{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7KJ5ZEQS7FSMGWLNPG4DPXSELI","short_pith_number":"pith:7KJ5ZEQS","canonical_record":{"source":{"id":"1412.5529","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-15T22:22:34Z","cross_cats_sorted":["math.NA","physics.geo-ph"],"title_canon_sha256":"a632ea0d6f87160c8942731a75ceb434b4990a68f5e759040220dd0d9506bfec","abstract_canon_sha256":"d78daa0ef6987bf6ea9b82ae0877e5b3b83e273bb2704de325c040a3b1837212"},"schema_version":"1.0"},"canonical_sha256":"fa93dc9212f964c3596d79b837de445a274f36f7ec6c1a430b8ab8f18489004e","source":{"kind":"arxiv","id":"1412.5529","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5529","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5529v3","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5529","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"7KJ5ZEQS7FSM","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7KJ5ZEQS7FSMGWLN","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7KJ5ZEQS","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7KJ5ZEQS7FSMGWLNPG4DPXSELI","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5529","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-15T22:22:34Z","cross_cats_sorted":["math.NA","physics.geo-ph"],"title_canon_sha256":"a632ea0d6f87160c8942731a75ceb434b4990a68f5e759040220dd0d9506bfec","abstract_canon_sha256":"d78daa0ef6987bf6ea9b82ae0877e5b3b83e273bb2704de325c040a3b1837212"},"schema_version":"1.0"},"canonical_sha256":"fa93dc9212f964c3596d79b837de445a274f36f7ec6c1a430b8ab8f18489004e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:13.419454Z","signature_b64":"6vnofAJ4qC0+QYWgMW/FGXTBpnl1umn7NDSHqrJADtE0JkmPM5EsK5ElFu/OWQEXGz/eTSkvDrrCyR0Rilx5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa93dc9212f964c3596d79b837de445a274f36f7ec6c1a430b8ab8f18489004e","last_reissued_at":"2026-05-18T02:18:13.419086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:13.419086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5529","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BkhCpxQ/AH8Lw1QNZK0Nhy2l1+mC4E/63/S1LWp5iJb9aNup12yPmoPbPimR/UeNcGQnF/G3+3RZC7siIWmmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T19:00:02.806576Z"},"content_sha256":"a60f01fc68144045e1f1da09cfe22b8a3a8321ac59133e5e132302e477fe803b","schema_version":"1.0","event_id":"sha256:a60f01fc68144045e1f1da09cfe22b8a3a8321ac59133e5e132302e477fe803b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7KJ5ZEQS7FSMGWLNPG4DPXSELI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Particle velocity based universal algorithm for numerical simulation of hydraulic fractures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.geo-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Gennady Mishuris, Michal Wrobel","submitted_at":"2014-12-15T22:22:34Z","abstract_excerpt":"In the paper, we propose a new effective mathematical formulation and resulting universal numerical algorithm capable of tackling various HF models in the framework of a unified approach. The presented numerical scheme is not limited to any particular elasticity model or crack propagation regime. Its basic assumptions are: i) proper choice of independent and dependent variables (with the direct utilization of a new one - the reduced particle velocity), ii) tracing the fracture front by use of the speed equation which can be integrated in a closed form and sets an explicit relation between the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5529","kind":"arxiv","version":3},"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":"2026-05-18T02:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nng9mjWZqBRAD6mjBre+jPZDDDpHi7moj3KOaRZ3sVKBMTa7E0mNi5Ef+TBm84bGhD21XmGGq8c0wQ3pegngAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T19:00:02.806910Z"},"content_sha256":"e1802dc166574977e046c780368af84f32b9820f0bdfb4bf44ccccde8025c8f7","schema_version":"1.0","event_id":"sha256:e1802dc166574977e046c780368af84f32b9820f0bdfb4bf44ccccde8025c8f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7KJ5ZEQS7FSMGWLNPG4DPXSELI/bundle.json","state_url":"https://pith.science/pith/7KJ5ZEQS7FSMGWLNPG4DPXSELI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7KJ5ZEQS7FSMGWLNPG4DPXSELI/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":"2026-07-01T19:00:02Z","links":{"resolver":"https://pith.science/pith/7KJ5ZEQS7FSMGWLNPG4DPXSELI","bundle":"https://pith.science/pith/7KJ5ZEQS7FSMGWLNPG4DPXSELI/bundle.json","state":"https://pith.science/pith/7KJ5ZEQS7FSMGWLNPG4DPXSELI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7KJ5ZEQS7FSMGWLNPG4DPXSELI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7KJ5ZEQS7FSMGWLNPG4DPXSELI","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":"d78daa0ef6987bf6ea9b82ae0877e5b3b83e273bb2704de325c040a3b1837212","cross_cats_sorted":["math.NA","physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-15T22:22:34Z","title_canon_sha256":"a632ea0d6f87160c8942731a75ceb434b4990a68f5e759040220dd0d9506bfec"},"schema_version":"1.0","source":{"id":"1412.5529","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5529","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5529v3","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5529","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"7KJ5ZEQS7FSM","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7KJ5ZEQS7FSMGWLN","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7KJ5ZEQS","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:e1802dc166574977e046c780368af84f32b9820f0bdfb4bf44ccccde8025c8f7","target":"graph","created_at":"2026-05-18T02:18:13Z","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":"In the paper, we propose a new effective mathematical formulation and resulting universal numerical algorithm capable of tackling various HF models in the framework of a unified approach. The presented numerical scheme is not limited to any particular elasticity model or crack propagation regime. Its basic assumptions are: i) proper choice of independent and dependent variables (with the direct utilization of a new one - the reduced particle velocity), ii) tracing the fracture front by use of the speed equation which can be integrated in a closed form and sets an explicit relation between the ","authors_text":"Gennady Mishuris, Michal Wrobel","cross_cats":["math.NA","physics.geo-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-15T22:22:34Z","title":"Particle velocity based universal algorithm for numerical simulation of hydraulic fractures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5529","kind":"arxiv","version":3},"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:a60f01fc68144045e1f1da09cfe22b8a3a8321ac59133e5e132302e477fe803b","target":"record","created_at":"2026-05-18T02:18:13Z","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":"d78daa0ef6987bf6ea9b82ae0877e5b3b83e273bb2704de325c040a3b1837212","cross_cats_sorted":["math.NA","physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-15T22:22:34Z","title_canon_sha256":"a632ea0d6f87160c8942731a75ceb434b4990a68f5e759040220dd0d9506bfec"},"schema_version":"1.0","source":{"id":"1412.5529","kind":"arxiv","version":3}},"canonical_sha256":"fa93dc9212f964c3596d79b837de445a274f36f7ec6c1a430b8ab8f18489004e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa93dc9212f964c3596d79b837de445a274f36f7ec6c1a430b8ab8f18489004e","first_computed_at":"2026-05-18T02:18:13.419086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:13.419086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6vnofAJ4qC0+QYWgMW/FGXTBpnl1umn7NDSHqrJADtE0JkmPM5EsK5ElFu/OWQEXGz/eTSkvDrrCyR0Rilx5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:13.419454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5529","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a60f01fc68144045e1f1da09cfe22b8a3a8321ac59133e5e132302e477fe803b","sha256:e1802dc166574977e046c780368af84f32b9820f0bdfb4bf44ccccde8025c8f7"],"state_sha256":"f96a9fcaefe28b08a9577fca3de2ed080e8671d86c5be642858199fae79f1afe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3q8LQeRRsYOMr7wqQmtwWFWhmti47W+Prvnb1nN00ko5vOFn058LQHW8HokKYPfQ37jygJ2PJuCjfEGqWQKeDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T19:00:02.808784Z","bundle_sha256":"ba2d34ffa927456977d3021f78ad7ffa7a79a291174366103c7885e37aef62c3"}}