{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CT2LX2DVREWWPUSFQMAUCUKTCE","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":"13f0a6fbf0b939fd6626d358e390433fa2c67e3240b000e81b42746f19e207c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-08-17T00:06:07Z","title_canon_sha256":"4a29bcae78223abfd26c512b0458a9f903c1f197da2a7ecc098b8807056c8b54"},"schema_version":"1.0","source":{"id":"1308.3743","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3743","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3743v2","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3743","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"CT2LX2DVREWW","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CT2LX2DVREWWPUSF","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CT2LX2DV","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:7ea0285c02289382ff7e0319a706f0f8cee449cd35948830bc935ffd4a317cdc","target":"graph","created_at":"2026-05-18T02:20:59Z","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":"We show how one can twist the definition of Hochschild homology of an algebra or a DG algebra by inserting a possibly non-additive trace functor. We then prove that many of the usual properties of Hochschild homology survive such a generalization. In some cases this even includes Keller's Localization Theorem.","authors_text":"D. Kaledin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-08-17T00:06:07Z","title":"Trace theories and localization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3743","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":"sha256:49c7e176bf229c79c2e1772bd1141f36571ee817a8b8c8d2f92fc79b1f803377","target":"record","created_at":"2026-05-18T02:20:59Z","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":"13f0a6fbf0b939fd6626d358e390433fa2c67e3240b000e81b42746f19e207c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-08-17T00:06:07Z","title_canon_sha256":"4a29bcae78223abfd26c512b0458a9f903c1f197da2a7ecc098b8807056c8b54"},"schema_version":"1.0","source":{"id":"1308.3743","kind":"arxiv","version":2}},"canonical_sha256":"14f4bbe875892d67d2458301415153111acc52950406aa2f7d28defc300234df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14f4bbe875892d67d2458301415153111acc52950406aa2f7d28defc300234df","first_computed_at":"2026-05-18T02:20:59.565496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:59.565496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R2DKpcOEwWSTcDVrg0gZ+U0WBrde4L56YdASrrKExFTrRXwe8pqIM8CFQpIlLQuswCyRjrcylVEzrvZLvrQHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:59.566124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3743","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49c7e176bf229c79c2e1772bd1141f36571ee817a8b8c8d2f92fc79b1f803377","sha256:7ea0285c02289382ff7e0319a706f0f8cee449cd35948830bc935ffd4a317cdc"],"state_sha256":"48475f28a226064f515cc694d81206a961db085afa79377904e6832be4ff15c8"}