{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TMGPYNNARPUDFAH3C54XSI7VEU","short_pith_number":"pith:TMGPYNNA","canonical_record":{"source":{"id":"1610.07120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-23T03:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"8d1dc337bcbfb55ab0702d138fd2942d335ae32448e737070de32710a9a121ed","abstract_canon_sha256":"9b821e7cd5a4804d0b315e718b68ebceede9798930bc26f124105eadf91f9940"},"schema_version":"1.0"},"canonical_sha256":"9b0cfc35a08be83280fb17797923f5250f35621e900e89eb6f78d1d1b7897ff6","source":{"kind":"arxiv","id":"1610.07120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07120","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07120v1","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07120","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"TMGPYNNARPUD","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TMGPYNNARPUDFAH3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TMGPYNNA","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TMGPYNNARPUDFAH3C54XSI7VEU","target":"record","payload":{"canonical_record":{"source":{"id":"1610.07120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-23T03:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"8d1dc337bcbfb55ab0702d138fd2942d335ae32448e737070de32710a9a121ed","abstract_canon_sha256":"9b821e7cd5a4804d0b315e718b68ebceede9798930bc26f124105eadf91f9940"},"schema_version":"1.0"},"canonical_sha256":"9b0cfc35a08be83280fb17797923f5250f35621e900e89eb6f78d1d1b7897ff6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.520547Z","signature_b64":"0w7T88eW8SwtI3dbaSB6Jdnc2/AGdmpVQKV42URdKJjqxOPQMzUuOQoaVsNXw9JKpwG59glGF2atTF84zJDbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b0cfc35a08be83280fb17797923f5250f35621e900e89eb6f78d1d1b7897ff6","last_reissued_at":"2026-05-18T00:35:55.520026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.520026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.07120","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":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Qz1FdQO9YYfxs98fW5J760J1rBn+UZWReWY7pAMeXqck9ZzxUUUokY6yth/oh5PnV/F9kc5lEVFi7MkJyGPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:18:31.316710Z"},"content_sha256":"7ce9b40e120bba8bc55e64d35436a4c104bcb5ea2f92db7eb41c3a8cd244d497","schema_version":"1.0","event_id":"sha256:7ce9b40e120bba8bc55e64d35436a4c104bcb5ea2f92db7eb41c3a8cd244d497"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TMGPYNNARPUDFAH3C54XSI7VEU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterative coupling of flow, geomechanics and adaptive phase-field fracture including level-set crack width approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Mary F. Wheeler, Sanghyun Lee, Thomas Wick","submitted_at":"2016-10-23T03:38:02Z","abstract_excerpt":"In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field approach. The extension to fixed-stress splitting to propagating phase-field fractures and systematic investigation of its properties are important enhancements to existing studies. Moreover, we provide an accurate computation of the fracture opening using level-set approaches and a subsequent finite element interpolation of the width. The latter enters as fract"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07120","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":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2o65F7BZDoFvrHtpGy6rJ6aMMjPI4/ofL9i3OG8zWU3+nDEy6kvQ5hAxwYBUYTW2HipmIzpYJw/rib7ocZKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:18:31.317414Z"},"content_sha256":"2b2a55e2d6f6adde9166667aa837e3b22175cd24d0a07bf9a3ca0e1b224e2d43","schema_version":"1.0","event_id":"sha256:2b2a55e2d6f6adde9166667aa837e3b22175cd24d0a07bf9a3ca0e1b224e2d43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMGPYNNARPUDFAH3C54XSI7VEU/bundle.json","state_url":"https://pith.science/pith/TMGPYNNARPUDFAH3C54XSI7VEU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMGPYNNARPUDFAH3C54XSI7VEU/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":"2026-05-25T17:18:31Z","links":{"resolver":"https://pith.science/pith/TMGPYNNARPUDFAH3C54XSI7VEU","bundle":"https://pith.science/pith/TMGPYNNARPUDFAH3C54XSI7VEU/bundle.json","state":"https://pith.science/pith/TMGPYNNARPUDFAH3C54XSI7VEU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMGPYNNARPUDFAH3C54XSI7VEU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TMGPYNNARPUDFAH3C54XSI7VEU","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":"9b821e7cd5a4804d0b315e718b68ebceede9798930bc26f124105eadf91f9940","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-23T03:38:02Z","title_canon_sha256":"8d1dc337bcbfb55ab0702d138fd2942d335ae32448e737070de32710a9a121ed"},"schema_version":"1.0","source":{"id":"1610.07120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07120","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07120v1","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07120","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"TMGPYNNARPUD","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TMGPYNNARPUDFAH3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TMGPYNNA","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:2b2a55e2d6f6adde9166667aa837e3b22175cd24d0a07bf9a3ca0e1b224e2d43","target":"graph","created_at":"2026-05-18T00:35:55Z","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 this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field approach. The extension to fixed-stress splitting to propagating phase-field fractures and systematic investigation of its properties are important enhancements to existing studies. Moreover, we provide an accurate computation of the fracture opening using level-set approaches and a subsequent finite element interpolation of the width. The latter enters as fract","authors_text":"Mary F. Wheeler, Sanghyun Lee, Thomas Wick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-23T03:38:02Z","title":"Iterative coupling of flow, geomechanics and adaptive phase-field fracture including level-set crack width approaches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07120","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":"sha256:7ce9b40e120bba8bc55e64d35436a4c104bcb5ea2f92db7eb41c3a8cd244d497","target":"record","created_at":"2026-05-18T00:35:55Z","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":"9b821e7cd5a4804d0b315e718b68ebceede9798930bc26f124105eadf91f9940","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-23T03:38:02Z","title_canon_sha256":"8d1dc337bcbfb55ab0702d138fd2942d335ae32448e737070de32710a9a121ed"},"schema_version":"1.0","source":{"id":"1610.07120","kind":"arxiv","version":1}},"canonical_sha256":"9b0cfc35a08be83280fb17797923f5250f35621e900e89eb6f78d1d1b7897ff6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b0cfc35a08be83280fb17797923f5250f35621e900e89eb6f78d1d1b7897ff6","first_computed_at":"2026-05-18T00:35:55.520026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.520026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0w7T88eW8SwtI3dbaSB6Jdnc2/AGdmpVQKV42URdKJjqxOPQMzUuOQoaVsNXw9JKpwG59glGF2atTF84zJDbCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.520547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ce9b40e120bba8bc55e64d35436a4c104bcb5ea2f92db7eb41c3a8cd244d497","sha256:2b2a55e2d6f6adde9166667aa837e3b22175cd24d0a07bf9a3ca0e1b224e2d43"],"state_sha256":"e5ffd88e8f6f64ebf21172a41482ad10c00b57fbb879eaf021d752f10d923714"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BY7oaqtQncUZMNHcLcvCADCZKcfSffmcgauBVw0xs5Edv/wY9cBOtlFaUW5HCviMmULc6jEp3O9cx2MJKfqGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:18:31.320926Z","bundle_sha256":"1e2a0fe9275eb08c880824b0aa41f6be08c84883fd7d7a590fc02407db405628"}}