{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6ANOWRAFLR7WNGWYQJZMEGPFCQ","short_pith_number":"pith:6ANOWRAF","schema_version":"1.0","canonical_sha256":"f01aeb44055c7f669ad88272c219e5141c8c6e867a0efd49a5ede30fdf5081dc","source":{"kind":"arxiv","id":"1412.5479","version":1},"attestation_state":"computed","paper":{"title":"Biharmonic hypersurfaces in space forms with three distinct principal curvatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ram Shankar Gupta","submitted_at":"2014-12-17T16:58:06Z","abstract_excerpt":"In this paper, we have studied biharmonic hypersurfaces in space form $\\bar{M}^{n+1}(c)$ with constant sectional curvature $c$. We have obtained that biharmonic hypersurfaces $M^{n}$ with at most three distinct principal curvatures in $\\bar{M}^{n+1}(c)$ has constant mean curvature. We also obtain the full classification of biharmonic hypersurfaces with at most three distinct principal curvatures in arbitrary dimension space form $\\bar{M}^{n+1}(c)$."},"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":"1412.5479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-17T16:58:06Z","cross_cats_sorted":[],"title_canon_sha256":"ab72be9018af15092d7ff2aca3e9de595c5a777167d2d1c62149b0b893a85bd2","abstract_canon_sha256":"14d72245c4f298c8e865474e4ae7c752468b8f27e5b14f59e00f6990171f4b4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:02.891996Z","signature_b64":"5OF5X3dOAgy6w+5Z8H6yM90j7z9tOV2CnyGf7ElEj9oNkd2NKEIZdvQTJleZb4D8eDFVPQTKgxshdIps+UvZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f01aeb44055c7f669ad88272c219e5141c8c6e867a0efd49a5ede30fdf5081dc","last_reissued_at":"2026-05-18T02:31:02.891633Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:02.891633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biharmonic hypersurfaces in space forms with three distinct principal curvatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ram Shankar Gupta","submitted_at":"2014-12-17T16:58:06Z","abstract_excerpt":"In this paper, we have studied biharmonic hypersurfaces in space form $\\bar{M}^{n+1}(c)$ with constant sectional curvature $c$. We have obtained that biharmonic hypersurfaces $M^{n}$ with at most three distinct principal curvatures in $\\bar{M}^{n+1}(c)$ has constant mean curvature. We also obtain the full classification of biharmonic hypersurfaces with at most three distinct principal curvatures in arbitrary dimension space form $\\bar{M}^{n+1}(c)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5479","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":"1412.5479","created_at":"2026-05-18T02:31:02.891685+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5479v1","created_at":"2026-05-18T02:31:02.891685+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5479","created_at":"2026-05-18T02:31:02.891685+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ANOWRAFLR7W","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ANOWRAFLR7WNGWY","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ANOWRAF","created_at":"2026-05-18T12:28:16.859392+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/6ANOWRAFLR7WNGWYQJZMEGPFCQ","json":"https://pith.science/pith/6ANOWRAFLR7WNGWYQJZMEGPFCQ.json","graph_json":"https://pith.science/api/pith-number/6ANOWRAFLR7WNGWYQJZMEGPFCQ/graph.json","events_json":"https://pith.science/api/pith-number/6ANOWRAFLR7WNGWYQJZMEGPFCQ/events.json","paper":"https://pith.science/paper/6ANOWRAF"},"agent_actions":{"view_html":"https://pith.science/pith/6ANOWRAFLR7WNGWYQJZMEGPFCQ","download_json":"https://pith.science/pith/6ANOWRAFLR7WNGWYQJZMEGPFCQ.json","view_paper":"https://pith.science/paper/6ANOWRAF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5479&json=true","fetch_graph":"https://pith.science/api/pith-number/6ANOWRAFLR7WNGWYQJZMEGPFCQ/graph.json","fetch_events":"https://pith.science/api/pith-number/6ANOWRAFLR7WNGWYQJZMEGPFCQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ANOWRAFLR7WNGWYQJZMEGPFCQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ANOWRAFLR7WNGWYQJZMEGPFCQ/action/storage_attestation","attest_author":"https://pith.science/pith/6ANOWRAFLR7WNGWYQJZMEGPFCQ/action/author_attestation","sign_citation":"https://pith.science/pith/6ANOWRAFLR7WNGWYQJZMEGPFCQ/action/citation_signature","submit_replication":"https://pith.science/pith/6ANOWRAFLR7WNGWYQJZMEGPFCQ/action/replication_record"}},"created_at":"2026-05-18T02:31:02.891685+00:00","updated_at":"2026-05-18T02:31:02.891685+00:00"}