{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5UYPQZ6ADP2U3TXDQSH2IS2M6C","short_pith_number":"pith:5UYPQZ6A","schema_version":"1.0","canonical_sha256":"ed30f867c01bf54dcee3848fa44b4cf082cef97f7577660501d0f2e15c452fde","source":{"kind":"arxiv","id":"1709.02550","version":1},"attestation_state":"computed","paper":{"title":"Fractional analogue of k-Hessian operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yijing Wu","submitted_at":"2017-09-08T05:57:57Z","abstract_excerpt":"Applying ideas of fractional analogue of Monge-Amp\\'ere operator by L. Caffarelli and F. Charro, we consider an analogue of fractional k-Hessian operators expressed as concave envelopes of fractional linear operators, and reproduce the same regularity results when k=2.\n  Under the set up of global solutions prescribing data at infinity and global barriers, the key estimate is to prove that fractional 2-Hessian operator is strictly elliptic. Then we can apply nonlocal Evans-Krylov theorem to prove such solutions are classical."},"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":"1709.02550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-08T05:57:57Z","cross_cats_sorted":[],"title_canon_sha256":"e1823877ed73c22c62f4dcf04cb2d4366295842243d0113e7b5f9f8bc90e568f","abstract_canon_sha256":"90e05e5086ee8d9e7242e1e5c22dbedefc30976a79b0b750cf2a88e9b678d7e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:45.410108Z","signature_b64":"Dq1Tf2z2OO6hiSnkDU7be/DUnPSJ4O9q5+jcrJPYIRDKiXUMcOsua3BeK9urxLwgYQQAm/Yy5XBXBzVs5OzZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed30f867c01bf54dcee3848fa44b4cf082cef97f7577660501d0f2e15c452fde","last_reissued_at":"2026-05-18T00:35:45.409405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:45.409405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional analogue of k-Hessian operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yijing Wu","submitted_at":"2017-09-08T05:57:57Z","abstract_excerpt":"Applying ideas of fractional analogue of Monge-Amp\\'ere operator by L. Caffarelli and F. Charro, we consider an analogue of fractional k-Hessian operators expressed as concave envelopes of fractional linear operators, and reproduce the same regularity results when k=2.\n  Under the set up of global solutions prescribing data at infinity and global barriers, the key estimate is to prove that fractional 2-Hessian operator is strictly elliptic. Then we can apply nonlocal Evans-Krylov theorem to prove such solutions are classical."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02550","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":"1709.02550","created_at":"2026-05-18T00:35:45.409510+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.02550v1","created_at":"2026-05-18T00:35:45.409510+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02550","created_at":"2026-05-18T00:35:45.409510+00:00"},{"alias_kind":"pith_short_12","alias_value":"5UYPQZ6ADP2U","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5UYPQZ6ADP2U3TXD","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5UYPQZ6A","created_at":"2026-05-18T12:31:00.734936+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/5UYPQZ6ADP2U3TXDQSH2IS2M6C","json":"https://pith.science/pith/5UYPQZ6ADP2U3TXDQSH2IS2M6C.json","graph_json":"https://pith.science/api/pith-number/5UYPQZ6ADP2U3TXDQSH2IS2M6C/graph.json","events_json":"https://pith.science/api/pith-number/5UYPQZ6ADP2U3TXDQSH2IS2M6C/events.json","paper":"https://pith.science/paper/5UYPQZ6A"},"agent_actions":{"view_html":"https://pith.science/pith/5UYPQZ6ADP2U3TXDQSH2IS2M6C","download_json":"https://pith.science/pith/5UYPQZ6ADP2U3TXDQSH2IS2M6C.json","view_paper":"https://pith.science/paper/5UYPQZ6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.02550&json=true","fetch_graph":"https://pith.science/api/pith-number/5UYPQZ6ADP2U3TXDQSH2IS2M6C/graph.json","fetch_events":"https://pith.science/api/pith-number/5UYPQZ6ADP2U3TXDQSH2IS2M6C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5UYPQZ6ADP2U3TXDQSH2IS2M6C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5UYPQZ6ADP2U3TXDQSH2IS2M6C/action/storage_attestation","attest_author":"https://pith.science/pith/5UYPQZ6ADP2U3TXDQSH2IS2M6C/action/author_attestation","sign_citation":"https://pith.science/pith/5UYPQZ6ADP2U3TXDQSH2IS2M6C/action/citation_signature","submit_replication":"https://pith.science/pith/5UYPQZ6ADP2U3TXDQSH2IS2M6C/action/replication_record"}},"created_at":"2026-05-18T00:35:45.409510+00:00","updated_at":"2026-05-18T00:35:45.409510+00:00"}