{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CGJVXSOCUTRNGFGFVTLDZ2U3A6","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":"cae846a18bdf7290d1379f711f3eb18555cf7a0548db8992edb25b30f9ca831e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-30T15:25:31Z","title_canon_sha256":"6c431063a1efdc5541d1598f3072e7c19989c2e0cae60ca76737b8b5df1a29bc"},"schema_version":"1.0","source":{"id":"1801.00143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00143","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00143v1","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00143","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"CGJVXSOCUTRN","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CGJVXSOCUTRNGFGF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CGJVXSOC","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:7d592bc0aeccf78b5e7d7365831eeda1470b02bcc8d23fd3b876fa512148ca07","target":"graph","created_at":"2026-05-18T00:26:59Z","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"},"paper":{"abstract_excerpt":"After we introduced biwreaths and biwreath-like objects in our previous paper, in the present one we define paired wreaths. In a paired wreath there is a monad $B$ and a comonad $F$ over the same 0-cell in a 2-category $\\K$, so that $F$ is a left wreath around $B$ and $B$ is a right cowreath around $F$, and moreover, $FB$ is a bimonad in $\\K$. The corresponding 1-cell $FB$ in the setting of a biwreath and a biwreath-like object was not necessarilly a bimonad. We obtain a 2-categorical version of the Radford biproduct and Sweedler's crossed (co)product, that are on one hand, both a biwreath and","authors_text":"Bojana Femi\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-30T15:25:31Z","title":"Paired wreaths: towards a 2-categorical atlas of cross products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00143","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":"sha256:43b1fa48042a4878f7bf6094936fcca1f721da69a4ef0dad4cfe1442c791308d","target":"record","created_at":"2026-05-18T00:26:59Z","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":"cae846a18bdf7290d1379f711f3eb18555cf7a0548db8992edb25b30f9ca831e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-30T15:25:31Z","title_canon_sha256":"6c431063a1efdc5541d1598f3072e7c19989c2e0cae60ca76737b8b5df1a29bc"},"schema_version":"1.0","source":{"id":"1801.00143","kind":"arxiv","version":1}},"canonical_sha256":"11935bc9c2a4e2d314c5acd63cea9b078414b1314d6187cd751218a2c43df535","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11935bc9c2a4e2d314c5acd63cea9b078414b1314d6187cd751218a2c43df535","first_computed_at":"2026-05-18T00:26:59.290028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:59.290028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XQmo5hj/ZcvODC0+oNRqE7mEYE6RcPV8Ie4uIaxeCAO6k7e3qMBDgadYN+LLxX1Co71iC1BkIQiK9q4Kt9LfBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:59.290768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43b1fa48042a4878f7bf6094936fcca1f721da69a4ef0dad4cfe1442c791308d","sha256:7d592bc0aeccf78b5e7d7365831eeda1470b02bcc8d23fd3b876fa512148ca07"],"state_sha256":"0f7c2993d3d601396d619250714adbe7c1cb6ea096fd159f55d77220e920f9b6"}