{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XESUZT5QTSUIKD7D23LVCPQD3X","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":"5b8bd4ebd72e3fe9e36a33430cdc59ab23bec3b531de8f01c2a7271b4cc74575","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-26T11:12:41Z","title_canon_sha256":"38299d2ed1f8cf8b5b956280846dd8a34a092bd7db326f3e1c0575cd861912f9"},"schema_version":"1.0","source":{"id":"1308.5544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5544","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5544v1","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5544","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"XESUZT5QTSUI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XESUZT5QTSUIKD7D","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XESUZT5Q","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:62aa4d813da5c15bde0fdd2e149f9a05cc27eb2ca21341b8a8127532607e5e29","target":"graph","created_at":"2026-05-18T01:22:25Z","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, firstly, inspired by Nat\\'{a}rio's recent work \\cite{Na}, we use the isoperimetric inequality to derive some Alexandrov-Fenchel type inequalities for closed convex hypersurfaces in the hyperbolic space $\\H^{n+1}$ and in the sphere $\\SS^{n+1}$. We also get the rigidity in the spherical case. Secondly, we use the inverse mean curvature flow in sphere \\cite{gerh,Mak-Sch} to prove an optimal Sobolev type inequality for closed convex hypersurfaces in the sphere.","authors_text":"Changwei Xiong, Yong Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-26T11:12:41Z","title":"Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5544","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":"sha256:49451c9e8333784af9dbe6ae5a63b0923ba7c35f1df97b46ac1ed75a86121a52","target":"record","created_at":"2026-05-18T01:22:25Z","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":"5b8bd4ebd72e3fe9e36a33430cdc59ab23bec3b531de8f01c2a7271b4cc74575","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-26T11:12:41Z","title_canon_sha256":"38299d2ed1f8cf8b5b956280846dd8a34a092bd7db326f3e1c0575cd861912f9"},"schema_version":"1.0","source":{"id":"1308.5544","kind":"arxiv","version":1}},"canonical_sha256":"b9254ccfb09ca8850fe3d6d7513e03ddd0829bebaa48bd7895e99f9a1d8181c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9254ccfb09ca8850fe3d6d7513e03ddd0829bebaa48bd7895e99f9a1d8181c0","first_computed_at":"2026-05-18T01:22:25.035229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:25.035229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"muC/QQwkY5Fnu9/a0LCZp0wp3SOedpj/VdOIJJ/t529niu2yDskxUvJTYaxVeLZOiMskyGBYVIJWMTNiTklFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:25.036171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49451c9e8333784af9dbe6ae5a63b0923ba7c35f1df97b46ac1ed75a86121a52","sha256:62aa4d813da5c15bde0fdd2e149f9a05cc27eb2ca21341b8a8127532607e5e29"],"state_sha256":"1088385aa85656c905c2ac29eb1cd5779e5bbb46df72189b11b6148aff789434"}