{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FUUFTFFN5ONWZ6GSQO7C47Q2W5","short_pith_number":"pith:FUUFTFFN","schema_version":"1.0","canonical_sha256":"2d285994adeb9b6cf8d283be2e7e1ab775de0203c2da7f1db61a7bb5aaacac17","source":{"kind":"arxiv","id":"1506.08509","version":2},"attestation_state":"computed","paper":{"title":"Sparse Generalized Multiscale Finite Element Methods and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eric Chung, Guanglian Li, Wing Tat Leung, Yalchin Efendiev","submitted_at":"2015-06-29T04:52:20Z","abstract_excerpt":"In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method. In these approaches, multiscale basis functions are constructed using local snapshot spaces, where a snapshot space is a large space that represents the solution behavior in a coarse block. In a number of applications (e.g., those discussed in the paper), one may have a sparsity in the snapshot space for an appropriate choice of a snapshot space. More precisely, the solution may only involve a portion of the snapshot space. In this case, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.08509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-29T04:52:20Z","cross_cats_sorted":[],"title_canon_sha256":"a7a95099200f350dcfc6a3fba7e5381769c9d231896aa1e99789d49cc30852c6","abstract_canon_sha256":"59e6cb6a4c06d3118c90898251b11b286baa647c3016bfaf142c1cb6edf3a0b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:59.497481Z","signature_b64":"3ugZ+h82GSzFyH+6xYYgC0+2/RtK0DQ/eZsO9ComT9qzB9C9OgFFUcV96Uh4rhq2D+kjCXLjbG93OsAvtf6gBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d285994adeb9b6cf8d283be2e7e1ab775de0203c2da7f1db61a7bb5aaacac17","last_reissued_at":"2026-05-18T01:35:59.496971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:59.496971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse Generalized Multiscale Finite Element Methods and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eric Chung, Guanglian Li, Wing Tat Leung, Yalchin Efendiev","submitted_at":"2015-06-29T04:52:20Z","abstract_excerpt":"In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method. In these approaches, multiscale basis functions are constructed using local snapshot spaces, where a snapshot space is a large space that represents the solution behavior in a coarse block. In a number of applications (e.g., those discussed in the paper), one may have a sparsity in the snapshot space for an appropriate choice of a snapshot space. More precisely, the solution may only involve a portion of the snapshot space. In this case, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08509","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.08509","created_at":"2026-05-18T01:35:59.497039+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08509v2","created_at":"2026-05-18T01:35:59.497039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08509","created_at":"2026-05-18T01:35:59.497039+00:00"},{"alias_kind":"pith_short_12","alias_value":"FUUFTFFN5ONW","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"FUUFTFFN5ONWZ6GS","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"FUUFTFFN","created_at":"2026-05-18T12:29:22.688609+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5","json":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5.json","graph_json":"https://pith.science/api/pith-number/FUUFTFFN5ONWZ6GSQO7C47Q2W5/graph.json","events_json":"https://pith.science/api/pith-number/FUUFTFFN5ONWZ6GSQO7C47Q2W5/events.json","paper":"https://pith.science/paper/FUUFTFFN"},"agent_actions":{"view_html":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5","download_json":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5.json","view_paper":"https://pith.science/paper/FUUFTFFN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08509&json=true","fetch_graph":"https://pith.science/api/pith-number/FUUFTFFN5ONWZ6GSQO7C47Q2W5/graph.json","fetch_events":"https://pith.science/api/pith-number/FUUFTFFN5ONWZ6GSQO7C47Q2W5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5/action/storage_attestation","attest_author":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5/action/author_attestation","sign_citation":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5/action/citation_signature","submit_replication":"https://pith.science/pith/FUUFTFFN5ONWZ6GSQO7C47Q2W5/action/replication_record"}},"created_at":"2026-05-18T01:35:59.497039+00:00","updated_at":"2026-05-18T01:35:59.497039+00:00"}