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Then, if $KK^{F}_{*}(A, B) = 0$ for all $F \\le G$ {\\em finite cyclic}, then $KK^{G}_{*}(A, B) = 0$."},"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":"1101.1859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-01-10T16:08:40Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"c20380c15108c94aafe103331341856ab38734cca8cbdf8c59cf7598a1d206e7","abstract_canon_sha256":"62c19430526b9ab66c42fd7d29c12c162ab39dccb732135b7a637ff8582a84fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:36.896107Z","signature_b64":"xZjAXzn7+i7wYBYL/IRKvYVug4VRuhsuog2JzRx7kTrWoH+gvJtUBoWknr7OvB7BAMtq/yWFwIrkV8vUg302DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab4d68feaddcab7283e26d2ae094a793c55efba0569673103a3dd1542d0be5bf","last_reissued_at":"2026-05-18T03:59:36.895400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:36.895400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Restriction maps in equivariant $KK$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Otgonbayar Uuye","submitted_at":"2011-01-10T16:08:40Z","abstract_excerpt":"We extend McClure's results on the restriction maps in equivariant $K$-theory to bivariant $K$-theory:\n  Let $G$ be a compact Lie group and $A$ and $B$ be $G$-$C^*$-algebras. Suppose that $KK^{H}_{n}(A, B)$ is a finitely generated $R(G)$-module for every $H \\le G$ closed and $n \\in \\Z$. Then, if $KK^{F}_{*}(A, B) = 0$ for all $F \\le G$ {\\em finite cyclic}, then $KK^{G}_{*}(A, B) = 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1859","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":"1101.1859","created_at":"2026-05-18T03:59:36.895509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.1859v1","created_at":"2026-05-18T03:59:36.895509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1859","created_at":"2026-05-18T03:59:36.895509+00:00"},{"alias_kind":"pith_short_12","alias_value":"VNGWR7VN3SVX","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VNGWR7VN3SVXFA7C","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VNGWR7VN","created_at":"2026-05-18T12:26:44.992195+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/VNGWR7VN3SVXFA7CNUVOBFFHSP","json":"https://pith.science/pith/VNGWR7VN3SVXFA7CNUVOBFFHSP.json","graph_json":"https://pith.science/api/pith-number/VNGWR7VN3SVXFA7CNUVOBFFHSP/graph.json","events_json":"https://pith.science/api/pith-number/VNGWR7VN3SVXFA7CNUVOBFFHSP/events.json","paper":"https://pith.science/paper/VNGWR7VN"},"agent_actions":{"view_html":"https://pith.science/pith/VNGWR7VN3SVXFA7CNUVOBFFHSP","download_json":"https://pith.science/pith/VNGWR7VN3SVXFA7CNUVOBFFHSP.json","view_paper":"https://pith.science/paper/VNGWR7VN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.1859&json=true","fetch_graph":"https://pith.science/api/pith-number/VNGWR7VN3SVXFA7CNUVOBFFHSP/graph.json","fetch_events":"https://pith.science/api/pith-number/VNGWR7VN3SVXFA7CNUVOBFFHSP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VNGWR7VN3SVXFA7CNUVOBFFHSP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VNGWR7VN3SVXFA7CNUVOBFFHSP/action/storage_attestation","attest_author":"https://pith.science/pith/VNGWR7VN3SVXFA7CNUVOBFFHSP/action/author_attestation","sign_citation":"https://pith.science/pith/VNGWR7VN3SVXFA7CNUVOBFFHSP/action/citation_signature","submit_replication":"https://pith.science/pith/VNGWR7VN3SVXFA7CNUVOBFFHSP/action/replication_record"}},"created_at":"2026-05-18T03:59:36.895509+00:00","updated_at":"2026-05-18T03:59:36.895509+00:00"}