{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OLTAUQEPBF6HOKQF7C72INZIAU","short_pith_number":"pith:OLTAUQEP","schema_version":"1.0","canonical_sha256":"72e60a408f097c772a05f8bfa4372805211a0bf5a12e88cc795df99a8a022ca3","source":{"kind":"arxiv","id":"1402.3280","version":3},"attestation_state":"computed","paper":{"title":"$K$-theory and homotopies of 2-cocycles on transformation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Elizabeth Gillaspy","submitted_at":"2014-02-13T20:46:16Z","abstract_excerpt":"This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles $\\omega = \\{\\omega_t\\}_{t \\in [0,1]}$ on a locally compact Hausdorff groupoid $\\mathcal{G}$ induces an isomorphism of the $K$-theory groups of the reduced twisted groupoid $C^*$-algebras: $K_*(C^*_r(\\mathcal{G}, \\omega_0)) \\cong K_*(C^*_r(\\mathcal{G}, \\omega_1)).$ Generalizing work of Echterhoff, L\\\"uck, Phillips, and Walters from 2010, we show that if $\\mathcal{G} = G \\ltimes X$ is a second countable locally compact transformation group, then whenever $G$ satisfies the Baum"},"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":"1402.3280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-02-13T20:46:16Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"e4ae7a782db33636f5e35e08c4c4fb62d4a8c0a5250411454b3310ac1cb615ad","abstract_canon_sha256":"26842bdfa1727390260b4202688732d3162cb6299add89b576ec08df4720e7bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:24.152725Z","signature_b64":"V2ZODH0w4G9lrkHWtMUHC8ch+0cxhOGXXRgBv1ZyZK3+NP5VYGXW+ICTMpbCHZD68qH1NK3sDrbFRj4u5WgpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72e60a408f097c772a05f8bfa4372805211a0bf5a12e88cc795df99a8a022ca3","last_reissued_at":"2026-05-18T02:43:24.152183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:24.152183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$K$-theory and homotopies of 2-cocycles on transformation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Elizabeth Gillaspy","submitted_at":"2014-02-13T20:46:16Z","abstract_excerpt":"This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles $\\omega = \\{\\omega_t\\}_{t \\in [0,1]}$ on a locally compact Hausdorff groupoid $\\mathcal{G}$ induces an isomorphism of the $K$-theory groups of the reduced twisted groupoid $C^*$-algebras: $K_*(C^*_r(\\mathcal{G}, \\omega_0)) \\cong K_*(C^*_r(\\mathcal{G}, \\omega_1)).$ Generalizing work of Echterhoff, L\\\"uck, Phillips, and Walters from 2010, we show that if $\\mathcal{G} = G \\ltimes X$ is a second countable locally compact transformation group, then whenever $G$ satisfies the Baum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3280","kind":"arxiv","version":3},"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":"1402.3280","created_at":"2026-05-18T02:43:24.152264+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.3280v3","created_at":"2026-05-18T02:43:24.152264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3280","created_at":"2026-05-18T02:43:24.152264+00:00"},{"alias_kind":"pith_short_12","alias_value":"OLTAUQEPBF6H","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OLTAUQEPBF6HOKQF","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OLTAUQEP","created_at":"2026-05-18T12:28:41.024544+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/OLTAUQEPBF6HOKQF7C72INZIAU","json":"https://pith.science/pith/OLTAUQEPBF6HOKQF7C72INZIAU.json","graph_json":"https://pith.science/api/pith-number/OLTAUQEPBF6HOKQF7C72INZIAU/graph.json","events_json":"https://pith.science/api/pith-number/OLTAUQEPBF6HOKQF7C72INZIAU/events.json","paper":"https://pith.science/paper/OLTAUQEP"},"agent_actions":{"view_html":"https://pith.science/pith/OLTAUQEPBF6HOKQF7C72INZIAU","download_json":"https://pith.science/pith/OLTAUQEPBF6HOKQF7C72INZIAU.json","view_paper":"https://pith.science/paper/OLTAUQEP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.3280&json=true","fetch_graph":"https://pith.science/api/pith-number/OLTAUQEPBF6HOKQF7C72INZIAU/graph.json","fetch_events":"https://pith.science/api/pith-number/OLTAUQEPBF6HOKQF7C72INZIAU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OLTAUQEPBF6HOKQF7C72INZIAU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OLTAUQEPBF6HOKQF7C72INZIAU/action/storage_attestation","attest_author":"https://pith.science/pith/OLTAUQEPBF6HOKQF7C72INZIAU/action/author_attestation","sign_citation":"https://pith.science/pith/OLTAUQEPBF6HOKQF7C72INZIAU/action/citation_signature","submit_replication":"https://pith.science/pith/OLTAUQEPBF6HOKQF7C72INZIAU/action/replication_record"}},"created_at":"2026-05-18T02:43:24.152264+00:00","updated_at":"2026-05-18T02:43:24.152264+00:00"}