{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:W7GUSTUXLL7XLQXMNSMNZBQ5LJ","short_pith_number":"pith:W7GUSTUX","schema_version":"1.0","canonical_sha256":"b7cd494e975aff75c2ec6c98dc861d5a74d61869f6adc2d4505e6597c2578056","source":{"kind":"arxiv","id":"1312.6103","version":1},"attestation_state":"computed","paper":{"title":"A Dundas-McCarthy theorem for bimodules over exact categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Emanuele Dotto","submitted_at":"2013-12-20T20:37:42Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.6103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-20T20:37:42Z","cross_cats_sorted":[],"title_canon_sha256":"ccc4b2a633035464c166c7858531af494041bc99080335bde084261d0f381ec5","abstract_canon_sha256":"569aeb39b28789a453a14bbc689dd287e5a2dce2c053408d2a493c6900e6cc98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:01.084257Z","signature_b64":"HV+nwMicIvjqn+ROOVeWNbyUvw0KTop+dHcMSlPcbTtUqJ7uley7eix+We1znTIw8yELNYMUHPydbmsBHlymAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7cd494e975aff75c2ec6c98dc861d5a74d61869f6adc2d4505e6597c2578056","last_reissued_at":"2026-05-17T23:56:01.083562Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:01.083562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Dundas-McCarthy theorem for bimodules over exact categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Emanuele Dotto","submitted_at":"2013-12-20T20:37:42Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6103","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1312.6103","created_at":"2026-05-17T23:56:01.083664+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.6103v1","created_at":"2026-05-17T23:56:01.083664+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6103","created_at":"2026-05-17T23:56:01.083664+00:00"},{"alias_kind":"pith_short_12","alias_value":"W7GUSTUXLL7X","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"W7GUSTUXLL7XLQXM","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"W7GUSTUX","created_at":"2026-05-18T12:28:04.890932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ","json":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ.json","graph_json":"https://pith.science/api/pith-number/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/graph.json","events_json":"https://pith.science/api/pith-number/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/events.json","paper":"https://pith.science/paper/W7GUSTUX"},"agent_actions":{"view_html":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ","download_json":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ.json","view_paper":"https://pith.science/paper/W7GUSTUX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.6103&json=true","fetch_graph":"https://pith.science/api/pith-number/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/graph.json","fetch_events":"https://pith.science/api/pith-number/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/action/storage_attestation","attest_author":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/action/author_attestation","sign_citation":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/action/citation_signature","submit_replication":"https://pith.science/pith/W7GUSTUXLL7XLQXMNSMNZBQ5LJ/action/replication_record"}},"created_at":"2026-05-17T23:56:01.083664+00:00","updated_at":"2026-05-17T23:56:01.083664+00:00"}