{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BASB3FMBMHVCJLTWG5OTRIHKYC","short_pith_number":"pith:BASB3FMB","schema_version":"1.0","canonical_sha256":"08241d958161ea24ae76375d38a0eac0ad7ce86d6208f36ae8dd489ca60e0c82","source":{"kind":"arxiv","id":"1409.2190","version":2},"attestation_state":"computed","paper":{"title":"Minkowski formulae and Alexandrov theorems in spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mu-Tao Wang, Xiangwen Zhang, Ye-Kai Wang","submitted_at":"2014-09-08T02:32:29Z","abstract_excerpt":"The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit \"hidden symmetry\" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimension-two submanifold with constant normalized null expansion (null mean curvature) must lie in a shear-free (umbilical) null hypersurface. These results are generalized for higher order curvature invariants. In particular, the notion of mixed higher order mean curvature is intr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.2190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-08T02:32:29Z","cross_cats_sorted":[],"title_canon_sha256":"ade54eb74ec458d6b1c91023ff521c449624e3455ee6eb4b66097f0832d12bc5","abstract_canon_sha256":"893dc42de656b53bd55d77199639663785b67bec30139b6e824bcbf5d1934b77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:35.446791Z","signature_b64":"rP+RY9S1Rpx+E61v0O41I9KCY5QL3R0JPUUwL9u7vdC9ixlFPgOMeuZt5RGsC6PmIpCHpofjtcWUycgfg9c+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08241d958161ea24ae76375d38a0eac0ad7ce86d6208f36ae8dd489ca60e0c82","last_reissued_at":"2026-05-18T01:11:35.446087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:35.446087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minkowski formulae and Alexandrov theorems in spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mu-Tao Wang, Xiangwen Zhang, Ye-Kai Wang","submitted_at":"2014-09-08T02:32:29Z","abstract_excerpt":"The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit \"hidden symmetry\" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimension-two submanifold with constant normalized null expansion (null mean curvature) must lie in a shear-free (umbilical) null hypersurface. These results are generalized for higher order curvature invariants. In particular, the notion of mixed higher order mean curvature is intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2190","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.2190","created_at":"2026-05-18T01:11:35.446202+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.2190v2","created_at":"2026-05-18T01:11:35.446202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2190","created_at":"2026-05-18T01:11:35.446202+00:00"},{"alias_kind":"pith_short_12","alias_value":"BASB3FMBMHVC","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BASB3FMBMHVCJLTW","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BASB3FMB","created_at":"2026-05-18T12:28:22.404517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC","json":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC.json","graph_json":"https://pith.science/api/pith-number/BASB3FMBMHVCJLTWG5OTRIHKYC/graph.json","events_json":"https://pith.science/api/pith-number/BASB3FMBMHVCJLTWG5OTRIHKYC/events.json","paper":"https://pith.science/paper/BASB3FMB"},"agent_actions":{"view_html":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC","download_json":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC.json","view_paper":"https://pith.science/paper/BASB3FMB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.2190&json=true","fetch_graph":"https://pith.science/api/pith-number/BASB3FMBMHVCJLTWG5OTRIHKYC/graph.json","fetch_events":"https://pith.science/api/pith-number/BASB3FMBMHVCJLTWG5OTRIHKYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC/action/storage_attestation","attest_author":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC/action/author_attestation","sign_citation":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC/action/citation_signature","submit_replication":"https://pith.science/pith/BASB3FMBMHVCJLTWG5OTRIHKYC/action/replication_record"}},"created_at":"2026-05-18T01:11:35.446202+00:00","updated_at":"2026-05-18T01:11:35.446202+00:00"}