{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F3QY72JTT4UR47AULARA2RQZQA","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":"098207a9293d4a22aa75e1cbe05091556110d3b68cf052541c0369f27daafa2f","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-13T18:23:54Z","title_canon_sha256":"3ef24cc729ec30b858779738b3e31e84bfebeb25e9e7a5ba3d4682c051c54772"},"schema_version":"1.0","source":{"id":"1112.2992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2992","created_at":"2026-05-18T04:06:31Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2992v1","created_at":"2026-05-18T04:06:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2992","created_at":"2026-05-18T04:06:31Z"},{"alias_kind":"pith_short_12","alias_value":"F3QY72JTT4UR","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F3QY72JTT4UR47AU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F3QY72JT","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:928a62fc222cfd172b7cba29e4615a75348084dd882be09b9259b4b35e5bef78","target":"graph","created_at":"2026-05-18T04:06:31Z","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 study new coalgebra structures on the tensor product of two coalgebras $C$ and $D$ by twisting the tensor product coalgebra via a twist map $\\Psi: C \\otimes D \\rightarrow D \\otimes C$. We deal with the general case in which the counit of the tensor product coalgebra is deformed as well. Some classes of such deformations are analyzed and a notion of equivalence of twists is discussed. We also present the dual deformation of tensor product algebras and provide examples.","authors_text":"Chiara Pagani, Lucio S. Cirio","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-13T18:23:54Z","title":"Deformation of tensor product (co)algebras via non-(co)normal twists"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2992","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":"sha256:40bef1bfee2e7b66321ef1f1504a6e9dcbcb019bc12abff7c4ef478fb4e942da","target":"record","created_at":"2026-05-18T04:06:31Z","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":"098207a9293d4a22aa75e1cbe05091556110d3b68cf052541c0369f27daafa2f","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-13T18:23:54Z","title_canon_sha256":"3ef24cc729ec30b858779738b3e31e84bfebeb25e9e7a5ba3d4682c051c54772"},"schema_version":"1.0","source":{"id":"1112.2992","kind":"arxiv","version":1}},"canonical_sha256":"2ee18fe9339f291e7c1458220d4619802cb0326afb23f8fac9e25937216eaeb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ee18fe9339f291e7c1458220d4619802cb0326afb23f8fac9e25937216eaeb2","first_computed_at":"2026-05-18T04:06:31.828793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:31.828793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jf857awHUpSxRb17VkSrM1Z9mZGee4rYTtzklRqiC/uyLS3OoigfrGR8FGQ5B7IOOq/BF3UdUCI3qK0J4hDmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:31.829572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40bef1bfee2e7b66321ef1f1504a6e9dcbcb019bc12abff7c4ef478fb4e942da","sha256:928a62fc222cfd172b7cba29e4615a75348084dd882be09b9259b4b35e5bef78"],"state_sha256":"7d953030ec2a7d90990c6df59a8df2cfc4161d20c28bde91a4ef84987094e720"}