{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BOSYKHOOHF2E2OMZN6VVARDQWF","short_pith_number":"pith:BOSYKHOO","canonical_record":{"source":{"id":"1810.12761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-30T14:15:19Z","cross_cats_sorted":[],"title_canon_sha256":"9f90f95fb99b9b7a7e0ee521e32a9a4530bde745274e18d8be18e59610fae180","abstract_canon_sha256":"c29e50d55f7ebfa0bae96e82af341f2ff28428e06fabbbe81a54594f9a9cbe9e"},"schema_version":"1.0"},"canonical_sha256":"0ba5851dce39744d39996fab504470b1712321d40e1473df8bccf58b55d85c12","source":{"kind":"arxiv","id":"1810.12761","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12761","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12761v1","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12761","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"BOSYKHOOHF2E","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BOSYKHOOHF2E2OMZ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BOSYKHOO","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BOSYKHOOHF2E2OMZN6VVARDQWF","target":"record","payload":{"canonical_record":{"source":{"id":"1810.12761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-30T14:15:19Z","cross_cats_sorted":[],"title_canon_sha256":"9f90f95fb99b9b7a7e0ee521e32a9a4530bde745274e18d8be18e59610fae180","abstract_canon_sha256":"c29e50d55f7ebfa0bae96e82af341f2ff28428e06fabbbe81a54594f9a9cbe9e"},"schema_version":"1.0"},"canonical_sha256":"0ba5851dce39744d39996fab504470b1712321d40e1473df8bccf58b55d85c12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:30.055864Z","signature_b64":"8Jve/F792i1+vMRkpZu8HON3tjPOPbKLuT3IcpW1K82oIjWg1+TQXuBMCyXwANhQz1Ke+uDqSbH50Rc8EfzrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ba5851dce39744d39996fab504470b1712321d40e1473df8bccf58b55d85c12","last_reissued_at":"2026-05-17T23:44:30.055181Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:30.055181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.12761","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":"2026-05-17T23:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uoxka73yr0VRCWfOrGTzV8TJHsC5IC0m5zK/VEPS41NrxuOXTED7jAbA7usu6bOIyrO3PFz1+AQ9LtTs5pLrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:50:42.953440Z"},"content_sha256":"4d08ec2e65480737f4ab09bc64e359b246daf23a26e4e4309f4438c55501017a","schema_version":"1.0","event_id":"sha256:4d08ec2e65480737f4ab09bc64e359b246daf23a26e4e4309f4438c55501017a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BOSYKHOOHF2E2OMZN6VVARDQWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A multiscale flux basis for mortar mixed discretizations of reduced Darcy-Forchheimer fracture models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alessio Fumagalli, Ana Budi\\v{s}a, Elyes Ahmed","submitted_at":"2018-10-30T14:15:19Z","abstract_excerpt":"In this paper, a multiscale flux basis algorithm is developed to efficiently solve a flow problem in fractured porous media. Here, we take into account a mixed-dimensional setting of the discrete fracture matrix model, where the fracture network is represented as lower-dimensional object. We assume the linear Darcy model in the rock matrix and the non-linear Forchheimer model in the fractures. In our formulation, we are able to reformulate the matrix-fracture problem to only the fracture network problem and, therefore, significantly reduce the computational cost. The resulting problem is then "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12761","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":"2026-05-17T23:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Lyg4DnaV7AyCYlVy1acdVNPyZoA5La4HPaYNDQsrFhbIZm81MPOkAWtped/GdMCVXkhCIFlInXk/s9S4OK8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:50:42.954151Z"},"content_sha256":"35287b7e4fc06edd77f3729c78ffd57b6b5f3f5fb13ba6f7a787995e47f36403","schema_version":"1.0","event_id":"sha256:35287b7e4fc06edd77f3729c78ffd57b6b5f3f5fb13ba6f7a787995e47f36403"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BOSYKHOOHF2E2OMZN6VVARDQWF/bundle.json","state_url":"https://pith.science/pith/BOSYKHOOHF2E2OMZN6VVARDQWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BOSYKHOOHF2E2OMZN6VVARDQWF/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":"2026-06-09T15:50:42Z","links":{"resolver":"https://pith.science/pith/BOSYKHOOHF2E2OMZN6VVARDQWF","bundle":"https://pith.science/pith/BOSYKHOOHF2E2OMZN6VVARDQWF/bundle.json","state":"https://pith.science/pith/BOSYKHOOHF2E2OMZN6VVARDQWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BOSYKHOOHF2E2OMZN6VVARDQWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BOSYKHOOHF2E2OMZN6VVARDQWF","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":"c29e50d55f7ebfa0bae96e82af341f2ff28428e06fabbbe81a54594f9a9cbe9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-30T14:15:19Z","title_canon_sha256":"9f90f95fb99b9b7a7e0ee521e32a9a4530bde745274e18d8be18e59610fae180"},"schema_version":"1.0","source":{"id":"1810.12761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12761","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12761v1","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12761","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"BOSYKHOOHF2E","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BOSYKHOOHF2E2OMZ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BOSYKHOO","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:35287b7e4fc06edd77f3729c78ffd57b6b5f3f5fb13ba6f7a787995e47f36403","target":"graph","created_at":"2026-05-17T23:44:30Z","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 paper, a multiscale flux basis algorithm is developed to efficiently solve a flow problem in fractured porous media. Here, we take into account a mixed-dimensional setting of the discrete fracture matrix model, where the fracture network is represented as lower-dimensional object. We assume the linear Darcy model in the rock matrix and the non-linear Forchheimer model in the fractures. In our formulation, we are able to reformulate the matrix-fracture problem to only the fracture network problem and, therefore, significantly reduce the computational cost. The resulting problem is then ","authors_text":"Alessio Fumagalli, Ana Budi\\v{s}a, Elyes Ahmed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-30T14:15:19Z","title":"A multiscale flux basis for mortar mixed discretizations of reduced Darcy-Forchheimer fracture models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12761","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":"sha256:4d08ec2e65480737f4ab09bc64e359b246daf23a26e4e4309f4438c55501017a","target":"record","created_at":"2026-05-17T23:44:30Z","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":"c29e50d55f7ebfa0bae96e82af341f2ff28428e06fabbbe81a54594f9a9cbe9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-30T14:15:19Z","title_canon_sha256":"9f90f95fb99b9b7a7e0ee521e32a9a4530bde745274e18d8be18e59610fae180"},"schema_version":"1.0","source":{"id":"1810.12761","kind":"arxiv","version":1}},"canonical_sha256":"0ba5851dce39744d39996fab504470b1712321d40e1473df8bccf58b55d85c12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ba5851dce39744d39996fab504470b1712321d40e1473df8bccf58b55d85c12","first_computed_at":"2026-05-17T23:44:30.055181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:30.055181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Jve/F792i1+vMRkpZu8HON3tjPOPbKLuT3IcpW1K82oIjWg1+TQXuBMCyXwANhQz1Ke+uDqSbH50Rc8EfzrBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:30.055864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d08ec2e65480737f4ab09bc64e359b246daf23a26e4e4309f4438c55501017a","sha256:35287b7e4fc06edd77f3729c78ffd57b6b5f3f5fb13ba6f7a787995e47f36403"],"state_sha256":"887d7e1494f9af8159fc672c3f74634826b2b7567b0084a13370123bd4ad324c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6SIRk0gOd4wmQ1uhiyAE90h0yTBPkSkDIlFx+wbqJN7CELbbHmu/2T7ugeqdVEPSqqNGAtwqob7vH8KUlT8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:50:42.958154Z","bundle_sha256":"5934fb07edc881018b04f96d7d32e9829d588f36d696664d1857e78eab15abe7"}}