{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YSAEBVGVZZJ2R5FOL3WVTEWWRE","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":"04e199e6a54a82cc11814f36f314a25a6acd6a42a829d253605e6ff816d72c07","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2009-10-24T05:35:34Z","title_canon_sha256":"ee6d3ed66529b2be3d182a7d848ca66e6e7f915d7144173af6ab55d7d604abd8"},"schema_version":"1.0","source":{"id":"0910.4622","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.4622","created_at":"2026-05-18T02:24:46Z"},{"alias_kind":"arxiv_version","alias_value":"0910.4622v2","created_at":"2026-05-18T02:24:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4622","created_at":"2026-05-18T02:24:46Z"},{"alias_kind":"pith_short_12","alias_value":"YSAEBVGVZZJ2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YSAEBVGVZZJ2R5FO","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YSAEBVGV","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:91203b5582f95a3600fc05001f6676d5ac476a1a721c72733a42520f6c6d9d29","target":"graph","created_at":"2026-05-18T02:24:46Z","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":"The aim of this paper is to provide a unifying categorical framework for the many examples of para-(co)cyclic modules arising from Hopf cyclic theory. Functoriality of the coefficients is immediate in this approach. A functor corresponding to Connes's cyclic duality is constructed. Our methods allow, in particular, to extend Hopf cyclic theory to (Hopf) bialgebroids.","authors_text":"Dragos Stefan, Gabriella B\\\"ohm","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2009-10-24T05:35:34Z","title":"A categorical approach to cyclic duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4622","kind":"arxiv","version":2},"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":"sha256:09e0dd1ac29b44c7b8b337743406593042eb3f68b7f7466c509df9f11bf74ae9","target":"record","created_at":"2026-05-18T02:24:46Z","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":"04e199e6a54a82cc11814f36f314a25a6acd6a42a829d253605e6ff816d72c07","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2009-10-24T05:35:34Z","title_canon_sha256":"ee6d3ed66529b2be3d182a7d848ca66e6e7f915d7144173af6ab55d7d604abd8"},"schema_version":"1.0","source":{"id":"0910.4622","kind":"arxiv","version":2}},"canonical_sha256":"c48040d4d5ce53a8f4ae5eed5992d68909eaeaab640801d6d4bf5618602c6947","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c48040d4d5ce53a8f4ae5eed5992d68909eaeaab640801d6d4bf5618602c6947","first_computed_at":"2026-05-18T02:24:46.629293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:46.629293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b3zP+gJQ96SFjTm/A8HP9KIBZ0DiCz7j09BtqXJky44Fq62iyjwfbn6hrxk94KqaFpsxfxhxuaO4azF/jyPGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:46.629742Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.4622","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09e0dd1ac29b44c7b8b337743406593042eb3f68b7f7466c509df9f11bf74ae9","sha256:91203b5582f95a3600fc05001f6676d5ac476a1a721c72733a42520f6c6d9d29"],"state_sha256":"1b687255713125612d163cb7df20cfbffed214a2cd0834f50e03a9736b5f4893"}