{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5YWVSXHWS5OVX4DL6BRUHBSSNO","short_pith_number":"pith:5YWVSXHW","schema_version":"1.0","canonical_sha256":"ee2d595cf6975d5bf06bf0634386526ba0b374563a513a0ccd88aa70f5e46866","source":{"kind":"arxiv","id":"1409.2678","version":4},"attestation_state":"computed","paper":{"title":"A regularity theory for random elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Antoine Gloria, Felix Otto, Stefan Neukamm","submitted_at":"2014-09-09T11:00:27Z","abstract_excerpt":"Since the seminal results by Avellaneda \\& Lin it is known that elliptic operators with periodic coefficients enjoy the same regularity theory as the Laplacian on large scales. In a recent inspiring work, Armstrong \\& Smart proved large-scale Lipschitz estimates for such operators with random coefficients satisfying a finite-range of dependence assumption. In the present contribution, we extend the \\emph{intrinsic large-scale} regularity of Avellaneda \\& Lin (namely, intrinsic large-scale Schauder and Calder\\'eron-Zygmund estimates) to elliptic systems with random coefficients. The scale at wh"},"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":"1409.2678","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T11:00:27Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9cd82a9693d399b2024013abcdde31ffde9e64f0c08bb55e70fd9ec17fc7a159","abstract_canon_sha256":"fbf4f7953144ed3fa9c3eb5896385d170e91f73d1449ed8f547bca05c5927a8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:10:48.426000Z","signature_b64":"KBgGsfvACq7psJEIfpDH4vv8pH1GTVPBpIiTKKo7IC/Ddo7r7hIYc0IhsKj63FR9FvmM2iCMQ8AnV2T1mvSMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee2d595cf6975d5bf06bf0634386526ba0b374563a513a0ccd88aa70f5e46866","last_reissued_at":"2026-07-05T00:10:48.425622Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:10:48.425622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A regularity theory for random elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Antoine Gloria, Felix Otto, Stefan Neukamm","submitted_at":"2014-09-09T11:00:27Z","abstract_excerpt":"Since the seminal results by Avellaneda \\& Lin it is known that elliptic operators with periodic coefficients enjoy the same regularity theory as the Laplacian on large scales. In a recent inspiring work, Armstrong \\& Smart proved large-scale Lipschitz estimates for such operators with random coefficients satisfying a finite-range of dependence assumption. In the present contribution, we extend the \\emph{intrinsic large-scale} regularity of Avellaneda \\& Lin (namely, intrinsic large-scale Schauder and Calder\\'eron-Zygmund estimates) to elliptic systems with random coefficients. The scale at wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2678","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1409.2678/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1409.2678","created_at":"2026-07-05T00:10:48.425682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.2678v4","created_at":"2026-07-05T00:10:48.425682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2678","created_at":"2026-07-05T00:10:48.425682+00:00"},{"alias_kind":"pith_short_12","alias_value":"5YWVSXHWS5OV","created_at":"2026-07-05T00:10:48.425682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5YWVSXHWS5OVX4DL","created_at":"2026-07-05T00:10:48.425682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5YWVSXHW","created_at":"2026-07-05T00:10:48.425682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.09493","citing_title":"Quantitative estimates for high-contrast random media","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO","json":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO.json","graph_json":"https://pith.science/api/pith-number/5YWVSXHWS5OVX4DL6BRUHBSSNO/graph.json","events_json":"https://pith.science/api/pith-number/5YWVSXHWS5OVX4DL6BRUHBSSNO/events.json","paper":"https://pith.science/paper/5YWVSXHW"},"agent_actions":{"view_html":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO","download_json":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO.json","view_paper":"https://pith.science/paper/5YWVSXHW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.2678&json=true","fetch_graph":"https://pith.science/api/pith-number/5YWVSXHWS5OVX4DL6BRUHBSSNO/graph.json","fetch_events":"https://pith.science/api/pith-number/5YWVSXHWS5OVX4DL6BRUHBSSNO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO/action/storage_attestation","attest_author":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO/action/author_attestation","sign_citation":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO/action/citation_signature","submit_replication":"https://pith.science/pith/5YWVSXHWS5OVX4DL6BRUHBSSNO/action/replication_record"}},"created_at":"2026-07-05T00:10:48.425682+00:00","updated_at":"2026-07-05T00:10:48.425682+00:00"}