{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KI7WSFFFU5JDJQAJT44BERVPFQ","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":"016e08a4a8d9c855c1c67494bb3bc1913569f95bf73b23903bbf0422791bb073","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-04-08T17:57:04Z","title_canon_sha256":"9a4a42e8bf735ee096fd904255b51289249b1ee6d361f4c69f6ce0d3348dfd11"},"schema_version":"1.0","source":{"id":"1904.04230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04230","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04230v1","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04230","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"KI7WSFFFU5JD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KI7WSFFFU5JDJQAJ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KI7WSFFF","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:e25f02c650ce6eea9585e2ff443ec561c1c1b8e78cf8223b2008ae276d1265e2","target":"graph","created_at":"2026-05-17T23:49:06Z","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 examine Hopf cyclic cohomology in the same context as the analysis of the geometry of loop spaces $LX$ in derived algebraic geometry and the resulting close relationship between $S^1$-equivariant quasi-coherent sheaves on $LX$ and $D_X$-modules. Furthermore, the Hopf setting serves as a toy case for the categorification of Chern character theory. More precisely, this examination naturally leads to a definition of mixed anti-Yetter-Drinfeld contramodules which reduces to that of the usual mixed complexes for the trivial Hopf algebra and generalizes the notion of stable anti-Yetter-Drinfeld c","authors_text":"Ilya Shapiro","cross_cats":["math.CT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-04-08T17:57:04Z","title":"Categorified Chern character and cyclic cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04230","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":"sha256:685bc55c41a7cc976f632e410686b1d8c94661388a74e16a6a359994fcfaa788","target":"record","created_at":"2026-05-17T23:49:06Z","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":"016e08a4a8d9c855c1c67494bb3bc1913569f95bf73b23903bbf0422791bb073","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-04-08T17:57:04Z","title_canon_sha256":"9a4a42e8bf735ee096fd904255b51289249b1ee6d361f4c69f6ce0d3348dfd11"},"schema_version":"1.0","source":{"id":"1904.04230","kind":"arxiv","version":1}},"canonical_sha256":"523f6914a5a75234c0099f381246af2c3f71c9927c7643af283a6f7e19ff10ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"523f6914a5a75234c0099f381246af2c3f71c9927c7643af283a6f7e19ff10ab","first_computed_at":"2026-05-17T23:49:06.702393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:06.702393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eHarGw8qgZk0M3obX76EBI9orSDr4DI7MyT5l8Fr0muj/ZIsgYt+vmrNBzkJFlvxxyTT07p+UE6K4ntKdsMdCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:06.703012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:685bc55c41a7cc976f632e410686b1d8c94661388a74e16a6a359994fcfaa788","sha256:e25f02c650ce6eea9585e2ff443ec561c1c1b8e78cf8223b2008ae276d1265e2"],"state_sha256":"2c4582e5007e6c1f1c073b2dd88bc1755d104c8a330781539cdab151d0ca375d"}