{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XWE5NSZSC7LGCWJY2O65OVOCJB","short_pith_number":"pith:XWE5NSZS","schema_version":"1.0","canonical_sha256":"bd89d6cb3217d6615938d3bdd755c248689c39d4c1dda816708adb8c38b18e19","source":{"kind":"arxiv","id":"1209.4974","version":2},"attestation_state":"computed","paper":{"title":"Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.NA","authors_text":"Guillaume Bal, Wenjia Jing","submitted_at":"2012-09-22T09:19:36Z","abstract_excerpt":"This paper analyzes the random fluctuations obtained by a heterogeneous multi-scale first-order finite element method applied to solve elliptic equations with a random potential. We show that the random fluctuations of such solutions are correctly estimated by the heterogeneous multi-scale algorithm when appropriate fine-scale problems are solved on subsets that cover the whole computational domain. However, when the fine-scale problems are solved over patches that do not cover the entire domain, the random fluctuations may or may not be estimated accurately. In the case of random potentials w"},"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":"1209.4974","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-22T09:19:36Z","cross_cats_sorted":["math.AP","math.PR"],"title_canon_sha256":"2707c7ca7c8890bdaf8080464913c4e5c94895b02f43a7d9b83d45f157916ca2","abstract_canon_sha256":"78bb357a13ab22ce9d9b439d7b4e0cf46cb1ef779fbd1422b78eb0485f5acc23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.446934Z","signature_b64":"Nl8rACNOsOCwg5sDAitEUjCfdDtPwV1Wey+VT5Svp6szs1ORWDL4xjixElZgahgKlWgNrs3fNCJ1B/VYXDAOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd89d6cb3217d6615938d3bdd755c248689c39d4c1dda816708adb8c38b18e19","last_reissued_at":"2026-05-17T23:53:18.446348Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.446348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.NA","authors_text":"Guillaume Bal, Wenjia Jing","submitted_at":"2012-09-22T09:19:36Z","abstract_excerpt":"This paper analyzes the random fluctuations obtained by a heterogeneous multi-scale first-order finite element method applied to solve elliptic equations with a random potential. We show that the random fluctuations of such solutions are correctly estimated by the heterogeneous multi-scale algorithm when appropriate fine-scale problems are solved on subsets that cover the whole computational domain. However, when the fine-scale problems are solved over patches that do not cover the entire domain, the random fluctuations may or may not be estimated accurately. In the case of random potentials w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4974","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":"1209.4974","created_at":"2026-05-17T23:53:18.446436+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4974v2","created_at":"2026-05-17T23:53:18.446436+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4974","created_at":"2026-05-17T23:53:18.446436+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWE5NSZSC7LG","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWE5NSZSC7LGCWJY","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWE5NSZS","created_at":"2026-05-18T12:27:27.928770+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/XWE5NSZSC7LGCWJY2O65OVOCJB","json":"https://pith.science/pith/XWE5NSZSC7LGCWJY2O65OVOCJB.json","graph_json":"https://pith.science/api/pith-number/XWE5NSZSC7LGCWJY2O65OVOCJB/graph.json","events_json":"https://pith.science/api/pith-number/XWE5NSZSC7LGCWJY2O65OVOCJB/events.json","paper":"https://pith.science/paper/XWE5NSZS"},"agent_actions":{"view_html":"https://pith.science/pith/XWE5NSZSC7LGCWJY2O65OVOCJB","download_json":"https://pith.science/pith/XWE5NSZSC7LGCWJY2O65OVOCJB.json","view_paper":"https://pith.science/paper/XWE5NSZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4974&json=true","fetch_graph":"https://pith.science/api/pith-number/XWE5NSZSC7LGCWJY2O65OVOCJB/graph.json","fetch_events":"https://pith.science/api/pith-number/XWE5NSZSC7LGCWJY2O65OVOCJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWE5NSZSC7LGCWJY2O65OVOCJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWE5NSZSC7LGCWJY2O65OVOCJB/action/storage_attestation","attest_author":"https://pith.science/pith/XWE5NSZSC7LGCWJY2O65OVOCJB/action/author_attestation","sign_citation":"https://pith.science/pith/XWE5NSZSC7LGCWJY2O65OVOCJB/action/citation_signature","submit_replication":"https://pith.science/pith/XWE5NSZSC7LGCWJY2O65OVOCJB/action/replication_record"}},"created_at":"2026-05-17T23:53:18.446436+00:00","updated_at":"2026-05-17T23:53:18.446436+00:00"}