{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WWL5JPWB2V6SPY64NQLIOMYOY5","short_pith_number":"pith:WWL5JPWB","canonical_record":{"source":{"id":"1001.1108","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-07T17:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"80533eb5d1e1387c3a538a07bccd169feb3c59740102640929669cd8e02b8d96","abstract_canon_sha256":"46d20686c23d3c3d4266fe7d580079bcf9999665fe6a60cff9a3cb26f819a9f2"},"schema_version":"1.0"},"canonical_sha256":"b597d4bec1d57d27e3dc6c1687330ec757d71d8eb3788eb107008c8d90e976f6","source":{"kind":"arxiv","id":"1001.1108","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1108","created_at":"2026-05-18T04:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1108v2","created_at":"2026-05-18T04:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1108","created_at":"2026-05-18T04:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"WWL5JPWB2V6S","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WWL5JPWB2V6SPY64","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WWL5JPWB","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WWL5JPWB2V6SPY64NQLIOMYOY5","target":"record","payload":{"canonical_record":{"source":{"id":"1001.1108","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-07T17:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"80533eb5d1e1387c3a538a07bccd169feb3c59740102640929669cd8e02b8d96","abstract_canon_sha256":"46d20686c23d3c3d4266fe7d580079bcf9999665fe6a60cff9a3cb26f819a9f2"},"schema_version":"1.0"},"canonical_sha256":"b597d4bec1d57d27e3dc6c1687330ec757d71d8eb3788eb107008c8d90e976f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:06.080139Z","signature_b64":"Cj3Pa6AJlEdgXOdKJJi8BtlseecO1n3C+oe3rU68GqhkxtxArcEbWdQdjeBM5vSp62CLBl8ff27t1ZFIou5DCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b597d4bec1d57d27e3dc6c1687330ec757d71d8eb3788eb107008c8d90e976f6","last_reissued_at":"2026-05-18T04:35:06.079517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:06.079517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.1108","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8BJMsINJm5EUs8Kp2hNsW5uKW9isjslLfYPM83S45nMRlQ9wM/3+f0RW2sx7USTAAFCSAoG6VKffqqOyQsuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:17:29.997851Z"},"content_sha256":"eda35de18fc280d6e02a8b1fb889280d108182e69b1cafe3b7b7b55a7e55c73e","schema_version":"1.0","event_id":"sha256:eda35de18fc280d6e02a8b1fb889280d108182e69b1cafe3b7b7b55a7e55c73e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WWL5JPWB2V6SPY64NQLIOMYOY5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pointed Hopf algebras over the 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, M. Gra\\~na, N. Andruskiewitsch","submitted_at":"2010-01-07T17:12:26Z","abstract_excerpt":"We show that every finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group is a group algebra, except for the Fischer group Fi22, the Baby Monster and the Monster. For these three groups, we give a short list of irreducible Yetter-Drinfeld modules whose Nichols algebra is not known to be finite-dimensional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1108","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UWyp4zxQu5ItZVQS00iASKe+ScJGE+uYJmCGCN2nezyTNekn9CqJ1si6DRcz1j589GtBHyolf3RkIoU6D2hgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:17:29.998223Z"},"content_sha256":"d71908b6b1835898817f40755b898742877b83f0db9c01276822dfecf2cd3598","schema_version":"1.0","event_id":"sha256:d71908b6b1835898817f40755b898742877b83f0db9c01276822dfecf2cd3598"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWL5JPWB2V6SPY64NQLIOMYOY5/bundle.json","state_url":"https://pith.science/pith/WWL5JPWB2V6SPY64NQLIOMYOY5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWL5JPWB2V6SPY64NQLIOMYOY5/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":"2026-06-25T23:17:29Z","links":{"resolver":"https://pith.science/pith/WWL5JPWB2V6SPY64NQLIOMYOY5","bundle":"https://pith.science/pith/WWL5JPWB2V6SPY64NQLIOMYOY5/bundle.json","state":"https://pith.science/pith/WWL5JPWB2V6SPY64NQLIOMYOY5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWL5JPWB2V6SPY64NQLIOMYOY5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WWL5JPWB2V6SPY64NQLIOMYOY5","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":"46d20686c23d3c3d4266fe7d580079bcf9999665fe6a60cff9a3cb26f819a9f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-07T17:12:26Z","title_canon_sha256":"80533eb5d1e1387c3a538a07bccd169feb3c59740102640929669cd8e02b8d96"},"schema_version":"1.0","source":{"id":"1001.1108","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1108","created_at":"2026-05-18T04:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1108v2","created_at":"2026-05-18T04:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1108","created_at":"2026-05-18T04:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"WWL5JPWB2V6S","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WWL5JPWB2V6SPY64","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WWL5JPWB","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d71908b6b1835898817f40755b898742877b83f0db9c01276822dfecf2cd3598","target":"graph","created_at":"2026-05-18T04:35:06Z","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":"We show that every finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group is a group algebra, except for the Fischer group Fi22, the Baby Monster and the Monster. For these three groups, we give a short list of irreducible Yetter-Drinfeld modules whose Nichols algebra is not known to be finite-dimensional.","authors_text":"F. Fantino, L. Vendramin, M. Gra\\~na, N. Andruskiewitsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-07T17:12:26Z","title":"Pointed Hopf algebras over the sporadic simple groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1108","kind":"arxiv","version":2},"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:eda35de18fc280d6e02a8b1fb889280d108182e69b1cafe3b7b7b55a7e55c73e","target":"record","created_at":"2026-05-18T04:35:06Z","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":"46d20686c23d3c3d4266fe7d580079bcf9999665fe6a60cff9a3cb26f819a9f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-07T17:12:26Z","title_canon_sha256":"80533eb5d1e1387c3a538a07bccd169feb3c59740102640929669cd8e02b8d96"},"schema_version":"1.0","source":{"id":"1001.1108","kind":"arxiv","version":2}},"canonical_sha256":"b597d4bec1d57d27e3dc6c1687330ec757d71d8eb3788eb107008c8d90e976f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b597d4bec1d57d27e3dc6c1687330ec757d71d8eb3788eb107008c8d90e976f6","first_computed_at":"2026-05-18T04:35:06.079517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:06.079517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cj3Pa6AJlEdgXOdKJJi8BtlseecO1n3C+oe3rU68GqhkxtxArcEbWdQdjeBM5vSp62CLBl8ff27t1ZFIou5DCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:06.080139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1108","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eda35de18fc280d6e02a8b1fb889280d108182e69b1cafe3b7b7b55a7e55c73e","sha256:d71908b6b1835898817f40755b898742877b83f0db9c01276822dfecf2cd3598"],"state_sha256":"64b47af7db098b4743ff5a62793780cd6b064cffee4367d82706557078c9c75a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uK5Ywz127Yxc2ZgDSUGDDj9zb8xJJScQ8Qve9RSL3GUAQW6NQNiDNe/qApeIwGGajcQ65Yf6N5kjlUhDP4hBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:17:30.000169Z","bundle_sha256":"10917aad10db3068e305372919d38df8578cd733e6fa6fe1636de7c301f60798"}}