{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QSC5RQJFVKK63KZ2QP3LX6SF2C","short_pith_number":"pith:QSC5RQJF","canonical_record":{"source":{"id":"1001.3977","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-22T12:45:20Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"a97731cfbb23376abcfd7ac37417fd7fa833d9fd54efb5a5ad21b2089b39d2dd","abstract_canon_sha256":"95b541ce74d673bb81d52e246b19ebd7d1c1f6d1c42b667c5ad0be6aadb4e53f"},"schema_version":"1.0"},"canonical_sha256":"8485d8c125aa95edab3a83f6bbfa45d0b0432c07dd2c83f9f850b57ffd5c1831","source":{"kind":"arxiv","id":"1001.3977","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3977","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3977v2","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3977","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"pith_short_12","alias_value":"QSC5RQJFVKK6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QSC5RQJFVKK63KZ2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QSC5RQJF","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QSC5RQJFVKK63KZ2QP3LX6SF2C","target":"record","payload":{"canonical_record":{"source":{"id":"1001.3977","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-22T12:45:20Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"a97731cfbb23376abcfd7ac37417fd7fa833d9fd54efb5a5ad21b2089b39d2dd","abstract_canon_sha256":"95b541ce74d673bb81d52e246b19ebd7d1c1f6d1c42b667c5ad0be6aadb4e53f"},"schema_version":"1.0"},"canonical_sha256":"8485d8c125aa95edab3a83f6bbfa45d0b0432c07dd2c83f9f850b57ffd5c1831","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:36.873087Z","signature_b64":"9P5VxgZx0GncbP706SITZjbWBdTFZQ6kVfn8G4o3UwDbperRj+O5gTlPsjjRMhqqY76o0LevXiG3UDJCEX6kAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8485d8c125aa95edab3a83f6bbfa45d0b0432c07dd2c83f9f850b57ffd5c1831","last_reissued_at":"2026-05-18T04:30:36.872450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:36.872450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.3977","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":"2026-05-18T04:30:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aaTH21ftYFFrBvD/nCVjaLrWalOs3r+OIRf9eSwe9taUJmKHRMk2Z1joX83ocb9XKshKjDIwbXUAblfdPED9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:23:22.565856Z"},"content_sha256":"be815dd73758469f8436faf132dad91ca89840dc373ebf22230f1f782102fd1e","schema_version":"1.0","event_id":"sha256:be815dd73758469f8436faf132dad91ca89840dc373ebf22230f1f782102fd1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QSC5RQJFVKK63KZ2QP3LX6SF2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete reducibility theorems for modules over pointed Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"David Radford, Hans-J\\\"urgen Schneider, Nicol\\'as Andruskiewitsch","submitted_at":"2010-01-22T12:45:20Z","abstract_excerpt":"We investigate the representation theory of a large class of pointed Hopf algebras, extending results of Lusztig and others. We classify all simple modules in a suitable category and determine the weight multiplicities; we establish a complete reducibility theorem in this category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3977","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":"2026-05-18T04:30:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ozax4GA3P/jg3Lt79QSXkbiIQWVUkW1EsUWlQZXZygKCsyTf0+lZK8WVkuReCwsOl2EP3JBSolAK6mDr9FDwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:23:22.566420Z"},"content_sha256":"50601b404cc04115f385c0216b41594a90689dd68759cbc9fc8c3d637a8937d7","schema_version":"1.0","event_id":"sha256:50601b404cc04115f385c0216b41594a90689dd68759cbc9fc8c3d637a8937d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSC5RQJFVKK63KZ2QP3LX6SF2C/bundle.json","state_url":"https://pith.science/pith/QSC5RQJFVKK63KZ2QP3LX6SF2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSC5RQJFVKK63KZ2QP3LX6SF2C/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":"2026-05-31T10:23:22Z","links":{"resolver":"https://pith.science/pith/QSC5RQJFVKK63KZ2QP3LX6SF2C","bundle":"https://pith.science/pith/QSC5RQJFVKK63KZ2QP3LX6SF2C/bundle.json","state":"https://pith.science/pith/QSC5RQJFVKK63KZ2QP3LX6SF2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSC5RQJFVKK63KZ2QP3LX6SF2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QSC5RQJFVKK63KZ2QP3LX6SF2C","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":"95b541ce74d673bb81d52e246b19ebd7d1c1f6d1c42b667c5ad0be6aadb4e53f","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-22T12:45:20Z","title_canon_sha256":"a97731cfbb23376abcfd7ac37417fd7fa833d9fd54efb5a5ad21b2089b39d2dd"},"schema_version":"1.0","source":{"id":"1001.3977","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3977","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3977v2","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3977","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"pith_short_12","alias_value":"QSC5RQJFVKK6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QSC5RQJFVKK63KZ2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QSC5RQJF","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:50601b404cc04115f385c0216b41594a90689dd68759cbc9fc8c3d637a8937d7","target":"graph","created_at":"2026-05-18T04:30:36Z","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 investigate the representation theory of a large class of pointed Hopf algebras, extending results of Lusztig and others. We classify all simple modules in a suitable category and determine the weight multiplicities; we establish a complete reducibility theorem in this category.","authors_text":"David Radford, Hans-J\\\"urgen Schneider, Nicol\\'as Andruskiewitsch","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-22T12:45:20Z","title":"Complete reducibility theorems for modules over pointed Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3977","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:be815dd73758469f8436faf132dad91ca89840dc373ebf22230f1f782102fd1e","target":"record","created_at":"2026-05-18T04:30:36Z","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":"95b541ce74d673bb81d52e246b19ebd7d1c1f6d1c42b667c5ad0be6aadb4e53f","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-22T12:45:20Z","title_canon_sha256":"a97731cfbb23376abcfd7ac37417fd7fa833d9fd54efb5a5ad21b2089b39d2dd"},"schema_version":"1.0","source":{"id":"1001.3977","kind":"arxiv","version":2}},"canonical_sha256":"8485d8c125aa95edab3a83f6bbfa45d0b0432c07dd2c83f9f850b57ffd5c1831","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8485d8c125aa95edab3a83f6bbfa45d0b0432c07dd2c83f9f850b57ffd5c1831","first_computed_at":"2026-05-18T04:30:36.872450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:36.872450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9P5VxgZx0GncbP706SITZjbWBdTFZQ6kVfn8G4o3UwDbperRj+O5gTlPsjjRMhqqY76o0LevXiG3UDJCEX6kAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:36.873087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.3977","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be815dd73758469f8436faf132dad91ca89840dc373ebf22230f1f782102fd1e","sha256:50601b404cc04115f385c0216b41594a90689dd68759cbc9fc8c3d637a8937d7"],"state_sha256":"1e75796bcda031d3b4ff353642a7aeaaf1d8d6922796abfd2dd878f53c50da5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fE8cqUd6k9r4/MjJ5WM828sTXW8ljrnuJGhuvr3ccpWMwVjkeJm6dqhOyI7yhHEHWULyr8zZMb4e1431sggcBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:23:22.569369Z","bundle_sha256":"bc9b0138759bfc38a5f06bebaa2d37a514fcfb9e496bf9a7d1b145bad70a7d46"}}