{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HWHA5BNKAGZCBAEU45PKSTKOHI","short_pith_number":"pith:HWHA5BNK","schema_version":"1.0","canonical_sha256":"3d8e0e85aa01b2208094e75ea94d4e3a173f34b0271a2c084e06b3f8cc337b13","source":{"kind":"arxiv","id":"1610.03206","version":1},"attestation_state":"computed","paper":{"title":"Harnack's Inequality and A Priori Estimates for Fractional Powers of Non-symmetric Differential Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cristian Rios, Gast\\'on Beltritti, Hugo Aimar, Ivana G\\'omez","submitted_at":"2016-10-11T06:16:47Z","abstract_excerpt":"We obtain a new general extension theorem in Banach spaces for operators which are not required to be symmetric, and apply it to obtain Harnack estimates and a priori regularity for solutions of fractional powers of several second order differential operators. These include weighted elliptic and subellitptic operators in divergence form (nonnecessarily self-adjoint), and nondivergence form operators with rough coefficients. We utilize the reflection extension technique introduced by Caffarelli and Silvestre."},"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":"1610.03206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-11T06:16:47Z","cross_cats_sorted":[],"title_canon_sha256":"4a3f537dafeb8bd558ad8c414d62b6a6d523abea1c02ec3c634cfca1ca79268e","abstract_canon_sha256":"1215a428fa62e5be8f01f65eb3e66dbc588d738c6726d3114d70f8175d8d3009"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:46.254040Z","signature_b64":"eskfK+OhNI8xMqWLgc4zDFMuZ9VPrLJ+olueyFvlsR6T7P4edllCudkzf3NNLMXh2RXkqqbQa/8R0QwH+UJ7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d8e0e85aa01b2208094e75ea94d4e3a173f34b0271a2c084e06b3f8cc337b13","last_reissued_at":"2026-05-18T01:02:46.253655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:46.253655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harnack's Inequality and A Priori Estimates for Fractional Powers of Non-symmetric Differential Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cristian Rios, Gast\\'on Beltritti, Hugo Aimar, Ivana G\\'omez","submitted_at":"2016-10-11T06:16:47Z","abstract_excerpt":"We obtain a new general extension theorem in Banach spaces for operators which are not required to be symmetric, and apply it to obtain Harnack estimates and a priori regularity for solutions of fractional powers of several second order differential operators. These include weighted elliptic and subellitptic operators in divergence form (nonnecessarily self-adjoint), and nondivergence form operators with rough coefficients. We utilize the reflection extension technique introduced by Caffarelli and Silvestre."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03206","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.03206","created_at":"2026-05-18T01:02:46.253710+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.03206v1","created_at":"2026-05-18T01:02:46.253710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03206","created_at":"2026-05-18T01:02:46.253710+00:00"},{"alias_kind":"pith_short_12","alias_value":"HWHA5BNKAGZC","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"HWHA5BNKAGZCBAEU","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"HWHA5BNK","created_at":"2026-05-18T12:30:22.444734+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/HWHA5BNKAGZCBAEU45PKSTKOHI","json":"https://pith.science/pith/HWHA5BNKAGZCBAEU45PKSTKOHI.json","graph_json":"https://pith.science/api/pith-number/HWHA5BNKAGZCBAEU45PKSTKOHI/graph.json","events_json":"https://pith.science/api/pith-number/HWHA5BNKAGZCBAEU45PKSTKOHI/events.json","paper":"https://pith.science/paper/HWHA5BNK"},"agent_actions":{"view_html":"https://pith.science/pith/HWHA5BNKAGZCBAEU45PKSTKOHI","download_json":"https://pith.science/pith/HWHA5BNKAGZCBAEU45PKSTKOHI.json","view_paper":"https://pith.science/paper/HWHA5BNK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.03206&json=true","fetch_graph":"https://pith.science/api/pith-number/HWHA5BNKAGZCBAEU45PKSTKOHI/graph.json","fetch_events":"https://pith.science/api/pith-number/HWHA5BNKAGZCBAEU45PKSTKOHI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HWHA5BNKAGZCBAEU45PKSTKOHI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HWHA5BNKAGZCBAEU45PKSTKOHI/action/storage_attestation","attest_author":"https://pith.science/pith/HWHA5BNKAGZCBAEU45PKSTKOHI/action/author_attestation","sign_citation":"https://pith.science/pith/HWHA5BNKAGZCBAEU45PKSTKOHI/action/citation_signature","submit_replication":"https://pith.science/pith/HWHA5BNKAGZCBAEU45PKSTKOHI/action/replication_record"}},"created_at":"2026-05-18T01:02:46.253710+00:00","updated_at":"2026-05-18T01:02:46.253710+00:00"}