{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UM3IPVT2XYSSFMADYYBKFIGEAQ","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":"c3f5c57ad174cc45cbb262ebab3ca035cc15ff3dd9c346c6a58b9205ccf0a04c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-01T07:19:50Z","title_canon_sha256":"f4e85dda76f6c4f8cdaf9d1bcb946718abc74401d44798186969d87200affc51"},"schema_version":"1.0","source":{"id":"2505.00360","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00360","created_at":"2026-07-05T10:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00360v2","created_at":"2026-07-05T10:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00360","created_at":"2026-07-05T10:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"UM3IPVT2XYSS","created_at":"2026-07-05T10:59:09Z"},{"alias_kind":"pith_short_16","alias_value":"UM3IPVT2XYSSFMAD","created_at":"2026-07-05T10:59:09Z"},{"alias_kind":"pith_short_8","alias_value":"UM3IPVT2","created_at":"2026-07-05T10:59:09Z"}],"graph_snapshots":[{"event_id":"sha256:b0f20ef71dbb22d1835c4939f8d263a732399112c04fb62f2b7916598b8c3ecf","target":"graph","created_at":"2026-07-05T10:59:09Z","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/2505.00360/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study interior curvature estimates for convex graphs which satisfy the quotient equation $\\frac{\\sigma_{n}}{\\sigma_{n-2}}(\\lambda)=f(X)>0$ in this paper.","authors_text":"Jianxiang Liu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-01T07:19:50Z","title":"Interior curvature estimate for curvature quotient equations on convex hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00360","kind":"arxiv","version":2},"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:f2c22a5c24ec8a045d9041f32a856559455c030d25aab571cef85846ef542f24","target":"record","created_at":"2026-07-05T10:59:09Z","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":"c3f5c57ad174cc45cbb262ebab3ca035cc15ff3dd9c346c6a58b9205ccf0a04c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-01T07:19:50Z","title_canon_sha256":"f4e85dda76f6c4f8cdaf9d1bcb946718abc74401d44798186969d87200affc51"},"schema_version":"1.0","source":{"id":"2505.00360","kind":"arxiv","version":2}},"canonical_sha256":"a33687d67abe2522b003c602a2a0c4040793ab063e345f66c9ff432d50dbf457","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a33687d67abe2522b003c602a2a0c4040793ab063e345f66c9ff432d50dbf457","first_computed_at":"2026-07-05T10:59:09.899540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:59:09.899540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2nhZZZlpYthdO50OoMSz7ATFJYTz+KBX/5ukHNlykvNC8YXpjPIzjW+3NmGLpcxOHkE+n0/7CvZHz9HlijfnAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:59:09.900027Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.00360","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2c22a5c24ec8a045d9041f32a856559455c030d25aab571cef85846ef542f24","sha256:b0f20ef71dbb22d1835c4939f8d263a732399112c04fb62f2b7916598b8c3ecf"],"state_sha256":"5aa182a7f506f717e93a7a55489298324999dff6e40b4d38f59c5afd1bfbfff9"}