{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GHJWR67TTW3SNXYNXAOMIDCVXL","short_pith_number":"pith:GHJWR67T","canonical_record":{"source":{"id":"1310.7073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-10-26T04:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"319888c8533ee70a9a7451fad5fdf9fc78506824331b5826686f7a98dba10e7a","abstract_canon_sha256":"a7f459374e95dd790664b3d52c0c5c0e39cb752d9ccaf45dafa11f8bd5986af9"},"schema_version":"1.0"},"canonical_sha256":"31d368fbf39db726df0db81cc40c55bad1235799f960c688de344c1a0a6413ad","source":{"kind":"arxiv","id":"1310.7073","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7073","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7073v3","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7073","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"GHJWR67TTW3S","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GHJWR67TTW3SNXYN","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GHJWR67T","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GHJWR67TTW3SNXYNXAOMIDCVXL","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-10-26T04:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"319888c8533ee70a9a7451fad5fdf9fc78506824331b5826686f7a98dba10e7a","abstract_canon_sha256":"a7f459374e95dd790664b3d52c0c5c0e39cb752d9ccaf45dafa11f8bd5986af9"},"schema_version":"1.0"},"canonical_sha256":"31d368fbf39db726df0db81cc40c55bad1235799f960c688de344c1a0a6413ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:33.208936Z","signature_b64":"qri2blbJOq0AQEZo7jUC8lRbe9dX+SkRqwvf/gKjtK1FkjRzlbgkiOzWzla4LlwCwUN9YCPq0zh5LDyd1FwUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31d368fbf39db726df0db81cc40c55bad1235799f960c688de344c1a0a6413ad","last_reissued_at":"2026-05-18T01:37:33.208180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:33.208180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7073","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":"2026-05-18T01:37:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aIXoaBPGybVnao++ewjvg9529lSnYwsciDDZmyXIooH5voOZ+BuMAK199iCgMoZK4QKI0ojff83jubKROcBQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:23:50.983168Z"},"content_sha256":"941795ba2bb56dac68aa9d37dc4b66065e08fc4a263ccfed77da6044af2c103d","schema_version":"1.0","event_id":"sha256:941795ba2bb56dac68aa9d37dc4b66065e08fc4a263ccfed77da6044af2c103d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GHJWR67TTW3SNXYNXAOMIDCVXL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Xingting Wang","submitted_at":"2013-10-26T04:50:43Z","abstract_excerpt":"We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair associated with these extensions, we construct a cohomology group, which classifies all the extensions up to equivalence. Moreover, we present a $1$-$1$ correspondence between the isomorphism classes and a group quotient of the cohomology group deleting some exceptional points, where the group respects the automorphisms of the abelian matched pair and the e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7073","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":"2026-05-18T01:37:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ciWZ26/mSHKPd9QWnv3aHpOJv8LbnKTRC2lzoMQD4pJuPtKJ1AEkkAsHOYAlZ4dpDkXOMSoNHs/RVd55YaVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:23:50.983843Z"},"content_sha256":"a2a921c05c2f8fa138d0b74510e392d16fa6b52336c7567ed120cd1e4c2bd251","schema_version":"1.0","event_id":"sha256:a2a921c05c2f8fa138d0b74510e392d16fa6b52336c7567ed120cd1e4c2bd251"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHJWR67TTW3SNXYNXAOMIDCVXL/bundle.json","state_url":"https://pith.science/pith/GHJWR67TTW3SNXYNXAOMIDCVXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHJWR67TTW3SNXYNXAOMIDCVXL/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":"2026-05-31T05:23:50Z","links":{"resolver":"https://pith.science/pith/GHJWR67TTW3SNXYNXAOMIDCVXL","bundle":"https://pith.science/pith/GHJWR67TTW3SNXYNXAOMIDCVXL/bundle.json","state":"https://pith.science/pith/GHJWR67TTW3SNXYNXAOMIDCVXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHJWR67TTW3SNXYNXAOMIDCVXL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GHJWR67TTW3SNXYNXAOMIDCVXL","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":"a7f459374e95dd790664b3d52c0c5c0e39cb752d9ccaf45dafa11f8bd5986af9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-10-26T04:50:43Z","title_canon_sha256":"319888c8533ee70a9a7451fad5fdf9fc78506824331b5826686f7a98dba10e7a"},"schema_version":"1.0","source":{"id":"1310.7073","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7073","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7073v3","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7073","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"GHJWR67TTW3S","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GHJWR67TTW3SNXYN","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GHJWR67T","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:a2a921c05c2f8fa138d0b74510e392d16fa6b52336c7567ed120cd1e4c2bd251","target":"graph","created_at":"2026-05-18T01:37:33Z","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 classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair associated with these extensions, we construct a cohomology group, which classifies all the extensions up to equivalence. Moreover, we present a $1$-$1$ correspondence between the isomorphism classes and a group quotient of the cohomology group deleting some exceptional points, where the group respects the automorphisms of the abelian matched pair and the e","authors_text":"Xingting Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-10-26T04:50:43Z","title":"Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7073","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":"sha256:941795ba2bb56dac68aa9d37dc4b66065e08fc4a263ccfed77da6044af2c103d","target":"record","created_at":"2026-05-18T01:37:33Z","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":"a7f459374e95dd790664b3d52c0c5c0e39cb752d9ccaf45dafa11f8bd5986af9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-10-26T04:50:43Z","title_canon_sha256":"319888c8533ee70a9a7451fad5fdf9fc78506824331b5826686f7a98dba10e7a"},"schema_version":"1.0","source":{"id":"1310.7073","kind":"arxiv","version":3}},"canonical_sha256":"31d368fbf39db726df0db81cc40c55bad1235799f960c688de344c1a0a6413ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31d368fbf39db726df0db81cc40c55bad1235799f960c688de344c1a0a6413ad","first_computed_at":"2026-05-18T01:37:33.208180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:33.208180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qri2blbJOq0AQEZo7jUC8lRbe9dX+SkRqwvf/gKjtK1FkjRzlbgkiOzWzla4LlwCwUN9YCPq0zh5LDyd1FwUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:33.208936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7073","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:941795ba2bb56dac68aa9d37dc4b66065e08fc4a263ccfed77da6044af2c103d","sha256:a2a921c05c2f8fa138d0b74510e392d16fa6b52336c7567ed120cd1e4c2bd251"],"state_sha256":"31af35d9427b4f9ca1cf4fc873517f84e742df265d0780e2875d641c50a8c9b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cQJUeFFsiWYEM5x8TcAdsBmXdGeWXanpsQEtgeahYc5wlNx3SwaAHO6ZZIno7V3jq37LAS/4pUnoeAlmg6VVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:23:50.987439Z","bundle_sha256":"0bcafe46f0a10422b6a7da9e1417f746259e820c71ed4bb2def38ac2b1718159"}}