{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JLO73HFTGGAZX7NFFXEYQSKB56","short_pith_number":"pith:JLO73HFT","canonical_record":{"source":{"id":"1307.3025","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T09:21:38Z","cross_cats_sorted":[],"title_canon_sha256":"4999f7044d7b39c25f368009288ad82cd2fb4f87583e7e7189e8c73ccb5b96cf","abstract_canon_sha256":"1366efd61d428ac93800d8b5b7bcc7a7a3d730528437541a9bbfd1ba56774c1c"},"schema_version":"1.0"},"canonical_sha256":"4addfd9cb331819bfda52dc9884941ef97b55650c059ba1060fda423c414311b","source":{"kind":"arxiv","id":"1307.3025","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3025","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3025v2","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3025","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"JLO73HFTGGAZ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JLO73HFTGGAZX7NF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JLO73HFT","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JLO73HFTGGAZX7NFFXEYQSKB56","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3025","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T09:21:38Z","cross_cats_sorted":[],"title_canon_sha256":"4999f7044d7b39c25f368009288ad82cd2fb4f87583e7e7189e8c73ccb5b96cf","abstract_canon_sha256":"1366efd61d428ac93800d8b5b7bcc7a7a3d730528437541a9bbfd1ba56774c1c"},"schema_version":"1.0"},"canonical_sha256":"4addfd9cb331819bfda52dc9884941ef97b55650c059ba1060fda423c414311b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:31.529770Z","signature_b64":"/ssI+cGI6CFHqfrEduskGecscDgl+61JjQI/AiP2vk7XYzpfNjfuehIGovpJ1iFwHqN3bYV+hgvqfZCKghY0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4addfd9cb331819bfda52dc9884941ef97b55650c059ba1060fda423c414311b","last_reissued_at":"2026-05-18T02:47:31.529197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:31.529197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3025","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s1sbC/8g6yqAgmfARu0eY6DFWPu1XAFLY6OwJmdZ0B7+o+yhCF0lAJcE1dJgOe4fgd6VJD8/111vop1nOmbIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:08:38.971377Z"},"content_sha256":"34f94c779d4767749cd9e7a895b39dbe246d7a3999297e3c641753c8aa4b624b","schema_version":"1.0","event_id":"sha256:34f94c779d4767749cd9e7a895b39dbe246d7a3999297e3c641753c8aa4b624b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JLO73HFTGGAZX7NFFXEYQSKB56","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An extension of Hsiung-Minkowski formulas and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kwok-Kun Kwong","submitted_at":"2013-07-11T09:21:38Z","abstract_excerpt":"We prove a generalization of Hsiung-Minkowski formulas for closed submanifolds in semi-Riemannian manifolds with constant curvature. As a corollary, we obtain volume and area upper bounds for k-convex hypersurfaces in terms of a weighted total k-th mean curvature of the hypersurface. We also obtain some Alexandrov-type results and eigenvalue estimates for hypersurfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3025","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9+ulkV0YlaQugAtAEx+3hhI15doK8AlXKjHO5sLoR+e2id9SsMvqyyTpWty0VCH4PVKXIL6YHYcKOY1wjhziDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:08:38.971727Z"},"content_sha256":"09cbd9ebbf1069eb11d0eb7f6a3ab7d7c76df2488e4a6801472e954e396984d6","schema_version":"1.0","event_id":"sha256:09cbd9ebbf1069eb11d0eb7f6a3ab7d7c76df2488e4a6801472e954e396984d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JLO73HFTGGAZX7NFFXEYQSKB56/bundle.json","state_url":"https://pith.science/pith/JLO73HFTGGAZX7NFFXEYQSKB56/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JLO73HFTGGAZX7NFFXEYQSKB56/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T05:08:38Z","links":{"resolver":"https://pith.science/pith/JLO73HFTGGAZX7NFFXEYQSKB56","bundle":"https://pith.science/pith/JLO73HFTGGAZX7NFFXEYQSKB56/bundle.json","state":"https://pith.science/pith/JLO73HFTGGAZX7NFFXEYQSKB56/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JLO73HFTGGAZX7NFFXEYQSKB56/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JLO73HFTGGAZX7NFFXEYQSKB56","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":"1366efd61d428ac93800d8b5b7bcc7a7a3d730528437541a9bbfd1ba56774c1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T09:21:38Z","title_canon_sha256":"4999f7044d7b39c25f368009288ad82cd2fb4f87583e7e7189e8c73ccb5b96cf"},"schema_version":"1.0","source":{"id":"1307.3025","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3025","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3025v2","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3025","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"JLO73HFTGGAZ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JLO73HFTGGAZX7NF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JLO73HFT","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:09cbd9ebbf1069eb11d0eb7f6a3ab7d7c76df2488e4a6801472e954e396984d6","target":"graph","created_at":"2026-05-18T02:47:31Z","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 prove a generalization of Hsiung-Minkowski formulas for closed submanifolds in semi-Riemannian manifolds with constant curvature. As a corollary, we obtain volume and area upper bounds for k-convex hypersurfaces in terms of a weighted total k-th mean curvature of the hypersurface. We also obtain some Alexandrov-type results and eigenvalue estimates for hypersurfaces.","authors_text":"Kwok-Kun Kwong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T09:21:38Z","title":"An extension of Hsiung-Minkowski formulas and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3025","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":"sha256:34f94c779d4767749cd9e7a895b39dbe246d7a3999297e3c641753c8aa4b624b","target":"record","created_at":"2026-05-18T02:47:31Z","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":"1366efd61d428ac93800d8b5b7bcc7a7a3d730528437541a9bbfd1ba56774c1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-11T09:21:38Z","title_canon_sha256":"4999f7044d7b39c25f368009288ad82cd2fb4f87583e7e7189e8c73ccb5b96cf"},"schema_version":"1.0","source":{"id":"1307.3025","kind":"arxiv","version":2}},"canonical_sha256":"4addfd9cb331819bfda52dc9884941ef97b55650c059ba1060fda423c414311b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4addfd9cb331819bfda52dc9884941ef97b55650c059ba1060fda423c414311b","first_computed_at":"2026-05-18T02:47:31.529197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:31.529197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ssI+cGI6CFHqfrEduskGecscDgl+61JjQI/AiP2vk7XYzpfNjfuehIGovpJ1iFwHqN3bYV+hgvqfZCKghY0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:31.529770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3025","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34f94c779d4767749cd9e7a895b39dbe246d7a3999297e3c641753c8aa4b624b","sha256:09cbd9ebbf1069eb11d0eb7f6a3ab7d7c76df2488e4a6801472e954e396984d6"],"state_sha256":"df5f775245882dd8d49d6100165a4c851bb087d81d1fee56a3a81f3bceda486a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0dDrFPgFFB0t0Tdq5qX01wiBYKZwnue2njnEU4FOkaDJcz7YQc+wQm/Vr4BOgeVMzDJG7Cl52RfOPKSpl2CdDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:08:38.973686Z","bundle_sha256":"141a16b2d00b9d280ded29491e36e86065c5759638ebedf299db3a8b675cd9bb"}}