{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NHTYVD3CUJDPQU4WK56UQSFOWM","short_pith_number":"pith:NHTYVD3C","schema_version":"1.0","canonical_sha256":"69e78a8f62a246f85396577d4848aeb33248bfc669f3bf3470e7749e4e57f439","source":{"kind":"arxiv","id":"1408.0071","version":2},"attestation_state":"computed","paper":{"title":"Willmore submanifolds in the unit sphere via isoparametric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yuquan Xie","submitted_at":"2014-08-01T03:37:09Z","abstract_excerpt":"This paper is a continuation of [TY12] and [QTY13]. We show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore."},"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":"1408.0071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-01T03:37:09Z","cross_cats_sorted":[],"title_canon_sha256":"7df3ec04110ac188130a72b8d82876879718a40cd05bdedef19f5b66891d0069","abstract_canon_sha256":"33fcb4f859896065364976323f4cecaffa7aa09a738fe0566be4cf5268a59f6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:50.398151Z","signature_b64":"TnT7+vfMa+CKlyD/S2B/0nKGbNH6lN5FtXScAUVHq3Perbm06tpWYkVvUFHvrJySwjYdbcoNkA6xynoQmGaWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69e78a8f62a246f85396577d4848aeb33248bfc669f3bf3470e7749e4e57f439","last_reissued_at":"2026-05-18T02:45:50.397584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:50.397584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Willmore submanifolds in the unit sphere via isoparametric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yuquan Xie","submitted_at":"2014-08-01T03:37:09Z","abstract_excerpt":"This paper is a continuation of [TY12] and [QTY13]. We show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0071","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":"1408.0071","created_at":"2026-05-18T02:45:50.397674+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0071v2","created_at":"2026-05-18T02:45:50.397674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0071","created_at":"2026-05-18T02:45:50.397674+00:00"},{"alias_kind":"pith_short_12","alias_value":"NHTYVD3CUJDP","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NHTYVD3CUJDPQU4W","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NHTYVD3C","created_at":"2026-05-18T12:28:41.024544+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/NHTYVD3CUJDPQU4WK56UQSFOWM","json":"https://pith.science/pith/NHTYVD3CUJDPQU4WK56UQSFOWM.json","graph_json":"https://pith.science/api/pith-number/NHTYVD3CUJDPQU4WK56UQSFOWM/graph.json","events_json":"https://pith.science/api/pith-number/NHTYVD3CUJDPQU4WK56UQSFOWM/events.json","paper":"https://pith.science/paper/NHTYVD3C"},"agent_actions":{"view_html":"https://pith.science/pith/NHTYVD3CUJDPQU4WK56UQSFOWM","download_json":"https://pith.science/pith/NHTYVD3CUJDPQU4WK56UQSFOWM.json","view_paper":"https://pith.science/paper/NHTYVD3C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0071&json=true","fetch_graph":"https://pith.science/api/pith-number/NHTYVD3CUJDPQU4WK56UQSFOWM/graph.json","fetch_events":"https://pith.science/api/pith-number/NHTYVD3CUJDPQU4WK56UQSFOWM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NHTYVD3CUJDPQU4WK56UQSFOWM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NHTYVD3CUJDPQU4WK56UQSFOWM/action/storage_attestation","attest_author":"https://pith.science/pith/NHTYVD3CUJDPQU4WK56UQSFOWM/action/author_attestation","sign_citation":"https://pith.science/pith/NHTYVD3CUJDPQU4WK56UQSFOWM/action/citation_signature","submit_replication":"https://pith.science/pith/NHTYVD3CUJDPQU4WK56UQSFOWM/action/replication_record"}},"created_at":"2026-05-18T02:45:50.397674+00:00","updated_at":"2026-05-18T02:45:50.397674+00:00"}