{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LFT3WGYYFDFM4IGK4CRMCSCGPO","short_pith_number":"pith:LFT3WGYY","schema_version":"1.0","canonical_sha256":"5967bb1b1828cace20cae0a2c148467b8494340b51b3097d589d14e520d107a4","source":{"kind":"arxiv","id":"1503.05950","version":1},"attestation_state":"computed","paper":{"title":"Smooth local solutions to weingarten equations and $\\sigma_k$-equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qing Han, Tiancong Chen","submitted_at":"2015-03-19T21:32:00Z","abstract_excerpt":"In this paper, we study the existence of smooth local solutions to Weingarten equations and $\\sigma_k$-equations. We will prove that, for $2 \\leq k \\leq n$, the Weingarten equations and the $\\sigma_k$-equations always have smooth local solutions regardless of the sign of the functions in the right-hand side of the equations. We will demonstrate that the associate linearized equations are uniformly elliptic if we choose the initial approximate solutions appropriately."},"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":"1503.05950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-19T21:32:00Z","cross_cats_sorted":[],"title_canon_sha256":"fdc7af4ca555caf2d783a08bc6a39caf0c81fce5d5b71fbd2395a1463ec98e44","abstract_canon_sha256":"8fb53257f7a15ff48e71df611fc307d894a0fffe75625bab4fa820db9f596ced"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:49.049375Z","signature_b64":"BV4i0jMACiov4JGn8HJXkQMZOR78v16PCNcYCnp1NankukUE9Fq6j6+4eWUBxCbNv86AElm3Yh0GoxbYIFzABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5967bb1b1828cace20cae0a2c148467b8494340b51b3097d589d14e520d107a4","last_reissued_at":"2026-05-18T02:20:49.048658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:49.048658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smooth local solutions to weingarten equations and $\\sigma_k$-equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qing Han, Tiancong Chen","submitted_at":"2015-03-19T21:32:00Z","abstract_excerpt":"In this paper, we study the existence of smooth local solutions to Weingarten equations and $\\sigma_k$-equations. We will prove that, for $2 \\leq k \\leq n$, the Weingarten equations and the $\\sigma_k$-equations always have smooth local solutions regardless of the sign of the functions in the right-hand side of the equations. We will demonstrate that the associate linearized equations are uniformly elliptic if we choose the initial approximate solutions appropriately."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05950","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":"1503.05950","created_at":"2026-05-18T02:20:49.048767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.05950v1","created_at":"2026-05-18T02:20:49.048767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05950","created_at":"2026-05-18T02:20:49.048767+00:00"},{"alias_kind":"pith_short_12","alias_value":"LFT3WGYYFDFM","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LFT3WGYYFDFM4IGK","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LFT3WGYY","created_at":"2026-05-18T12:29:29.992203+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/LFT3WGYYFDFM4IGK4CRMCSCGPO","json":"https://pith.science/pith/LFT3WGYYFDFM4IGK4CRMCSCGPO.json","graph_json":"https://pith.science/api/pith-number/LFT3WGYYFDFM4IGK4CRMCSCGPO/graph.json","events_json":"https://pith.science/api/pith-number/LFT3WGYYFDFM4IGK4CRMCSCGPO/events.json","paper":"https://pith.science/paper/LFT3WGYY"},"agent_actions":{"view_html":"https://pith.science/pith/LFT3WGYYFDFM4IGK4CRMCSCGPO","download_json":"https://pith.science/pith/LFT3WGYYFDFM4IGK4CRMCSCGPO.json","view_paper":"https://pith.science/paper/LFT3WGYY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.05950&json=true","fetch_graph":"https://pith.science/api/pith-number/LFT3WGYYFDFM4IGK4CRMCSCGPO/graph.json","fetch_events":"https://pith.science/api/pith-number/LFT3WGYYFDFM4IGK4CRMCSCGPO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LFT3WGYYFDFM4IGK4CRMCSCGPO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LFT3WGYYFDFM4IGK4CRMCSCGPO/action/storage_attestation","attest_author":"https://pith.science/pith/LFT3WGYYFDFM4IGK4CRMCSCGPO/action/author_attestation","sign_citation":"https://pith.science/pith/LFT3WGYYFDFM4IGK4CRMCSCGPO/action/citation_signature","submit_replication":"https://pith.science/pith/LFT3WGYYFDFM4IGK4CRMCSCGPO/action/replication_record"}},"created_at":"2026-05-18T02:20:49.048767+00:00","updated_at":"2026-05-18T02:20:49.048767+00:00"}