{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H2YNYKNV3M6RIILJHXF6Y5WZXJ","short_pith_number":"pith:H2YNYKNV","canonical_record":{"source":{"id":"1807.01894","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-05T08:46:46Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"396cf0b4bc26b898f11ff54e08d5c5da38f456198e640292d93ef564ecaafbc0","abstract_canon_sha256":"02093e3dc62a2c4ef18692cc34c7ded96aed627957dec89c44522ee4709093e5"},"schema_version":"1.0"},"canonical_sha256":"3eb0dc29b5db3d1421693dcbec76d9ba5c36b2de64880d7efa648eefd75adb10","source":{"kind":"arxiv","id":"1807.01894","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01894","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01894v3","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01894","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"pith_short_12","alias_value":"H2YNYKNV3M6R","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H2YNYKNV3M6RIILJ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H2YNYKNV","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H2YNYKNV3M6RIILJHXF6Y5WZXJ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.01894","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-05T08:46:46Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"396cf0b4bc26b898f11ff54e08d5c5da38f456198e640292d93ef564ecaafbc0","abstract_canon_sha256":"02093e3dc62a2c4ef18692cc34c7ded96aed627957dec89c44522ee4709093e5"},"schema_version":"1.0"},"canonical_sha256":"3eb0dc29b5db3d1421693dcbec76d9ba5c36b2de64880d7efa648eefd75adb10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:54.456687Z","signature_b64":"APX5WbqFGGCjF2EtYOXHTyRBav76NzeUQzsK1ivq8U0Boi3x5ALCAinUL9RqOymSZ4VfhV4K9TCEdeqnMFCvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3eb0dc29b5db3d1421693dcbec76d9ba5c36b2de64880d7efa648eefd75adb10","last_reissued_at":"2026-05-17T23:51:54.456191Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:54.456191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.01894","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":"2026-05-17T23:51:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jeCIxgF2nOV1eAwidkH+q9MmqlBKg0jUc0qH3TXGJFc8XJq+czpBwF/dtf/ILnjCxZVJoGrNtemTL9lLDMECDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:50:56.774370Z"},"content_sha256":"090415b8ec90950bbecf77fc68b9a2fe735bec178ac3a435f33c440a4cf39e06","schema_version":"1.0","event_id":"sha256:090415b8ec90950bbecf77fc68b9a2fe735bec178ac3a435f33c440a4cf39e06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H2YNYKNV3M6RIILJHXF6Y5WZXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gelfand-Kirillov dimension of cosemisimple Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Alexandru Chirvasitu, Chelsea Walton, Xingting Wang","submitted_at":"2018-07-05T08:46:46Z","abstract_excerpt":"In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D'Andrea-Pinzari-Rossi (2017)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01894","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":"2026-05-17T23:51:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pZiKBovZ5yFqFVY/0DZ7c3znUzu4FslyGHdLF+NlRIuMd4tz8s+y1cjaAYZTWco/4uyHzEswyA0EjFxLQj4FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:50:56.775117Z"},"content_sha256":"4b0cf6073db65990a4aaf4447198a9a5d7c35c42ce05a60bdab1095670076bc6","schema_version":"1.0","event_id":"sha256:4b0cf6073db65990a4aaf4447198a9a5d7c35c42ce05a60bdab1095670076bc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H2YNYKNV3M6RIILJHXF6Y5WZXJ/bundle.json","state_url":"https://pith.science/pith/H2YNYKNV3M6RIILJHXF6Y5WZXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H2YNYKNV3M6RIILJHXF6Y5WZXJ/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":"2026-05-31T04:50:56Z","links":{"resolver":"https://pith.science/pith/H2YNYKNV3M6RIILJHXF6Y5WZXJ","bundle":"https://pith.science/pith/H2YNYKNV3M6RIILJHXF6Y5WZXJ/bundle.json","state":"https://pith.science/pith/H2YNYKNV3M6RIILJHXF6Y5WZXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H2YNYKNV3M6RIILJHXF6Y5WZXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H2YNYKNV3M6RIILJHXF6Y5WZXJ","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":"02093e3dc62a2c4ef18692cc34c7ded96aed627957dec89c44522ee4709093e5","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-05T08:46:46Z","title_canon_sha256":"396cf0b4bc26b898f11ff54e08d5c5da38f456198e640292d93ef564ecaafbc0"},"schema_version":"1.0","source":{"id":"1807.01894","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01894","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01894v3","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01894","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"pith_short_12","alias_value":"H2YNYKNV3M6R","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H2YNYKNV3M6RIILJ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H2YNYKNV","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:4b0cf6073db65990a4aaf4447198a9a5d7c35c42ce05a60bdab1095670076bc6","target":"graph","created_at":"2026-05-17T23:51:54Z","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":"In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D'Andrea-Pinzari-Rossi (2017).","authors_text":"Alexandru Chirvasitu, Chelsea Walton, Xingting Wang","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-05T08:46:46Z","title":"Gelfand-Kirillov dimension of cosemisimple Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01894","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":"sha256:090415b8ec90950bbecf77fc68b9a2fe735bec178ac3a435f33c440a4cf39e06","target":"record","created_at":"2026-05-17T23:51:54Z","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":"02093e3dc62a2c4ef18692cc34c7ded96aed627957dec89c44522ee4709093e5","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-05T08:46:46Z","title_canon_sha256":"396cf0b4bc26b898f11ff54e08d5c5da38f456198e640292d93ef564ecaafbc0"},"schema_version":"1.0","source":{"id":"1807.01894","kind":"arxiv","version":3}},"canonical_sha256":"3eb0dc29b5db3d1421693dcbec76d9ba5c36b2de64880d7efa648eefd75adb10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3eb0dc29b5db3d1421693dcbec76d9ba5c36b2de64880d7efa648eefd75adb10","first_computed_at":"2026-05-17T23:51:54.456191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:54.456191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"APX5WbqFGGCjF2EtYOXHTyRBav76NzeUQzsK1ivq8U0Boi3x5ALCAinUL9RqOymSZ4VfhV4K9TCEdeqnMFCvAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:54.456687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01894","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:090415b8ec90950bbecf77fc68b9a2fe735bec178ac3a435f33c440a4cf39e06","sha256:4b0cf6073db65990a4aaf4447198a9a5d7c35c42ce05a60bdab1095670076bc6"],"state_sha256":"0decfc8e90e4643fc342e72fc3947da66b64e6452805d6cf96c7867a512aa1ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fhGTi7Xm8WP7XM2HjF2RbDZtijMFoJdIsa94IR27ZHykqhUbu6zSr2XIhaG62D69Rk44niD1LrGGhypvmCWIBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:50:56.778593Z","bundle_sha256":"0294eaac7f3cf9e9df6531e5f8c41157514a663f4fc68ad3a5c9d1b13d1411ed"}}