{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Z2UUV6SA7QKNXG7WXV7HDANI37","short_pith_number":"pith:Z2UUV6SA","canonical_record":{"source":{"id":"1202.3613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-16T15:06:56Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"766ec4a3d139e0a4554535f3785f8f2df00f542f2848eb1b596ed52ff8b5d9ef","abstract_canon_sha256":"651ef57fa4511a86fa020c4e3f8968b0d2cbe32a8c556b1756d9578075fe7ea6"},"schema_version":"1.0"},"canonical_sha256":"cea94afa40fc14db9bf6bd7e7181a8dfc1870e68a854f75ef9f3474431be2f43","source":{"kind":"arxiv","id":"1202.3613","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3613","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3613v1","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3613","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"Z2UUV6SA7QKN","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z2UUV6SA7QKNXG7W","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z2UUV6SA","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Z2UUV6SA7QKNXG7WXV7HDANI37","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-16T15:06:56Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"766ec4a3d139e0a4554535f3785f8f2df00f542f2848eb1b596ed52ff8b5d9ef","abstract_canon_sha256":"651ef57fa4511a86fa020c4e3f8968b0d2cbe32a8c556b1756d9578075fe7ea6"},"schema_version":"1.0"},"canonical_sha256":"cea94afa40fc14db9bf6bd7e7181a8dfc1870e68a854f75ef9f3474431be2f43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:12.754470Z","signature_b64":"Scw5gQaj39b9493mIFTPmkG31rdH7bv0j5THXGZjb/M/PC6QWCquCk1Lp0DphIp6s1FsRRKdF3qHWV5tDZGkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea94afa40fc14db9bf6bd7e7181a8dfc1870e68a854f75ef9f3474431be2f43","last_reissued_at":"2026-05-18T04:02:12.753824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:12.753824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3613","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wY92EJRLStpAOysbsyF5LyNaqS2NQRa7X22LTV+5Ohj6Sdx1/3DHVo8Xb9fLEj15obP+dY10dyutzqC/xj99Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:49:14.458741Z"},"content_sha256":"a5e44ebee89cefe2691b2168334e3a122cd5d4617ec19b2b5af73b55dcab4b91","schema_version":"1.0","event_id":"sha256:a5e44ebee89cefe2691b2168334e3a122cd5d4617ec19b2b5af73b55dcab4b91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Z2UUV6SA7QKNXG7WXV7HDANI37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopf algebras---Variant notions and reconstruction theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RA","authors_text":"Joost Vercruysse","submitted_at":"2012-02-16T15:06:56Z","abstract_excerpt":"Hopf algebras are closely related to monoidal categories. More precise, $k$-Hopf algebras can be characterized as those algebras whose category of finite dimensional representations is an autonomous monoidal category such that the forgetful functor to $k$-vectorspaces is a strict monoidal functor. This result is known as the Tannaka reconstruction theorem (for Hopf algebras). Because of the importance of both Hopf algebras in various fields, over the last last few decades, many generalizations have been defined. We will survey these different generalizations from the point of view of the Tanna"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3613","kind":"arxiv","version":1},"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":"2026-05-18T04:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mf/OxCYZX9LP3jXmQyu7F4nbJqJpTIWi7Hy7cIUDA1yVZZ5ImP9ChRBIoNKAUBOGTH3DdzeM514pqz0BvaNxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:49:14.459094Z"},"content_sha256":"13a8943c8d467259fb973685f854c9e0f38333ae2e10d18ab03ce6a91265f2dd","schema_version":"1.0","event_id":"sha256:13a8943c8d467259fb973685f854c9e0f38333ae2e10d18ab03ce6a91265f2dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2UUV6SA7QKNXG7WXV7HDANI37/bundle.json","state_url":"https://pith.science/pith/Z2UUV6SA7QKNXG7WXV7HDANI37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2UUV6SA7QKNXG7WXV7HDANI37/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":"2026-06-05T12:49:14Z","links":{"resolver":"https://pith.science/pith/Z2UUV6SA7QKNXG7WXV7HDANI37","bundle":"https://pith.science/pith/Z2UUV6SA7QKNXG7WXV7HDANI37/bundle.json","state":"https://pith.science/pith/Z2UUV6SA7QKNXG7WXV7HDANI37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2UUV6SA7QKNXG7WXV7HDANI37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z2UUV6SA7QKNXG7WXV7HDANI37","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":"651ef57fa4511a86fa020c4e3f8968b0d2cbe32a8c556b1756d9578075fe7ea6","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-16T15:06:56Z","title_canon_sha256":"766ec4a3d139e0a4554535f3785f8f2df00f542f2848eb1b596ed52ff8b5d9ef"},"schema_version":"1.0","source":{"id":"1202.3613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3613","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3613v1","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3613","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"Z2UUV6SA7QKN","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z2UUV6SA7QKNXG7W","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z2UUV6SA","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:13a8943c8d467259fb973685f854c9e0f38333ae2e10d18ab03ce6a91265f2dd","target":"graph","created_at":"2026-05-18T04:02:12Z","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":"Hopf algebras are closely related to monoidal categories. More precise, $k$-Hopf algebras can be characterized as those algebras whose category of finite dimensional representations is an autonomous monoidal category such that the forgetful functor to $k$-vectorspaces is a strict monoidal functor. This result is known as the Tannaka reconstruction theorem (for Hopf algebras). Because of the importance of both Hopf algebras in various fields, over the last last few decades, many generalizations have been defined. We will survey these different generalizations from the point of view of the Tanna","authors_text":"Joost Vercruysse","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-16T15:06:56Z","title":"Hopf algebras---Variant notions and reconstruction theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3613","kind":"arxiv","version":1},"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:a5e44ebee89cefe2691b2168334e3a122cd5d4617ec19b2b5af73b55dcab4b91","target":"record","created_at":"2026-05-18T04:02:12Z","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":"651ef57fa4511a86fa020c4e3f8968b0d2cbe32a8c556b1756d9578075fe7ea6","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-16T15:06:56Z","title_canon_sha256":"766ec4a3d139e0a4554535f3785f8f2df00f542f2848eb1b596ed52ff8b5d9ef"},"schema_version":"1.0","source":{"id":"1202.3613","kind":"arxiv","version":1}},"canonical_sha256":"cea94afa40fc14db9bf6bd7e7181a8dfc1870e68a854f75ef9f3474431be2f43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea94afa40fc14db9bf6bd7e7181a8dfc1870e68a854f75ef9f3474431be2f43","first_computed_at":"2026-05-18T04:02:12.753824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:12.753824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Scw5gQaj39b9493mIFTPmkG31rdH7bv0j5THXGZjb/M/PC6QWCquCk1Lp0DphIp6s1FsRRKdF3qHWV5tDZGkCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:12.754470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5e44ebee89cefe2691b2168334e3a122cd5d4617ec19b2b5af73b55dcab4b91","sha256:13a8943c8d467259fb973685f854c9e0f38333ae2e10d18ab03ce6a91265f2dd"],"state_sha256":"6b0a0c1b5f076d90c6851b7aa3ad3158110642e89aa05c2226ebac21713cde7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D6KbZ+k+MvUz+xz0VGBX4sOmbyLKmttkybgGcdt87chYaeZGeV5oIXN5WEsHI+y5AqKZ9+8vXLEEkczfNj5WBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:49:14.461074Z","bundle_sha256":"034cce9c930804a569c901c479167450ad4ad034c7d7c98b986f9f2ff172a544"}}