{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6ANOWRAFLR7WNGWYQJZMEGPFCQ","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":"14d72245c4f298c8e865474e4ae7c752468b8f27e5b14f59e00f6990171f4b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-17T16:58:06Z","title_canon_sha256":"ab72be9018af15092d7ff2aca3e9de595c5a777167d2d1c62149b0b893a85bd2"},"schema_version":"1.0","source":{"id":"1412.5479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5479","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5479v1","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5479","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"6ANOWRAFLR7W","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6ANOWRAFLR7WNGWY","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6ANOWRAF","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:7629c2093aafce3be9d022ee2b3388bd5f0d77942db2355207d5968457d2c04c","target":"graph","created_at":"2026-05-18T02:31:02Z","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, 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 $\\bar{M}^{n+1}(c)$.","authors_text":"Ram Shankar Gupta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-17T16:58:06Z","title":"Biharmonic hypersurfaces in space forms with three distinct principal curvatures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5479","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:a2234e0658bf2c41d922cea720e36003ee569549b8573181936eac573a97c37e","target":"record","created_at":"2026-05-18T02:31:02Z","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":"14d72245c4f298c8e865474e4ae7c752468b8f27e5b14f59e00f6990171f4b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-17T16:58:06Z","title_canon_sha256":"ab72be9018af15092d7ff2aca3e9de595c5a777167d2d1c62149b0b893a85bd2"},"schema_version":"1.0","source":{"id":"1412.5479","kind":"arxiv","version":1}},"canonical_sha256":"f01aeb44055c7f669ad88272c219e5141c8c6e867a0efd49a5ede30fdf5081dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f01aeb44055c7f669ad88272c219e5141c8c6e867a0efd49a5ede30fdf5081dc","first_computed_at":"2026-05-18T02:31:02.891633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:02.891633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5OF5X3dOAgy6w+5Z8H6yM90j7z9tOV2CnyGf7ElEj9oNkd2NKEIZdvQTJleZb4D8eDFVPQTKgxshdIps+UvZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:02.891996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2234e0658bf2c41d922cea720e36003ee569549b8573181936eac573a97c37e","sha256:7629c2093aafce3be9d022ee2b3388bd5f0d77942db2355207d5968457d2c04c"],"state_sha256":"341be8890f53796c0a31d4cd8f927acaca13a4db9a7a8816220a97aa0206b293"}