{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PRQWQNAGWL367UMXRR7ZFC7GPQ","short_pith_number":"pith:PRQWQNAG","schema_version":"1.0","canonical_sha256":"7c61683406b2f7efd1978c7f928be67c1f0c6f4b348af327f851e8269d8e29be","source":{"kind":"arxiv","id":"1907.06523","version":1},"attestation_state":"computed","paper":{"title":"Normal curvature of pseudo-umblical submanifolds in a sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Majid Ali Choudhary","submitted_at":"2019-07-09T15:27:41Z","abstract_excerpt":"Let M be a compact pseudo-umbilical submanifold of the unit sphere S. In the present note, it is shown that if the normal curvature, scalar curvature S and square of the length of second fundamental form satisfy certain conditions, then M is totally geodesic."},"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":"1907.06523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-09T15:27:41Z","cross_cats_sorted":[],"title_canon_sha256":"ffe928ec46a2b7248d2aded9b4ed3e71c14880534c0c5a29dffd8bd1bde57d57","abstract_canon_sha256":"eea0caf3ed215f5ae7a606f9adc4f32f4b7f4365701360e2d156eebb915e2e8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:37.488977Z","signature_b64":"TVIA3jSAERgNMV4ObZkaiias3jjEcVB/T8zmWtlvLu/Vtpli2yPlhbjK0YsOi2ZUmgVZvQ5auRMtRBnGoHXvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c61683406b2f7efd1978c7f928be67c1f0c6f4b348af327f851e8269d8e29be","last_reissued_at":"2026-05-17T23:40:37.488552Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:37.488552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normal curvature of pseudo-umblical submanifolds in a sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Majid Ali Choudhary","submitted_at":"2019-07-09T15:27:41Z","abstract_excerpt":"Let M be a compact pseudo-umbilical submanifold of the unit sphere S. In the present note, it is shown that if the normal curvature, scalar curvature S and square of the length of second fundamental form satisfy certain conditions, then M is totally geodesic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06523","kind":"arxiv","version":1},"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":"1907.06523","created_at":"2026-05-17T23:40:37.488613+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.06523v1","created_at":"2026-05-17T23:40:37.488613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06523","created_at":"2026-05-17T23:40:37.488613+00:00"},{"alias_kind":"pith_short_12","alias_value":"PRQWQNAGWL36","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"PRQWQNAGWL367UMX","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"PRQWQNAG","created_at":"2026-05-18T12:33:24.271573+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/PRQWQNAGWL367UMXRR7ZFC7GPQ","json":"https://pith.science/pith/PRQWQNAGWL367UMXRR7ZFC7GPQ.json","graph_json":"https://pith.science/api/pith-number/PRQWQNAGWL367UMXRR7ZFC7GPQ/graph.json","events_json":"https://pith.science/api/pith-number/PRQWQNAGWL367UMXRR7ZFC7GPQ/events.json","paper":"https://pith.science/paper/PRQWQNAG"},"agent_actions":{"view_html":"https://pith.science/pith/PRQWQNAGWL367UMXRR7ZFC7GPQ","download_json":"https://pith.science/pith/PRQWQNAGWL367UMXRR7ZFC7GPQ.json","view_paper":"https://pith.science/paper/PRQWQNAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.06523&json=true","fetch_graph":"https://pith.science/api/pith-number/PRQWQNAGWL367UMXRR7ZFC7GPQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PRQWQNAGWL367UMXRR7ZFC7GPQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PRQWQNAGWL367UMXRR7ZFC7GPQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PRQWQNAGWL367UMXRR7ZFC7GPQ/action/storage_attestation","attest_author":"https://pith.science/pith/PRQWQNAGWL367UMXRR7ZFC7GPQ/action/author_attestation","sign_citation":"https://pith.science/pith/PRQWQNAGWL367UMXRR7ZFC7GPQ/action/citation_signature","submit_replication":"https://pith.science/pith/PRQWQNAGWL367UMXRR7ZFC7GPQ/action/replication_record"}},"created_at":"2026-05-17T23:40:37.488613+00:00","updated_at":"2026-05-17T23:40:37.488613+00:00"}