{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PK2DOGMLFLGVLPBQAJ7CNQNU26","short_pith_number":"pith:PK2DOGML","schema_version":"1.0","canonical_sha256":"7ab437198b2acd55bc30027e26c1b4d7bc6b8e04ca652d13e054156334850604","source":{"kind":"arxiv","id":"1107.0310","version":4},"attestation_state":"computed","paper":{"title":"On twisted conjugacy classes of type D in sporadic simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"F. Fantino, L. Vendramin","submitted_at":"2011-07-01T19:36:41Z","abstract_excerpt":"We classify twisted conjugacy classes of type D associated to the sporadic simple groups. This is an important step in the program of the classification of finite-dimensional pointed Hopf algebras with non-abelian coradical. As a by-product we prove that every complex finite-dimensional pointed Hopf algebra over the group of automorphisms of M12, J2, Suz, He, HN, T is the group algebra. In the appendix we improve the study of conjugacy classes of type D in sporadic simple groups."},"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":"1107.0310","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-01T19:36:41Z","cross_cats_sorted":[],"title_canon_sha256":"1e7f972f4b94f1c042e8021afb0277b57256fafddd231f6158dedd978ab2ed84","abstract_canon_sha256":"2b8cea4614c17bf3549acd5cfaaddd1788cd3bed7a59a066808f525c4932c6e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:53.959003Z","signature_b64":"KJZ2M6dpYZlhfbbiiHExAPf4eS36JDgUmFCJc9UatDT6BTnOM9zGU5Z+cpbIWnuYuWA47MQwuFcEmOBHO2RJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ab437198b2acd55bc30027e26c1b4d7bc6b8e04ca652d13e054156334850604","last_reissued_at":"2026-05-18T03:30:53.958278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:53.958278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On twisted conjugacy classes of type D in sporadic simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"F. Fantino, L. Vendramin","submitted_at":"2011-07-01T19:36:41Z","abstract_excerpt":"We classify twisted conjugacy classes of type D associated to the sporadic simple groups. This is an important step in the program of the classification of finite-dimensional pointed Hopf algebras with non-abelian coradical. As a by-product we prove that every complex finite-dimensional pointed Hopf algebra over the group of automorphisms of M12, J2, Suz, He, HN, T is the group algebra. In the appendix we improve the study of conjugacy classes of type D in sporadic simple groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0310","kind":"arxiv","version":4},"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":"1107.0310","created_at":"2026-05-18T03:30:53.958404+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.0310v4","created_at":"2026-05-18T03:30:53.958404+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0310","created_at":"2026-05-18T03:30:53.958404+00:00"},{"alias_kind":"pith_short_12","alias_value":"PK2DOGMLFLGV","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PK2DOGMLFLGVLPBQ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PK2DOGML","created_at":"2026-05-18T12:26:39.201973+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/PK2DOGMLFLGVLPBQAJ7CNQNU26","json":"https://pith.science/pith/PK2DOGMLFLGVLPBQAJ7CNQNU26.json","graph_json":"https://pith.science/api/pith-number/PK2DOGMLFLGVLPBQAJ7CNQNU26/graph.json","events_json":"https://pith.science/api/pith-number/PK2DOGMLFLGVLPBQAJ7CNQNU26/events.json","paper":"https://pith.science/paper/PK2DOGML"},"agent_actions":{"view_html":"https://pith.science/pith/PK2DOGMLFLGVLPBQAJ7CNQNU26","download_json":"https://pith.science/pith/PK2DOGMLFLGVLPBQAJ7CNQNU26.json","view_paper":"https://pith.science/paper/PK2DOGML","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.0310&json=true","fetch_graph":"https://pith.science/api/pith-number/PK2DOGMLFLGVLPBQAJ7CNQNU26/graph.json","fetch_events":"https://pith.science/api/pith-number/PK2DOGMLFLGVLPBQAJ7CNQNU26/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PK2DOGMLFLGVLPBQAJ7CNQNU26/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PK2DOGMLFLGVLPBQAJ7CNQNU26/action/storage_attestation","attest_author":"https://pith.science/pith/PK2DOGMLFLGVLPBQAJ7CNQNU26/action/author_attestation","sign_citation":"https://pith.science/pith/PK2DOGMLFLGVLPBQAJ7CNQNU26/action/citation_signature","submit_replication":"https://pith.science/pith/PK2DOGMLFLGVLPBQAJ7CNQNU26/action/replication_record"}},"created_at":"2026-05-18T03:30:53.958404+00:00","updated_at":"2026-05-18T03:30:53.958404+00:00"}