{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2U7BHW7SPCTSBXB54YJSAOSDHB","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":"17a8d90d2efdc521baeb8b768ac4100ef6ee6df496befd00aa24a10b832b178d","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-02-09T03:47:36Z","title_canon_sha256":"903cf14af8301ba8028825a1f21b1d77ca8bf1dad33dd7c0c3c56e16838b8561"},"schema_version":"1.0","source":{"id":"1202.1880","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1880","created_at":"2026-05-18T00:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1880v3","created_at":"2026-05-18T00:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1880","created_at":"2026-05-18T00:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"2U7BHW7SPCTS","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2U7BHW7SPCTSBXB5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2U7BHW7S","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:7fec83fe8af41d2df169a367c16bd1e0bdc17cf1143de2418cf8165db080eb13","target":"graph","created_at":"2026-05-18T00:15:59Z","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":"We define equivariant projective unitary stable bundles as the appropriate twists when defining K-theory as sections of bundles with fibers the space of Fredholm operators over a Hilbert space. We construct universal equivariant projective unitary stable bundles for the orbit types, and we use a specific model for these local universal spaces in order to glue them to obtain a universal equivariant projective unitary stable bundle for discrete and proper actions. We determine the homotopy type of the universal equivariant projective unitary stable bundle, and we show that the isomorphism classe","authors_text":"Bernardo Uribe, Jesus Espinoza, Michael Joachim, Noe Barcenas","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-02-09T03:47:36Z","title":"Universal twist in Equivariant K-theory for proper and discrete actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1880","kind":"arxiv","version":3},"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:c760f335ff5ea0628d5000ed14218e5e5cfa80a522d65953452742a7167714d0","target":"record","created_at":"2026-05-18T00:15:59Z","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":"17a8d90d2efdc521baeb8b768ac4100ef6ee6df496befd00aa24a10b832b178d","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-02-09T03:47:36Z","title_canon_sha256":"903cf14af8301ba8028825a1f21b1d77ca8bf1dad33dd7c0c3c56e16838b8561"},"schema_version":"1.0","source":{"id":"1202.1880","kind":"arxiv","version":3}},"canonical_sha256":"d53e13dbf278a720dc3de613203a4338756b57e22ff7754c784452642a01a4b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d53e13dbf278a720dc3de613203a4338756b57e22ff7754c784452642a01a4b2","first_computed_at":"2026-05-18T00:15:59.833373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:59.833373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gAJn7nEY9hwpu0RRhwdVUhvd2DBQUOo/PQkTzbzpPlFcwMRzNE2BmtMXNpFDxaEXO3IJL9nm5j241yfgbdHYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:59.833784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1880","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c760f335ff5ea0628d5000ed14218e5e5cfa80a522d65953452742a7167714d0","sha256:7fec83fe8af41d2df169a367c16bd1e0bdc17cf1143de2418cf8165db080eb13"],"state_sha256":"e10dda8696a253bd95875ca6eb51c3670fefab51cfbde688a463da59309127fc"}