{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2Q7PBMLNY7R3GBZSGIDVQPGMBL","short_pith_number":"pith:2Q7PBMLN","canonical_record":{"source":{"id":"1506.02427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-06-08T10:08:07Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"6098f8df36b2d9625f0de7450fec5c10012e5ed1ccec19d8f412ddcae724108b","abstract_canon_sha256":"b1630f9291e23ee7302028a00a2042a50eeded7fe65dfd4f981454feb86ca4c6"},"schema_version":"1.0"},"canonical_sha256":"d43ef0b16dc7e3b307323207583ccc0acd396cc462b0ad40fac4e5edd9947449","source":{"kind":"arxiv","id":"1506.02427","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02427","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02427v1","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02427","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"2Q7PBMLNY7R3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2Q7PBMLNY7R3GBZS","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2Q7PBMLN","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2Q7PBMLNY7R3GBZSGIDVQPGMBL","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-06-08T10:08:07Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"6098f8df36b2d9625f0de7450fec5c10012e5ed1ccec19d8f412ddcae724108b","abstract_canon_sha256":"b1630f9291e23ee7302028a00a2042a50eeded7fe65dfd4f981454feb86ca4c6"},"schema_version":"1.0"},"canonical_sha256":"d43ef0b16dc7e3b307323207583ccc0acd396cc462b0ad40fac4e5edd9947449","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:51.148340Z","signature_b64":"4PA1Ocjyn8Yw3qX1zJIHhfWW4SQPicQTDkmuDLpqgR6ss/O14Yqq4klUndqw2pFkmoFAGiYGz8NzzS34hFXWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d43ef0b16dc7e3b307323207583ccc0acd396cc462b0ad40fac4e5edd9947449","last_reissued_at":"2026-05-18T01:55:51.147793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:51.147793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02427","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":"2026-05-18T01:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rtQIl9pD/ALdiV5iGdlKTs0IFyiaVCyQVh6aTnmYNDhuYwy+1iip81+25CIGkQtQ5c0ZkFoW3KnRM0+OKWqgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:59:23.723238Z"},"content_sha256":"01aa3768d8f17126910a35959a53472eb49758cdc166a1fe52cfbcd9f3c57d2d","schema_version":"1.0","event_id":"sha256:01aa3768d8f17126910a35959a53472eb49758cdc166a1fe52cfbcd9f3c57d2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2Q7PBMLNY7R3GBZSGIDVQPGMBL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum homogeneous spaces of connected Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Ken Brown, Paul Gilmartin","submitted_at":"2015-06-08T10:08:07Z","abstract_excerpt":"Let H be a connected Hopf k-algebra of finite Gel'fand-Kirillov dimension over an algebraically closed field k of characteristic 0. The objects of study in this paper are the left or right coideal subalgebras T of H. They are shown to be deformations of commutative polynomial k-algebras. A number of well-known homological and other properties follow immediately from this fact. Further properties are described, examples are considered, invariants are constructed and a number of open questions are listed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02427","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":"2026-05-18T01:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IhU7OUVRyK8paCVVcqI3XJWGbaFXhfcVRPBESglyDndVT7Fx7kISo2vtjUr4BDrEkOf+I7WSu6WKbwWsJHn0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:59:23.723929Z"},"content_sha256":"76a5798d176c94df8b7dd930f290226c6ad6d75bd2b2267badf2156d7623c8de","schema_version":"1.0","event_id":"sha256:76a5798d176c94df8b7dd930f290226c6ad6d75bd2b2267badf2156d7623c8de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2Q7PBMLNY7R3GBZSGIDVQPGMBL/bundle.json","state_url":"https://pith.science/pith/2Q7PBMLNY7R3GBZSGIDVQPGMBL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2Q7PBMLNY7R3GBZSGIDVQPGMBL/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":"2026-06-11T23:59:23Z","links":{"resolver":"https://pith.science/pith/2Q7PBMLNY7R3GBZSGIDVQPGMBL","bundle":"https://pith.science/pith/2Q7PBMLNY7R3GBZSGIDVQPGMBL/bundle.json","state":"https://pith.science/pith/2Q7PBMLNY7R3GBZSGIDVQPGMBL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2Q7PBMLNY7R3GBZSGIDVQPGMBL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2Q7PBMLNY7R3GBZSGIDVQPGMBL","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":"b1630f9291e23ee7302028a00a2042a50eeded7fe65dfd4f981454feb86ca4c6","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-06-08T10:08:07Z","title_canon_sha256":"6098f8df36b2d9625f0de7450fec5c10012e5ed1ccec19d8f412ddcae724108b"},"schema_version":"1.0","source":{"id":"1506.02427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02427","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02427v1","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02427","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"2Q7PBMLNY7R3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2Q7PBMLNY7R3GBZS","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2Q7PBMLN","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:76a5798d176c94df8b7dd930f290226c6ad6d75bd2b2267badf2156d7623c8de","target":"graph","created_at":"2026-05-18T01:55:51Z","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":"Let H be a connected Hopf k-algebra of finite Gel'fand-Kirillov dimension over an algebraically closed field k of characteristic 0. The objects of study in this paper are the left or right coideal subalgebras T of H. They are shown to be deformations of commutative polynomial k-algebras. A number of well-known homological and other properties follow immediately from this fact. Further properties are described, examples are considered, invariants are constructed and a number of open questions are listed.","authors_text":"Ken Brown, Paul Gilmartin","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-06-08T10:08:07Z","title":"Quantum homogeneous spaces of connected Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02427","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":"sha256:01aa3768d8f17126910a35959a53472eb49758cdc166a1fe52cfbcd9f3c57d2d","target":"record","created_at":"2026-05-18T01:55:51Z","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":"b1630f9291e23ee7302028a00a2042a50eeded7fe65dfd4f981454feb86ca4c6","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-06-08T10:08:07Z","title_canon_sha256":"6098f8df36b2d9625f0de7450fec5c10012e5ed1ccec19d8f412ddcae724108b"},"schema_version":"1.0","source":{"id":"1506.02427","kind":"arxiv","version":1}},"canonical_sha256":"d43ef0b16dc7e3b307323207583ccc0acd396cc462b0ad40fac4e5edd9947449","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d43ef0b16dc7e3b307323207583ccc0acd396cc462b0ad40fac4e5edd9947449","first_computed_at":"2026-05-18T01:55:51.147793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:51.147793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4PA1Ocjyn8Yw3qX1zJIHhfWW4SQPicQTDkmuDLpqgR6ss/O14Yqq4klUndqw2pFkmoFAGiYGz8NzzS34hFXWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:51.148340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01aa3768d8f17126910a35959a53472eb49758cdc166a1fe52cfbcd9f3c57d2d","sha256:76a5798d176c94df8b7dd930f290226c6ad6d75bd2b2267badf2156d7623c8de"],"state_sha256":"e94ded09bdd842bf26bf822ec832adc1e0bcb25c57a5e94eb13ae487a7ca20a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zsrKf0p9lBhzd3FOPQKhwwiQnahYf/LGu9XQciEg71WblBWb7+JPdDNycXKmBsmxFNYC+LHSIJ+LqzLWRoglBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:59:23.728418Z","bundle_sha256":"27baee36f2a2eb4d9d19e56b4fdee85b35b42e354b0d930e9dbef70e1dbb314e"}}