{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RUZZ5ZCKPUU22MI6ZILOOAORDU","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":"f15e799c90d05b1d7264eb8841270920d950982ea4633f84777b18c266baa0a1","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-03-09T02:10:02Z","title_canon_sha256":"a0560b7b6bdbf3a2625fa955f2cd9f59fb34adaf72cf9779b3f4f7e3499210be"},"schema_version":"1.0","source":{"id":"0903.1472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1472","created_at":"2026-05-18T03:37:29Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1472v1","created_at":"2026-05-18T03:37:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1472","created_at":"2026-05-18T03:37:29Z"},{"alias_kind":"pith_short_12","alias_value":"RUZZ5ZCKPUU2","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RUZZ5ZCKPUU22MI6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RUZZ5ZCK","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:1bf3e4fcdbe57027620471d9973087fab186282d9c5aa39173125cc87a6f7c35","target":"graph","created_at":"2026-05-18T03:37:29Z","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":"This is a contribution to the project of quiver approaches to quasi-quantum groups initiated in arXiv:0902.1620. We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations. This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras, or equivalently cofree pointed coalgebras, and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras. We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded poin","authors_text":"Hua-Lin Huang","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-03-09T02:10:02Z","title":"From Projective Representations to Quasi-Quantum Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1472","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:fa3949d78cb9647976e80273b0d6c34a0fdcfb5b809e25959e7924b5597e4d3a","target":"record","created_at":"2026-05-18T03:37:29Z","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":"f15e799c90d05b1d7264eb8841270920d950982ea4633f84777b18c266baa0a1","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-03-09T02:10:02Z","title_canon_sha256":"a0560b7b6bdbf3a2625fa955f2cd9f59fb34adaf72cf9779b3f4f7e3499210be"},"schema_version":"1.0","source":{"id":"0903.1472","kind":"arxiv","version":1}},"canonical_sha256":"8d339ee44a7d29ad311eca16e701d11d14f6c0ebfbcb5a29e67c1e6cfe79e3a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d339ee44a7d29ad311eca16e701d11d14f6c0ebfbcb5a29e67c1e6cfe79e3a1","first_computed_at":"2026-05-18T03:37:29.234154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:29.234154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oh9CIWjVeNbHqZL8YSU91iPIKWajFbmonUG0IWB3L34koaM/gHDxKifoyJlg9uBeaSPolqq9F7I7jjoeSXalBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:29.234878Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa3949d78cb9647976e80273b0d6c34a0fdcfb5b809e25959e7924b5597e4d3a","sha256:1bf3e4fcdbe57027620471d9973087fab186282d9c5aa39173125cc87a6f7c35"],"state_sha256":"afbcc875df2d1303f35e18e6e08081d856c14c3273bf9c2918385c13d885b9df"}