{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2J3OE3QJDVZT7Q5HOQ56N73STX","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":"7f1f087ca20b6fb6cf684a50d73aafb3a5084ae5428b88a76106233aa35d92aa","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-21T18:10:33Z","title_canon_sha256":"cdc7b4c345d73e76eda3fab6451c0aeb97b1a95a221c3b480d5d9ed8ee0a0554"},"schema_version":"1.0","source":{"id":"2405.13134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.13134","created_at":"2026-07-05T08:21:58Z"},{"alias_kind":"arxiv_version","alias_value":"2405.13134v1","created_at":"2026-07-05T08:21:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.13134","created_at":"2026-07-05T08:21:58Z"},{"alias_kind":"pith_short_12","alias_value":"2J3OE3QJDVZT","created_at":"2026-07-05T08:21:58Z"},{"alias_kind":"pith_short_16","alias_value":"2J3OE3QJDVZT7Q5H","created_at":"2026-07-05T08:21:58Z"},{"alias_kind":"pith_short_8","alias_value":"2J3OE3QJ","created_at":"2026-07-05T08:21:58Z"}],"graph_snapshots":[{"event_id":"sha256:7b23c81036b65c4812fe855ab2ef1358788897ecbd15a2d56b0baaf72cc8819d","target":"graph","created_at":"2026-07-05T08:21:58Z","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/2405.13134/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the global $C^2$-estimates for the modified $\\sigma_2$ curvature equation with prescribed boundary mean curvature, and particularly, the local boundary $C^2$ estimates on three-manifolds.","authors_text":"Wei Wei, Xuezhang Chen","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-21T18:10:33Z","title":"Estimates for modified $\\sigma_{2}$ curvature equation on compact manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.13134","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":"sha256:9b7942bcb564e77209659e39768ee96a7934afed9ca48726845a9224377a3df6","target":"record","created_at":"2026-07-05T08:21:58Z","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":"7f1f087ca20b6fb6cf684a50d73aafb3a5084ae5428b88a76106233aa35d92aa","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-21T18:10:33Z","title_canon_sha256":"cdc7b4c345d73e76eda3fab6451c0aeb97b1a95a221c3b480d5d9ed8ee0a0554"},"schema_version":"1.0","source":{"id":"2405.13134","kind":"arxiv","version":1}},"canonical_sha256":"d276e26e091d733fc3a7743be6ff729dc67f2078db3f43889128e4c6ce5e79e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d276e26e091d733fc3a7743be6ff729dc67f2078db3f43889128e4c6ce5e79e4","first_computed_at":"2026-07-05T08:21:58.299885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:21:58.299885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wTeGgq8RzvC2NdeMR5KNn0O8JpU/n1SiAYZfTQBufdY35qFAhOKLs04L+/Vma0qYjdUjdMJJyab8RWh3ZEuaCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:21:58.300366Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.13134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b7942bcb564e77209659e39768ee96a7934afed9ca48726845a9224377a3df6","sha256:7b23c81036b65c4812fe855ab2ef1358788897ecbd15a2d56b0baaf72cc8819d"],"state_sha256":"b536f24c37b9073229f3844134f62857381afa8dac93e59708ee8b14c03d6222"}