{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:W3ENRDSF5JCRXH5YO2UJ3BPFQ4","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":"742bb9e71518eb223ab61fc61cf7fcba6d0f8f71327da5e97667958ec991508f","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.KT","submitted_at":"2002-08-22T15:15:30Z","title_canon_sha256":"209442f957c276a8a6116e677df19f29bc07ce6cbb489c34eba3d2266c6bb467"},"schema_version":"1.0","source":{"id":"math/0208164","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0208164","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0208164v2","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0208164","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"W3ENRDSF5JCR","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"W3ENRDSF5JCRXH5Y","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"W3ENRDSF","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:380679750e91b8568d5469570b58d4d09adacdac66f5b3af5798895f54e11bcc","target":"graph","created_at":"2026-05-18T02:38:00Z","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":"Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The universal equivariant Euler characteristic of M, which lives in a group U^G(M), counts the equivariant cells of M, taking the component structure of the various fixed point sets into account. We construct a natural homomorphism from U^G(M) to the equivariant KO-homology of M. The main result of this paper says that this map sends the universal equivariant Eul","authors_text":"Jonathan Rosenberg, Wolfgang Lueck","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.KT","submitted_at":"2002-08-22T15:15:30Z","title":"Equivariant Euler characteristics and K-homology Euler classes for proper cocompact G-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0208164","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":"sha256:17c7d341147bf442a9d69cb3135ecd809342ff097f0d4878668787bb9bc94b2e","target":"record","created_at":"2026-05-18T02:38:00Z","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":"742bb9e71518eb223ab61fc61cf7fcba6d0f8f71327da5e97667958ec991508f","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.KT","submitted_at":"2002-08-22T15:15:30Z","title_canon_sha256":"209442f957c276a8a6116e677df19f29bc07ce6cbb489c34eba3d2266c6bb467"},"schema_version":"1.0","source":{"id":"math/0208164","kind":"arxiv","version":2}},"canonical_sha256":"b6c8d88e45ea451b9fb876a89d85e5870cd8078d77d26b2e071d2f5f4cbc9d31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6c8d88e45ea451b9fb876a89d85e5870cd8078d77d26b2e071d2f5f4cbc9d31","first_computed_at":"2026-05-18T02:38:00.588777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:00.588777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1fbmXbUSMmFI1f37MCSIftnNKZn+P3y5zgpYFA/e5wdC4FdiYQVXKbTjm8i4e7lS7toS5IwrQvclIRrjtvYAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:00.589412Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0208164","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17c7d341147bf442a9d69cb3135ecd809342ff097f0d4878668787bb9bc94b2e","sha256:380679750e91b8568d5469570b58d4d09adacdac66f5b3af5798895f54e11bcc"],"state_sha256":"74d495f6cdc0403dd4dc18f96d3251c7282c98cb1960591b82a65b4321602ba0"}