{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W7GUSTUXLL7XLQXMNSMNZBQ5LJ","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":"569aeb39b28789a453a14bbc689dd287e5a2dce2c053408d2a493c6900e6cc98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-20T20:37:42Z","title_canon_sha256":"ccc4b2a633035464c166c7858531af494041bc99080335bde084261d0f381ec5"},"schema_version":"1.0","source":{"id":"1312.6103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6103","created_at":"2026-05-17T23:56:01Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6103v1","created_at":"2026-05-17T23:56:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6103","created_at":"2026-05-17T23:56:01Z"},{"alias_kind":"pith_short_12","alias_value":"W7GUSTUXLL7X","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W7GUSTUXLL7XLQXM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W7GUSTUX","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:00f76c59113bcd1bd347eb472b24eb6c1c9d2ff1780fc7bebb5aa4861dccded5","target":"graph","created_at":"2026-05-17T23:56:01Z","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":"From a bimodule $M$ over an exact category $C$, we define an exact category $C\\ltimes M$ with a projection down to $C$. This construction classifies certain split square zero extensions of exact categories. We show that the trace map induces an equivalence between the relative $K$-theory of $C\\ltimes M$ and its relative topological cyclic homology. When applied to the bimodule $\\hom(-,-\\otimes_AM)$ on the category of finitely generated projective modules over a ring $A$ one recovers the classical Dundas-McCarthy theorem for split square zero extensions of rings.","authors_text":"Emanuele Dotto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-20T20:37:42Z","title":"A Dundas-McCarthy theorem for bimodules over exact categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6103","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:a17263ccad0749783b618915081c5f2f7f2431abff464c0aa4363811834b2ca4","target":"record","created_at":"2026-05-17T23:56:01Z","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":"569aeb39b28789a453a14bbc689dd287e5a2dce2c053408d2a493c6900e6cc98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-20T20:37:42Z","title_canon_sha256":"ccc4b2a633035464c166c7858531af494041bc99080335bde084261d0f381ec5"},"schema_version":"1.0","source":{"id":"1312.6103","kind":"arxiv","version":1}},"canonical_sha256":"b7cd494e975aff75c2ec6c98dc861d5a74d61869f6adc2d4505e6597c2578056","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7cd494e975aff75c2ec6c98dc861d5a74d61869f6adc2d4505e6597c2578056","first_computed_at":"2026-05-17T23:56:01.083562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:01.083562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HV+nwMicIvjqn+ROOVeWNbyUvw0KTop+dHcMSlPcbTtUqJ7uley7eix+We1znTIw8yELNYMUHPydbmsBHlymAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:01.084257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a17263ccad0749783b618915081c5f2f7f2431abff464c0aa4363811834b2ca4","sha256:00f76c59113bcd1bd347eb472b24eb6c1c9d2ff1780fc7bebb5aa4861dccded5"],"state_sha256":"9b31d0b9dcad153f5835e94d4bc0e1052c4e6f8a6bdbbcda53337577614bec39"}