{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MHOVO2J3UMZFJNOQRJR224NBMJ","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":"6bdf08592851d595eeb26ac67c5f979619548063587b748350747af3f09ed8ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-12T13:06:54Z","title_canon_sha256":"9bec5f2a109ce7e33167e69f942fbb2adbdf755fd36e7347df73c389ecb5fbc7"},"schema_version":"1.0","source":{"id":"1803.04233","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04233","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04233v4","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04233","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"MHOVO2J3UMZF","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MHOVO2J3UMZFJNOQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MHOVO2J3","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:368664ed0183fa201606af8367352fd4628445d6dbe7c0af9c40eee6ee5bdc3d","target":"graph","created_at":"2026-05-18T00:11:17Z","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":"We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the Dirichlet and Neumann eigenfunctions.","authors_text":"Feng-Yu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-12T13:06:54Z","title":"Gradient and Hessian Estimates for Dirichlet and Neumann Eigenfunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04233","kind":"arxiv","version":4},"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":"sha256:6354226cc4c29216d7f00e0b921594fa217502e592f28a32a554d848f2d4740b","target":"record","created_at":"2026-05-18T00:11:17Z","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":"6bdf08592851d595eeb26ac67c5f979619548063587b748350747af3f09ed8ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-12T13:06:54Z","title_canon_sha256":"9bec5f2a109ce7e33167e69f942fbb2adbdf755fd36e7347df73c389ecb5fbc7"},"schema_version":"1.0","source":{"id":"1803.04233","kind":"arxiv","version":4}},"canonical_sha256":"61dd57693ba33254b5d08a63ad71a16259bb8b5639531e620ad3b254536242bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61dd57693ba33254b5d08a63ad71a16259bb8b5639531e620ad3b254536242bd","first_computed_at":"2026-05-18T00:11:17.722262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:17.722262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MLalalzXqnZ+xU342z8t2EgIpYNM/6UsfiTQVEuHGUei6uhx1W1Xnfd39HqgMmQBnviKUE77O6uq3O/mAC/wDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:17.722976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04233","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6354226cc4c29216d7f00e0b921594fa217502e592f28a32a554d848f2d4740b","sha256:368664ed0183fa201606af8367352fd4628445d6dbe7c0af9c40eee6ee5bdc3d"],"state_sha256":"23d3d5d2e920069ed888d1b550f3f1f61fb3dbd8a66cc6578595ce118402498e"}