{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EYTJU5QD2RWFCYGMOWMXI3XZ5V","short_pith_number":"pith:EYTJU5QD","schema_version":"1.0","canonical_sha256":"26269a7603d46c5160cc7599746ef9ed51fc0ebac23797c55b8a388e46134549","source":{"kind":"arxiv","id":"1303.6028","version":2},"attestation_state":"computed","paper":{"title":"Isoparametric functions on exotic spheres","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Chao Qian, Zizhou Tang","submitted_at":"2013-03-25T04:50:43Z","abstract_excerpt":"This paper extends widely the work in \\cite{GT13}. Existence and non-existence results of isoparametric functions on exotic spheres and Eells-Kuiper projective planes are established. In particular, every homotopy $n$-sphere ($n>4$) carries an isoparametric function (with certain metric) with 2 points as the focal set, in strong contrast to the classification of cohomogeneity one actions on homotopy spheres \\cite{St96} ( only exotic Kervaire spheres admit cohomogeneity one actions besides the standard spheres ). As an application, we improve a beautiful result of B\\'{e}rard-Bergery \\cite{BB77}"},"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":"1303.6028","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2013-03-25T04:50:43Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"58347f0483b4e694f9a32c6826e28e234452c5f65dad22422c04bff2b65d90b4","abstract_canon_sha256":"5cc5b14eb713595755a86289abb9bb0e7c8c56a3335521b58442bac9254af9d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:32.659368Z","signature_b64":"Z+uUtjmrofHWOXcSK7CFsrlvvy8dHNlpea2FJ69sCrvHDEYyO2YH7nIFnRvFbKzsnpWKyKfNP5D+TnjZMy/lDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26269a7603d46c5160cc7599746ef9ed51fc0ebac23797c55b8a388e46134549","last_reissued_at":"2026-05-18T02:30:32.658974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:32.658974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isoparametric functions on exotic spheres","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Chao Qian, Zizhou Tang","submitted_at":"2013-03-25T04:50:43Z","abstract_excerpt":"This paper extends widely the work in \\cite{GT13}. Existence and non-existence results of isoparametric functions on exotic spheres and Eells-Kuiper projective planes are established. In particular, every homotopy $n$-sphere ($n>4$) carries an isoparametric function (with certain metric) with 2 points as the focal set, in strong contrast to the classification of cohomogeneity one actions on homotopy spheres \\cite{St96} ( only exotic Kervaire spheres admit cohomogeneity one actions besides the standard spheres ). As an application, we improve a beautiful result of B\\'{e}rard-Bergery \\cite{BB77}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6028","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":"1303.6028","created_at":"2026-05-18T02:30:32.659031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.6028v2","created_at":"2026-05-18T02:30:32.659031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6028","created_at":"2026-05-18T02:30:32.659031+00:00"},{"alias_kind":"pith_short_12","alias_value":"EYTJU5QD2RWF","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EYTJU5QD2RWFCYGM","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EYTJU5QD","created_at":"2026-05-18T12:27:43.054852+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/EYTJU5QD2RWFCYGMOWMXI3XZ5V","json":"https://pith.science/pith/EYTJU5QD2RWFCYGMOWMXI3XZ5V.json","graph_json":"https://pith.science/api/pith-number/EYTJU5QD2RWFCYGMOWMXI3XZ5V/graph.json","events_json":"https://pith.science/api/pith-number/EYTJU5QD2RWFCYGMOWMXI3XZ5V/events.json","paper":"https://pith.science/paper/EYTJU5QD"},"agent_actions":{"view_html":"https://pith.science/pith/EYTJU5QD2RWFCYGMOWMXI3XZ5V","download_json":"https://pith.science/pith/EYTJU5QD2RWFCYGMOWMXI3XZ5V.json","view_paper":"https://pith.science/paper/EYTJU5QD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.6028&json=true","fetch_graph":"https://pith.science/api/pith-number/EYTJU5QD2RWFCYGMOWMXI3XZ5V/graph.json","fetch_events":"https://pith.science/api/pith-number/EYTJU5QD2RWFCYGMOWMXI3XZ5V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EYTJU5QD2RWFCYGMOWMXI3XZ5V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EYTJU5QD2RWFCYGMOWMXI3XZ5V/action/storage_attestation","attest_author":"https://pith.science/pith/EYTJU5QD2RWFCYGMOWMXI3XZ5V/action/author_attestation","sign_citation":"https://pith.science/pith/EYTJU5QD2RWFCYGMOWMXI3XZ5V/action/citation_signature","submit_replication":"https://pith.science/pith/EYTJU5QD2RWFCYGMOWMXI3XZ5V/action/replication_record"}},"created_at":"2026-05-18T02:30:32.659031+00:00","updated_at":"2026-05-18T02:30:32.659031+00:00"}