{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U3LKDIHIKBJI23KH5AF5Q62UVH","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":"5e495e0beeaea83c1625622b517cf0b88a80ef87bf457b896942c44b5b83dcf3","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-04-06T12:21:36Z","title_canon_sha256":"f267e6fe5ba5575053aa58dfe16c5cea2e389686a5af549ca1431737197a6d82"},"schema_version":"1.0","source":{"id":"1604.01588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01588","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01588v1","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01588","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"U3LKDIHIKBJI","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U3LKDIHIKBJI23KH","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U3LKDIHI","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:58c84fc4abbd323120d3a1c1edd3048789d5ee2006509040d69c22e6dc35474a","target":"graph","created_at":"2026-05-18T01:17:36Z","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":"In arxiv:1602.04254, we have defined polynomial Witt vectors functor from vector spaces over a perfect field $k$ of positive characteristic $p$ to abelian groups. In this paper, we use polynomial Witt vectors to construct a functorial Hochschild-Witt complex $WCH_*(A)$ for any associative unital $k$-algebra $A$, with homology groups $WHH_*(A)$. We prove that the group $WHH_0(A)$ coincides with the group of non-commutative Witt vectors defined by Hesselholt, while if $A$ is commutative, finitely generated, and smooth, the groups $WHH_i(A)$ are naturally identified with the terms $W\\Omega^i_A$ o","authors_text":"D. Kaledin","cross_cats":["math.AG","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-04-06T12:21:36Z","title":"Hochschild-Witt complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01588","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":"sha256:60f361b3f187cecfb6f83b03a48a0092c67e19c76c3ff66b855fb69bb0f37b6d","target":"record","created_at":"2026-05-18T01:17:36Z","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":"5e495e0beeaea83c1625622b517cf0b88a80ef87bf457b896942c44b5b83dcf3","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-04-06T12:21:36Z","title_canon_sha256":"f267e6fe5ba5575053aa58dfe16c5cea2e389686a5af549ca1431737197a6d82"},"schema_version":"1.0","source":{"id":"1604.01588","kind":"arxiv","version":1}},"canonical_sha256":"a6d6a1a0e850528d6d47e80bd87b54a9c394427ca0fb5a3f5cafee48ce88fb34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6d6a1a0e850528d6d47e80bd87b54a9c394427ca0fb5a3f5cafee48ce88fb34","first_computed_at":"2026-05-18T01:17:36.039781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:36.039781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jeE70z82GlwWT9HtbhiwtSPjB2VPzr++9t1X7NrT6fmJHI3MwyfczQeBpXQfscIMZfcAWhEaqMHdWHRYaEP4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:36.040307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60f361b3f187cecfb6f83b03a48a0092c67e19c76c3ff66b855fb69bb0f37b6d","sha256:58c84fc4abbd323120d3a1c1edd3048789d5ee2006509040d69c22e6dc35474a"],"state_sha256":"69bc705939e84244bc5ab985567e8082ad6f23b993d13207a3093a302a6030db"}