{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:UUEYYR4IB4MVN3R6Q4R4LN347U","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":"6bed4647a3a62ee460f3c2a7058340b91d13579f014d29c0c9ad062fbd24c3e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-03-13T08:15:49Z","title_canon_sha256":"a0befc316c53c7be30cd9cd828f84d173855bc3ef210c13591e5e241c69cfba8"},"schema_version":"1.0","source":{"id":"2003.06147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.06147","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"2003.06147v1","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.06147","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"UUEYYR4IB4MV","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_16","alias_value":"UUEYYR4IB4MVN3R6","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_8","alias_value":"UUEYYR4I","created_at":"2026-07-05T00:47:44Z"}],"graph_snapshots":[{"event_id":"sha256:3dfaf9cbb273fee2e7d999f71d6fb9de4019dd44a21c9d7ffd9790bbe3443b6c","target":"graph","created_at":"2026-07-05T00:47:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2003.06147/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider the Neumann problem of a class of mixed complex Hessian equations, and establish the global C^1 estimates a nd reduce the global second derivative estimate to the estimate of double normal second derivatives on the boundary. In particular, we can prove the global C^2 estimates and the existence theorems when k=n.","authors_text":"Chuan-Qiang Chen, Li Chen, Ni Xiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-03-13T08:15:49Z","title":"The Neumann problem for a class of mixed complex Hessian equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.06147","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:dd57af7d119a5cd613c7136ec4f929808f26a7e3d8313f3a6feeec8ece04cab9","target":"record","created_at":"2026-07-05T00:47:44Z","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":"6bed4647a3a62ee460f3c2a7058340b91d13579f014d29c0c9ad062fbd24c3e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-03-13T08:15:49Z","title_canon_sha256":"a0befc316c53c7be30cd9cd828f84d173855bc3ef210c13591e5e241c69cfba8"},"schema_version":"1.0","source":{"id":"2003.06147","kind":"arxiv","version":1}},"canonical_sha256":"a5098c47880f1956ee3e8723c5b77cfd07595746c56e6d176e59e91a3dc8be2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5098c47880f1956ee3e8723c5b77cfd07595746c56e6d176e59e91a3dc8be2f","first_computed_at":"2026-07-05T00:47:44.053015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:47:44.053015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EmU+o3+1wKJNhmGGgjmTHnXJ/z0egCwrhZVNam3lzuu3VBbm1j3gHhGxOqtYBRuDBjZo18aekUvV6/zai26nAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:47:44.053426Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.06147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd57af7d119a5cd613c7136ec4f929808f26a7e3d8313f3a6feeec8ece04cab9","sha256:3dfaf9cbb273fee2e7d999f71d6fb9de4019dd44a21c9d7ffd9790bbe3443b6c"],"state_sha256":"4bd610820db9b4f9b87432fb58b411b6a195bb60885661dd88d8968d0a2f63cb"}