{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6OMVRZUJPPTFERACPCFGOWZJGC","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":"b6a4914f6623694b406675b23495c95d01ff133c0cc8aecc5b668da9c02f84ac","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-02-11T11:29:17Z","title_canon_sha256":"2670c9cc58ae12ee3e7c6e66b623155e331a7d43900ab2e57bc9b41a24b75a41"},"schema_version":"1.0","source":{"id":"1302.2453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2453","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2453v1","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2453","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"6OMVRZUJPPTF","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6OMVRZUJPPTFERAC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6OMVRZUJ","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:4634b72ba23dce4a87a1d2beebcbacbf9b8316fb7ea4f7fe8f77bd4ab5f70d87","target":"graph","created_at":"2026-05-18T03:34:01Z","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":"We describe all the quasi-bialgebra structures of a group algebra over a torsion-free abelian group. They all come out to be triangular in a unique way. Moreover, up to an isomorphism, these quasi-bialgebra structures produce only one (braided) monoidal structure on the category of their representations. Applying these results to the algebra of Laurent polynomials, we recover two braided monoidal categories introduced in \\cite{CG} by S. Caenepeel and I. Goyvaerts in connection with Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras).","authors_text":"Alessandro Ardizzoni, Claudia Menini, Daniel Bulacu","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-02-11T11:29:17Z","title":"Quasi-bialgebra Structures and Torsion-free Abelian Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2453","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:d14705dcd52766912a6c2298e7cfc6f8c335d5fe4eb9df1c75d5f5bd3af1b5d7","target":"record","created_at":"2026-05-18T03:34:01Z","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":"b6a4914f6623694b406675b23495c95d01ff133c0cc8aecc5b668da9c02f84ac","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-02-11T11:29:17Z","title_canon_sha256":"2670c9cc58ae12ee3e7c6e66b623155e331a7d43900ab2e57bc9b41a24b75a41"},"schema_version":"1.0","source":{"id":"1302.2453","kind":"arxiv","version":1}},"canonical_sha256":"f39958e6897be6524402788a675b29309cbb1f257de5e1692cb694981a8de331","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f39958e6897be6524402788a675b29309cbb1f257de5e1692cb694981a8de331","first_computed_at":"2026-05-18T03:34:01.070998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:01.070998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vcDgPZ2jDBpAG5UrZ51Lqp6Xfmvp8e5ncQeYi6sqcYSuoTgdsuVkXPJip1c+q36kFLgYNnbMTbEBxRybna3GAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:01.071662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d14705dcd52766912a6c2298e7cfc6f8c335d5fe4eb9df1c75d5f5bd3af1b5d7","sha256:4634b72ba23dce4a87a1d2beebcbacbf9b8316fb7ea4f7fe8f77bd4ab5f70d87"],"state_sha256":"9c94b86ded41803ace4c0307dafd07b06ab920590f9713ae2609e8e9e3e036dd"}