{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q4ZLDMQ2CEFAMH5CSXKKDH7JC6","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":"d27245c5e12a5c2c4546a52915d1edc04233661ce086f836c6b1c28af51ed4f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-03-31T14:24:43Z","title_canon_sha256":"405e6571649f9f9c575f614c914d7e1907a07c29f1884af019a7f418ae9698a0"},"schema_version":"1.0","source":{"id":"1703.10912","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10912","created_at":"2026-05-18T00:42:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10912v2","created_at":"2026-05-18T00:42:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10912","created_at":"2026-05-18T00:42:29Z"},{"alias_kind":"pith_short_12","alias_value":"Q4ZLDMQ2CEFA","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4ZLDMQ2CEFAMH5C","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4ZLDMQ2","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:ff72341e8c20a492beffeb4f3d730f57a8db2c81c0942b6e27d67e68029015ac","target":"graph","created_at":"2026-05-18T00:42:29Z","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":"This is a survey on Kasparov's bivariant $KK$-theory in connection with the Baum-Connes conjecture on the $K$-theory of crossed products $A\\rtimes_rG$ by actions of a locally compact group $G$ on a C*-algebra $A$. In particular we shall discuss Kasparov's Dirac dual-Dirac method as well as the permanence properties of the conjecture and the \"Going-Down principle\" for the left hand side of the conjecture, which often allows to reduce $K$-theory computations for $A\\rtimes_rG$ to computations for crossed products by compact subgroups of $G$. We give several applications for this principle includi","authors_text":"Siegfried Echterhoff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-03-31T14:24:43Z","title":"Bivariant $KK$-Theory and the Baum-Connes conjecure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10912","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":"sha256:6edd88386d5f54f847b43fc06738fff91455e3a7367053736e4335e732fa4cfb","target":"record","created_at":"2026-05-18T00:42:29Z","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":"d27245c5e12a5c2c4546a52915d1edc04233661ce086f836c6b1c28af51ed4f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-03-31T14:24:43Z","title_canon_sha256":"405e6571649f9f9c575f614c914d7e1907a07c29f1884af019a7f418ae9698a0"},"schema_version":"1.0","source":{"id":"1703.10912","kind":"arxiv","version":2}},"canonical_sha256":"8732b1b21a110a061fa295d4a19fe9179a4156137f18f4ea15696ba11b3c4a75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8732b1b21a110a061fa295d4a19fe9179a4156137f18f4ea15696ba11b3c4a75","first_computed_at":"2026-05-18T00:42:29.049340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:29.049340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fmLq/N5j7a5NwP8fFGRyPDA8cjWn+zHETBr8R9W8/ti9PbnxyMWEWYR8Fr0W56GLjFTIwm9G4xh4NQqOmwEyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:29.049782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10912","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6edd88386d5f54f847b43fc06738fff91455e3a7367053736e4335e732fa4cfb","sha256:ff72341e8c20a492beffeb4f3d730f57a8db2c81c0942b6e27d67e68029015ac"],"state_sha256":"ca0c5a5b0c421a7690ec27b7ca7d3af8b5971471ae624b8011fd168a29ebb532"}