{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N22KK2EXX2OLGKUVLXBIDMOY5J","short_pith_number":"pith:N22KK2EX","canonical_record":{"source":{"id":"1403.6980","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-27T11:19:32Z","cross_cats_sorted":[],"title_canon_sha256":"4ebb6df2c2580cd3b80328ffaf8429fe22c3ee6498d3448974b462a386200644","abstract_canon_sha256":"ac9d1db1ebcc40cf74d809289a177d17aa54ee99f7d42e219bc52abbbb45625c"},"schema_version":"1.0"},"canonical_sha256":"6eb4a56897be9cb32a955dc281b1d8ea552f93aeac0cb88196d4855358407bc4","source":{"kind":"arxiv","id":"1403.6980","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6980","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6980v3","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6980","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"N22KK2EXX2OL","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N22KK2EXX2OLGKUV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N22KK2EX","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N22KK2EXX2OLGKUVLXBIDMOY5J","target":"record","payload":{"canonical_record":{"source":{"id":"1403.6980","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-27T11:19:32Z","cross_cats_sorted":[],"title_canon_sha256":"4ebb6df2c2580cd3b80328ffaf8429fe22c3ee6498d3448974b462a386200644","abstract_canon_sha256":"ac9d1db1ebcc40cf74d809289a177d17aa54ee99f7d42e219bc52abbbb45625c"},"schema_version":"1.0"},"canonical_sha256":"6eb4a56897be9cb32a955dc281b1d8ea552f93aeac0cb88196d4855358407bc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:53.549052Z","signature_b64":"TM9Pg9o2Zxg5hPeQfrIwFe7C3+i65tqHR7OwyI0eHN63hhxlDCPJX93tCi9s4uU7FGNdPEB2xktec5GaVOrfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6eb4a56897be9cb32a955dc281b1d8ea552f93aeac0cb88196d4855358407bc4","last_reissued_at":"2026-05-18T02:49:53.548422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:53.548422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.6980","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5C2EuTNKvdRbmRMCJ9Zd3+LJcDsB23ogbolViM71VNpYkHfJaE8/UStmiwOzLchM6UP/N1/3mLLXAnBbrrV0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:24:45.233006Z"},"content_sha256":"64923a15476506f4562681574b329863b9cbb9b82c1d9de3e26c412c524f1e68","schema_version":"1.0","event_id":"sha256:64923a15476506f4562681574b329863b9cbb9b82c1d9de3e26c412c524f1e68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N22KK2EXX2OLGKUVLXBIDMOY5J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recent progress in isoparametric functions and isoparametric hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chao Qian, Zizhou Tang","submitted_at":"2014-03-27T11:19:32Z","abstract_excerpt":"This paper gives a survey of recent progress in isoparametric functions and isoparametric hypersurfaces, mainly in two directions. (1) Isoparametric functions on Riemannian manifolds, including exotic spheres. The existences and non-existences will be considered. (2) The Yau conjecture on the first eigenvalues of the embedded minimal hypersurfaces in the unit spheres. The history and progress of the Yau conjecture on minimal isoparametric hypersurfaces will be stated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6980","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0qYoVBTh65PPtUH+7I1Aiy4Sg8ZN8F4Rqr3j/usaffaEhVfFMMofv/9Dq6FxhjhggGMVbZRt8Je9EclV+yd7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:24:45.233369Z"},"content_sha256":"5474556ef25e6e13fc019f146681e7b9c3945a818e2cc8cbb984be63ffb8f5c9","schema_version":"1.0","event_id":"sha256:5474556ef25e6e13fc019f146681e7b9c3945a818e2cc8cbb984be63ffb8f5c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N22KK2EXX2OLGKUVLXBIDMOY5J/bundle.json","state_url":"https://pith.science/pith/N22KK2EXX2OLGKUVLXBIDMOY5J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N22KK2EXX2OLGKUVLXBIDMOY5J/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T14:24:45Z","links":{"resolver":"https://pith.science/pith/N22KK2EXX2OLGKUVLXBIDMOY5J","bundle":"https://pith.science/pith/N22KK2EXX2OLGKUVLXBIDMOY5J/bundle.json","state":"https://pith.science/pith/N22KK2EXX2OLGKUVLXBIDMOY5J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N22KK2EXX2OLGKUVLXBIDMOY5J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N22KK2EXX2OLGKUVLXBIDMOY5J","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":"ac9d1db1ebcc40cf74d809289a177d17aa54ee99f7d42e219bc52abbbb45625c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-27T11:19:32Z","title_canon_sha256":"4ebb6df2c2580cd3b80328ffaf8429fe22c3ee6498d3448974b462a386200644"},"schema_version":"1.0","source":{"id":"1403.6980","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6980","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6980v3","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6980","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"N22KK2EXX2OL","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N22KK2EXX2OLGKUV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N22KK2EX","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:5474556ef25e6e13fc019f146681e7b9c3945a818e2cc8cbb984be63ffb8f5c9","target":"graph","created_at":"2026-05-18T02:49:53Z","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":"This paper gives a survey of recent progress in isoparametric functions and isoparametric hypersurfaces, mainly in two directions. (1) Isoparametric functions on Riemannian manifolds, including exotic spheres. The existences and non-existences will be considered. (2) The Yau conjecture on the first eigenvalues of the embedded minimal hypersurfaces in the unit spheres. The history and progress of the Yau conjecture on minimal isoparametric hypersurfaces will be stated.","authors_text":"Chao Qian, Zizhou Tang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-27T11:19:32Z","title":"Recent progress in isoparametric functions and isoparametric hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6980","kind":"arxiv","version":3},"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":"sha256:64923a15476506f4562681574b329863b9cbb9b82c1d9de3e26c412c524f1e68","target":"record","created_at":"2026-05-18T02:49:53Z","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":"ac9d1db1ebcc40cf74d809289a177d17aa54ee99f7d42e219bc52abbbb45625c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-27T11:19:32Z","title_canon_sha256":"4ebb6df2c2580cd3b80328ffaf8429fe22c3ee6498d3448974b462a386200644"},"schema_version":"1.0","source":{"id":"1403.6980","kind":"arxiv","version":3}},"canonical_sha256":"6eb4a56897be9cb32a955dc281b1d8ea552f93aeac0cb88196d4855358407bc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6eb4a56897be9cb32a955dc281b1d8ea552f93aeac0cb88196d4855358407bc4","first_computed_at":"2026-05-18T02:49:53.548422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:53.548422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TM9Pg9o2Zxg5hPeQfrIwFe7C3+i65tqHR7OwyI0eHN63hhxlDCPJX93tCi9s4uU7FGNdPEB2xktec5GaVOrfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:53.549052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6980","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64923a15476506f4562681574b329863b9cbb9b82c1d9de3e26c412c524f1e68","sha256:5474556ef25e6e13fc019f146681e7b9c3945a818e2cc8cbb984be63ffb8f5c9"],"state_sha256":"e36fdcee5a9b9d7656a23310217c19ff69257459491884ca767b98ba3e0a916a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bcHAtL2+Dlwr0B0LUyn7VRVZz0oc1PwNdwNEZuIVqikw9QZ1BVOvr3V0WgEn85KGvK4SL33fi2NxPlxpjI3DAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:24:45.235220Z","bundle_sha256":"d60b2da82af84aa2e39c9e28315891cf83d162cdbcd5521227a5dc618b7a7a5e"}}