{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IG4ZGMS36ZY7ZNHPOB6TRZFOXQ","short_pith_number":"pith:IG4ZGMS3","canonical_record":{"source":{"id":"1706.08446","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-26T15:51:43Z","cross_cats_sorted":[],"title_canon_sha256":"98d3ecceb848848ae9e52918fe3a5862a95e434b87d393f7109b2f6407b57bc4","abstract_canon_sha256":"655b12d27b5883d4fecd3ed83122997b340c5e13a91912edf8d3958015ea9a10"},"schema_version":"1.0"},"canonical_sha256":"41b993325bf671fcb4ef707d38e4aebc0734ab074034301661d37c94cd28f358","source":{"kind":"arxiv","id":"1706.08446","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08446","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08446v1","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08446","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"IG4ZGMS36ZY7","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IG4ZGMS36ZY7ZNHP","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IG4ZGMS3","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IG4ZGMS36ZY7ZNHPOB6TRZFOXQ","target":"record","payload":{"canonical_record":{"source":{"id":"1706.08446","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-26T15:51:43Z","cross_cats_sorted":[],"title_canon_sha256":"98d3ecceb848848ae9e52918fe3a5862a95e434b87d393f7109b2f6407b57bc4","abstract_canon_sha256":"655b12d27b5883d4fecd3ed83122997b340c5e13a91912edf8d3958015ea9a10"},"schema_version":"1.0"},"canonical_sha256":"41b993325bf671fcb4ef707d38e4aebc0734ab074034301661d37c94cd28f358","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:42.569823Z","signature_b64":"OhQ/P90dgTS8lMF25OftgV4qYYeg77blDWroVA8PnMG0SU0plZt3Ra5vUJBP5LlABdDHm/SQ+JRnrCz9DAhTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41b993325bf671fcb4ef707d38e4aebc0734ab074034301661d37c94cd28f358","last_reissued_at":"2026-05-18T00:41:42.569328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:42.569328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.08446","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":"2026-05-18T00:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMEEKqdTCDIlpC85oA44+qiVGVcl/tW1JsQGY8oZliX65O+qi9PugNIFLKgUPATXjIASJH3s81H54Iw1X3JWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:57:22.536121Z"},"content_sha256":"a6abbb4bb93f6acf45c3b7b0ecda7c4eded37c171bd2db9899d0c4d01efd65f1","schema_version":"1.0","event_id":"sha256:a6abbb4bb93f6acf45c3b7b0ecda7c4eded37c171bd2db9899d0c4d01efd65f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IG4ZGMS36ZY7ZNHPOB6TRZFOXQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite-dimensional quasi-Hopf algebras of Cartan type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Yinhuo Zhang, Yuping Yang","submitted_at":"2017-06-26T15:51:43Z","abstract_excerpt":"In this paper, we present a general method for constructing finite-dimensional quasi-Hopf algebras from finite abelian groups and braided vector spaces of Cartan type. The study of such quasi-Hopf algebras leads to the classification of finite-dimensional radically graded basic quasi-Hopf algebras over abelian groups with dimensions not divisible by $2,3,5,7$ and associators given by abelian $3$-cocycles. As special cases , the small quasi-quantum groups are introduced and studied. Many new explicit examples of finite-dimensional genuine quasi-Hopf algebras are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08446","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":"2026-05-18T00:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wRv0uQ7gSDJT86xy5zosuB9Sr2VvJE0mNR6S/ETHiWvU+yCO/ZlIbbOAVm/fwK0/eIpvs4cEg1KaCx7lCwKMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:57:22.536477Z"},"content_sha256":"095952abdfbdfb91585afb0519951717c1652b05b5f3966fa096b949e10e40cf","schema_version":"1.0","event_id":"sha256:095952abdfbdfb91585afb0519951717c1652b05b5f3966fa096b949e10e40cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IG4ZGMS36ZY7ZNHPOB6TRZFOXQ/bundle.json","state_url":"https://pith.science/pith/IG4ZGMS36ZY7ZNHPOB6TRZFOXQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IG4ZGMS36ZY7ZNHPOB6TRZFOXQ/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":"2026-06-20T21:57:22Z","links":{"resolver":"https://pith.science/pith/IG4ZGMS36ZY7ZNHPOB6TRZFOXQ","bundle":"https://pith.science/pith/IG4ZGMS36ZY7ZNHPOB6TRZFOXQ/bundle.json","state":"https://pith.science/pith/IG4ZGMS36ZY7ZNHPOB6TRZFOXQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IG4ZGMS36ZY7ZNHPOB6TRZFOXQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IG4ZGMS36ZY7ZNHPOB6TRZFOXQ","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":"655b12d27b5883d4fecd3ed83122997b340c5e13a91912edf8d3958015ea9a10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-26T15:51:43Z","title_canon_sha256":"98d3ecceb848848ae9e52918fe3a5862a95e434b87d393f7109b2f6407b57bc4"},"schema_version":"1.0","source":{"id":"1706.08446","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08446","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08446v1","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08446","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"IG4ZGMS36ZY7","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IG4ZGMS36ZY7ZNHP","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IG4ZGMS3","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:095952abdfbdfb91585afb0519951717c1652b05b5f3966fa096b949e10e40cf","target":"graph","created_at":"2026-05-18T00:41:42Z","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 paper, we present a general method for constructing finite-dimensional quasi-Hopf algebras from finite abelian groups and braided vector spaces of Cartan type. The study of such quasi-Hopf algebras leads to the classification of finite-dimensional radically graded basic quasi-Hopf algebras over abelian groups with dimensions not divisible by $2,3,5,7$ and associators given by abelian $3$-cocycles. As special cases , the small quasi-quantum groups are introduced and studied. Many new explicit examples of finite-dimensional genuine quasi-Hopf algebras are obtained.","authors_text":"Yinhuo Zhang, Yuping Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-26T15:51:43Z","title":"Finite-dimensional quasi-Hopf algebras of Cartan type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08446","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:a6abbb4bb93f6acf45c3b7b0ecda7c4eded37c171bd2db9899d0c4d01efd65f1","target":"record","created_at":"2026-05-18T00:41:42Z","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":"655b12d27b5883d4fecd3ed83122997b340c5e13a91912edf8d3958015ea9a10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-26T15:51:43Z","title_canon_sha256":"98d3ecceb848848ae9e52918fe3a5862a95e434b87d393f7109b2f6407b57bc4"},"schema_version":"1.0","source":{"id":"1706.08446","kind":"arxiv","version":1}},"canonical_sha256":"41b993325bf671fcb4ef707d38e4aebc0734ab074034301661d37c94cd28f358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41b993325bf671fcb4ef707d38e4aebc0734ab074034301661d37c94cd28f358","first_computed_at":"2026-05-18T00:41:42.569328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:42.569328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OhQ/P90dgTS8lMF25OftgV4qYYeg77blDWroVA8PnMG0SU0plZt3Ra5vUJBP5LlABdDHm/SQ+JRnrCz9DAhTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:42.569823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08446","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6abbb4bb93f6acf45c3b7b0ecda7c4eded37c171bd2db9899d0c4d01efd65f1","sha256:095952abdfbdfb91585afb0519951717c1652b05b5f3966fa096b949e10e40cf"],"state_sha256":"78f2a83aaf0300805d34941cd406a5f2c4442ccbc887a883262d6b702395d386"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wXNRuTu+uFSYRXwQq4y8ojMoQlegxtAQtERTlsYQbsArePYeiGBfvxnPybgDxUbyE103vSNmj/NyD5dakTwZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:57:22.538445Z","bundle_sha256":"933764a62dbe34f52b5710eb5ea2e83e3539f8d64dec047dc10fb1669e7e5f12"}}