2","canonical_record":{"source":{"id":"1301.2827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-01-13T21:42:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f84a6b027db4b40c11ee2cd550606750098eafb3038fa281e29a0b2345393be8","abstract_canon_sha256":"fab2d5f08d6a796801ed8bbcde5932b07114f58f8f16f68049296faa4d4d7f2b"},"schema_version":"1.0"},"canonical_sha256":"418ec7183a74237ea9a83c7a5178f37b3851734168aeefd8bf0f95d4761abcce","source":{"kind":"arxiv","id":"1301.2827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2827","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2827v1","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2827","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"IGHMOGB2OQRX","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IGHMOGB2OQRX5KNI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IGHMOGB2","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IGHMOGB2OQRX5KNIHR5FC6HTPM","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-01-13T21:42:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f84a6b027db4b40c11ee2cd550606750098eafb3038fa281e29a0b2345393be8","abstract_canon_sha256":"fab2d5f08d6a796801ed8bbcde5932b07114f58f8f16f68049296faa4d4d7f2b"},"schema_version":"1.0"},"canonical_sha256":"418ec7183a74237ea9a83c7a5178f37b3851734168aeefd8bf0f95d4761abcce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:34.464438Z","signature_b64":"Ji/KeWGtWeFtUFMTReNWSmX3dJaPmKEQ6EcoVNpMA27rnv5p/0R2xz1258Oat1vt6nO8fhYLH6jCwpJLl4i8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"418ec7183a74237ea9a83c7a5178f37b3851734168aeefd8bf0f95d4761abcce","last_reissued_at":"2026-05-18T03:07:34.463882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:34.463882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2827","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":"2026-05-18T03:07:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o9/k25jrmMBgse7YiFYTj3t+FXXEDfIpvjOOcEad7a79iX9reUOpvnAkA30agvu21td69YCwsU9+TbbMPYctAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:30:15.954255Z"},"content_sha256":"e562af3ed41f50a651b81801fbe9f9f73ff1563a0125855bb74445c680c83e54","schema_version":"1.0","event_id":"sha256:e562af3ed41f50a651b81801fbe9f9f73ff1563a0125855bb74445c680c83e54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IGHMOGB2OQRX5KNIHR5FC6HTPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Using Euler-Lagrange Variational Principle to Obtain Flow Relations for Generalized Newtonian Fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.flu-dyn","authors_text":"Taha Sochi","submitted_at":"2013-01-13T21:42:32Z","abstract_excerpt":"Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in the flow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models; which include power law, Bingham, Herschel-Bulkley, Carreau and Cross; are used for demonstration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2827","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":"2026-05-18T03:07:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8YD3KvQdy/7NqqAI7rWS927L9w03UOLgQFUpzvxUFTEw05OUN3BavL3Zb2OjlMrP7sS2o56TJ4e2qJyKKYGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:30:15.954973Z"},"content_sha256":"ccaea2d9b5f63fb1000070eeea45cb9aeb54c32650db237d760a6e5d99bb4a16","schema_version":"1.0","event_id":"sha256:ccaea2d9b5f63fb1000070eeea45cb9aeb54c32650db237d760a6e5d99bb4a16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGHMOGB2OQRX5KNIHR5FC6HTPM/bundle.json","state_url":"https://pith.science/pith/IGHMOGB2OQRX5KNIHR5FC6HTPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGHMOGB2OQRX5KNIHR5FC6HTPM/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":"2026-06-06T14:30:15Z","links":{"resolver":"https://pith.science/pith/IGHMOGB2OQRX5KNIHR5FC6HTPM","bundle":"https://pith.science/pith/IGHMOGB2OQRX5KNIHR5FC6HTPM/bundle.json","state":"https://pith.science/pith/IGHMOGB2OQRX5KNIHR5FC6HTPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGHMOGB2OQRX5KNIHR5FC6HTPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IGHMOGB2OQRX5KNIHR5FC6HTPM","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":"fab2d5f08d6a796801ed8bbcde5932b07114f58f8f16f68049296faa4d4d7f2b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-01-13T21:42:32Z","title_canon_sha256":"f84a6b027db4b40c11ee2cd550606750098eafb3038fa281e29a0b2345393be8"},"schema_version":"1.0","source":{"id":"1301.2827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2827","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2827v1","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2827","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"IGHMOGB2OQRX","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IGHMOGB2OQRX5KNI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IGHMOGB2","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:ccaea2d9b5f63fb1000070eeea45cb9aeb54c32650db237d760a6e5d99bb4a16","target":"graph","created_at":"2026-05-18T03:07:34Z","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":"Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in the flow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models; which include power law, Bingham, Herschel-Bulkley, Carreau and Cross; are used for demonstration.","authors_text":"Taha Sochi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-01-13T21:42:32Z","title":"Using Euler-Lagrange Variational Principle to Obtain Flow Relations for Generalized Newtonian Fluids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2827","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:e562af3ed41f50a651b81801fbe9f9f73ff1563a0125855bb74445c680c83e54","target":"record","created_at":"2026-05-18T03:07:34Z","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":"fab2d5f08d6a796801ed8bbcde5932b07114f58f8f16f68049296faa4d4d7f2b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-01-13T21:42:32Z","title_canon_sha256":"f84a6b027db4b40c11ee2cd550606750098eafb3038fa281e29a0b2345393be8"},"schema_version":"1.0","source":{"id":"1301.2827","kind":"arxiv","version":1}},"canonical_sha256":"418ec7183a74237ea9a83c7a5178f37b3851734168aeefd8bf0f95d4761abcce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"418ec7183a74237ea9a83c7a5178f37b3851734168aeefd8bf0f95d4761abcce","first_computed_at":"2026-05-18T03:07:34.463882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:34.463882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ji/KeWGtWeFtUFMTReNWSmX3dJaPmKEQ6EcoVNpMA27rnv5p/0R2xz1258Oat1vt6nO8fhYLH6jCwpJLl4i8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:34.464438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e562af3ed41f50a651b81801fbe9f9f73ff1563a0125855bb74445c680c83e54","sha256:ccaea2d9b5f63fb1000070eeea45cb9aeb54c32650db237d760a6e5d99bb4a16"],"state_sha256":"72130b4b1f2a613ea05d2f8b2b67e68c5fadb9336c5edbb28d6cac7f72af5d89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jBAz8M7Bq8wO9NTK1+ePfspzI1lpZ4rhyUCgKK42IMJvRVzMZdBuAtCx68oZvUSvjsve1cXfywZWo1VvHydDDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:30:15.958820Z","bundle_sha256":"bf5df945d396937c660c13ec20ad1456ce73d14f6753edd46322c398ea899b47"}}