{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LFT3WGYYFDFM4IGK4CRMCSCGPO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8fb53257f7a15ff48e71df611fc307d894a0fffe75625bab4fa820db9f596ced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-19T21:32:00Z","title_canon_sha256":"fdc7af4ca555caf2d783a08bc6a39caf0c81fce5d5b71fbd2395a1463ec98e44"},"schema_version":"1.0","source":{"id":"1503.05950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05950","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05950v1","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05950","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"LFT3WGYYFDFM","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LFT3WGYYFDFM4IGK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LFT3WGYY","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:079cbaee8f20b0518f2af2731dda988b29605f5060c14fa486743b833ca75c6c","target":"graph","created_at":"2026-05-18T02:20:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Qing Han, Tiancong Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-19T21:32:00Z","title":"Smooth local solutions to weingarten equations and $\\sigma_k$-equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05950","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5d27baf98f33710ad5a1878467f43a1d7c15f73d4b858d351b038e0ca8da802c","target":"record","created_at":"2026-05-18T02:20:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8fb53257f7a15ff48e71df611fc307d894a0fffe75625bab4fa820db9f596ced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-19T21:32:00Z","title_canon_sha256":"fdc7af4ca555caf2d783a08bc6a39caf0c81fce5d5b71fbd2395a1463ec98e44"},"schema_version":"1.0","source":{"id":"1503.05950","kind":"arxiv","version":1}},"canonical_sha256":"5967bb1b1828cace20cae0a2c148467b8494340b51b3097d589d14e520d107a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5967bb1b1828cace20cae0a2c148467b8494340b51b3097d589d14e520d107a4","first_computed_at":"2026-05-18T02:20:49.048658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:49.048658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BV4i0jMACiov4JGn8HJXkQMZOR78v16PCNcYCnp1NankukUE9Fq6j6+4eWUBxCbNv86AElm3Yh0GoxbYIFzABw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:49.049375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d27baf98f33710ad5a1878467f43a1d7c15f73d4b858d351b038e0ca8da802c","sha256:079cbaee8f20b0518f2af2731dda988b29605f5060c14fa486743b833ca75c6c"],"state_sha256":"f19c3426123afe9c6db2df82d63a0dad479bb0c1f175ff97a8a7cbad587536ef"}