{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E7HHGL44EF2XZB47ZSMVYAWRST","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":"b87efa0248859b0dc9aabf195e24e7564303312a32b3422455eb559c1c53fd11","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-08T06:59:48Z","title_canon_sha256":"0e1345388ec16372f8bb0993922cf243dc4648a2def6b4ad130136d8c6f7a7da"},"schema_version":"1.0","source":{"id":"2606.09107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09107","created_at":"2026-06-09T02:07:59Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09107v1","created_at":"2026-06-09T02:07:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09107","created_at":"2026-06-09T02:07:59Z"},{"alias_kind":"pith_short_12","alias_value":"E7HHGL44EF2X","created_at":"2026-06-09T02:07:59Z"},{"alias_kind":"pith_short_16","alias_value":"E7HHGL44EF2XZB47","created_at":"2026-06-09T02:07:59Z"},{"alias_kind":"pith_short_8","alias_value":"E7HHGL44","created_at":"2026-06-09T02:07:59Z"}],"graph_snapshots":[{"event_id":"sha256:bdaad2d4a2e6ddb699cc7c04dfee38d2cf0530eb05c71327600cce8625965651","target":"graph","created_at":"2026-06-09T02:07:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.09107/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the braided cochain complex and the braided cohomology of braided coalgebras in linear monoidal categories, and compare the braided cohomology of braided coalgebras living in different linear monoidal categories using relative morphisms. The symmetric cohomology was introduced for groups by Staic, and was generalized to cocommutative Hopf algebras by Shiba, Sanada, and the second author. This cohomology involves degreewise actions of the symmetric groups on a cochain complex, which come from the usual symmetric monoidal structure on the category of modules. We generalize this fram","authors_text":"Ayako Itaba, Shota Inoue","cross_cats":["math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-08T06:59:48Z","title":"Braided cohomology of quasi-triangular bialgebras and braided Morita invariance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09107","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:f0c95072a664a4296cde230d3be8e45d7c76dd8697130185a3b52c5bf97e0933","target":"record","created_at":"2026-06-09T02:07:59Z","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":"b87efa0248859b0dc9aabf195e24e7564303312a32b3422455eb559c1c53fd11","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-08T06:59:48Z","title_canon_sha256":"0e1345388ec16372f8bb0993922cf243dc4648a2def6b4ad130136d8c6f7a7da"},"schema_version":"1.0","source":{"id":"2606.09107","kind":"arxiv","version":1}},"canonical_sha256":"27ce732f9c21757c879fcc995c02d194f0cdd706dd882ae159c36a3c388919c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27ce732f9c21757c879fcc995c02d194f0cdd706dd882ae159c36a3c388919c9","first_computed_at":"2026-06-09T02:07:59.473555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:59.473555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UnWcgakIFSW6VZewZpsm0khviCkEH5MqsxoAd7IC2RIdUcgQQeYaefR0ywzTHsza9Dm+XU32lXe4kKHKayG4DQ==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:59.474542Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0c95072a664a4296cde230d3be8e45d7c76dd8697130185a3b52c5bf97e0933","sha256:bdaad2d4a2e6ddb699cc7c04dfee38d2cf0530eb05c71327600cce8625965651"],"state_sha256":"dcea78aa3bdacd6c317419a48faeafe439d52569bf3f1b3664ad12b201553b07"}