{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CJR7SVEX3VJLW63BXBQWFDWUKQ","short_pith_number":"pith:CJR7SVEX","canonical_record":{"source":{"id":"1105.2061","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-05-10T21:53:17Z","cross_cats_sorted":[],"title_canon_sha256":"b2960b33cc24d7080c2df2fd66261f9f9b03f53c3d1a40ebee1f6ca66ef219b7","abstract_canon_sha256":"0ea59bb1d8a84bc194a458b7a47ed55cf8cb203f9c0663039cba248925cf87d6"},"schema_version":"1.0"},"canonical_sha256":"1263f95497dd52bb7b61b861628ed45423818b8919625555a08dd3d6b87fae19","source":{"kind":"arxiv","id":"1105.2061","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2061","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2061v2","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2061","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"pith_short_12","alias_value":"CJR7SVEX3VJL","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CJR7SVEX3VJLW63B","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CJR7SVEX","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CJR7SVEX3VJLW63BXBQWFDWUKQ","target":"record","payload":{"canonical_record":{"source":{"id":"1105.2061","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-05-10T21:53:17Z","cross_cats_sorted":[],"title_canon_sha256":"b2960b33cc24d7080c2df2fd66261f9f9b03f53c3d1a40ebee1f6ca66ef219b7","abstract_canon_sha256":"0ea59bb1d8a84bc194a458b7a47ed55cf8cb203f9c0663039cba248925cf87d6"},"schema_version":"1.0"},"canonical_sha256":"1263f95497dd52bb7b61b861628ed45423818b8919625555a08dd3d6b87fae19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:21.667457Z","signature_b64":"4uZejWDKS+QFR4mWK6sNXxBbrhTO23Apub2xHXMtIgxCy1kuF95T6SfbI1IVwS5238QdDAe0IUHxibHJETZKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1263f95497dd52bb7b61b861628ed45423818b8919625555a08dd3d6b87fae19","last_reissued_at":"2026-05-18T03:55:21.666813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:21.666813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.2061","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I/vXuxX+3hGPCUlfCdL+0DMMKQ28oms6tNfOFAlEcYg0uSp1652ZaWaDM89C1LfeGsSQXgHg3eQRLoR0sDHnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:32:01.017838Z"},"content_sha256":"72e7f8a61d4959101e626359de90a712551762d31ef8dc4c1d253fa7297f9925","schema_version":"1.0","event_id":"sha256:72e7f8a61d4959101e626359de90a712551762d31ef8dc4c1d253fa7297f9925"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CJR7SVEX3VJLW63BXBQWFDWUKQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Expanded mixed multiscale finite element methods and their applications for flows in porous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dylan Copeland, J. David Moulton, Lijian Jiang","submitted_at":"2011-05-10T21:53:17Z","abstract_excerpt":"We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity and Lagrange multipliers. We use multiscale basis functions for the both velocity and gradient of pressure. In the expanded mixed MsFEM framework, we consider both cases of separable-scale and non-separable spatial scales. We specifically analyze the met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2061","kind":"arxiv","version":2},"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":"2026-05-18T03:55:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ch3DWkB4wMxR49fcwH8Fcy9AnnKGVGY57iTVZtGE4SBPrcFniL3HEVuRsh/WuBQdqIe4K2donei9kaV4BTCrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:32:01.018526Z"},"content_sha256":"a142458106d9109a8018bb53d5edb7120b3a96ecfd992df802fd6f9234a92ea2","schema_version":"1.0","event_id":"sha256:a142458106d9109a8018bb53d5edb7120b3a96ecfd992df802fd6f9234a92ea2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJR7SVEX3VJLW63BXBQWFDWUKQ/bundle.json","state_url":"https://pith.science/pith/CJR7SVEX3VJLW63BXBQWFDWUKQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJR7SVEX3VJLW63BXBQWFDWUKQ/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":"2026-05-26T07:32:01Z","links":{"resolver":"https://pith.science/pith/CJR7SVEX3VJLW63BXBQWFDWUKQ","bundle":"https://pith.science/pith/CJR7SVEX3VJLW63BXBQWFDWUKQ/bundle.json","state":"https://pith.science/pith/CJR7SVEX3VJLW63BXBQWFDWUKQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJR7SVEX3VJLW63BXBQWFDWUKQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CJR7SVEX3VJLW63BXBQWFDWUKQ","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":"0ea59bb1d8a84bc194a458b7a47ed55cf8cb203f9c0663039cba248925cf87d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-05-10T21:53:17Z","title_canon_sha256":"b2960b33cc24d7080c2df2fd66261f9f9b03f53c3d1a40ebee1f6ca66ef219b7"},"schema_version":"1.0","source":{"id":"1105.2061","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2061","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2061v2","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2061","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"pith_short_12","alias_value":"CJR7SVEX3VJL","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CJR7SVEX3VJLW63B","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CJR7SVEX","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:a142458106d9109a8018bb53d5edb7120b3a96ecfd992df802fd6f9234a92ea2","target":"graph","created_at":"2026-05-18T03:55:21Z","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 develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity and Lagrange multipliers. We use multiscale basis functions for the both velocity and gradient of pressure. In the expanded mixed MsFEM framework, we consider both cases of separable-scale and non-separable spatial scales. We specifically analyze the met","authors_text":"Dylan Copeland, J. David Moulton, Lijian Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-05-10T21:53:17Z","title":"Expanded mixed multiscale finite element methods and their applications for flows in porous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2061","kind":"arxiv","version":2},"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":"sha256:72e7f8a61d4959101e626359de90a712551762d31ef8dc4c1d253fa7297f9925","target":"record","created_at":"2026-05-18T03:55:21Z","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":"0ea59bb1d8a84bc194a458b7a47ed55cf8cb203f9c0663039cba248925cf87d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-05-10T21:53:17Z","title_canon_sha256":"b2960b33cc24d7080c2df2fd66261f9f9b03f53c3d1a40ebee1f6ca66ef219b7"},"schema_version":"1.0","source":{"id":"1105.2061","kind":"arxiv","version":2}},"canonical_sha256":"1263f95497dd52bb7b61b861628ed45423818b8919625555a08dd3d6b87fae19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1263f95497dd52bb7b61b861628ed45423818b8919625555a08dd3d6b87fae19","first_computed_at":"2026-05-18T03:55:21.666813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:21.666813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4uZejWDKS+QFR4mWK6sNXxBbrhTO23Apub2xHXMtIgxCy1kuF95T6SfbI1IVwS5238QdDAe0IUHxibHJETZKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:21.667457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2061","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72e7f8a61d4959101e626359de90a712551762d31ef8dc4c1d253fa7297f9925","sha256:a142458106d9109a8018bb53d5edb7120b3a96ecfd992df802fd6f9234a92ea2"],"state_sha256":"358f4b88f7c7a34ba4e7697f0b5136b52a5fd189396e4df83298a7ade983601f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eTyMxwOdrWpQgvKCeqnuDlbR7YAyWvNIVRQ9nUkdebVQ6ICzsKrQF2r7F7RrZVZ72dDDx1pMLQHG89HKQli9Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:32:01.022557Z","bundle_sha256":"07d251e955a09c7e11e17366eb664d53456bfd0703c379b28164adadf0502847"}}