{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:QPWHYGS5KVF6YHP5SS4WT4ZAXJ","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":"5d941ae849e94fe46eed6edfd2f07fe27d59a452282df1c5b190c894b8226481","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.AT","submitted_at":"2002-06-24T23:11:22Z","title_canon_sha256":"3c803434aeee62e86255c63bb64331a4c44c0188268ffc288807c747babb61e8"},"schema_version":"1.0","source":{"id":"math/0206257","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0206257","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0206257v4","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0206257","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"QPWHYGS5KVF6","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"QPWHYGS5KVF6YHP5","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"QPWHYGS5","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:b423d03db587b6aef7adec61a892b175aa1f95073f4578f90e0bef169e9e9a77","target":"graph","created_at":"2026-05-18T02:57:51Z","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":"Using a global version of the equivariant Chern character, we describe the complexified twisted equivariant K-theory of a space with a compact Lie group action in terms of fixed-point data. We apply this to the case of a compact Lie group acting on itself by conjugation, and relate the result to the Verlinde algebra and to the Kac numerator at q=1. Verlinde's formula is also discussed in this context.","authors_text":"Constantin Teleman, Daniel S. Freed, Michael J. Hopkins","cross_cats":["math.KT"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2002-06-24T23:11:22Z","title":"Twisted equivariant K-theory with complex coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206257","kind":"arxiv","version":4},"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":"sha256:98544234c08225dcfab76b51c225353ceec9a8a939fb745e6e5f3ee5be8d5bb6","target":"record","created_at":"2026-05-18T02:57:51Z","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":"5d941ae849e94fe46eed6edfd2f07fe27d59a452282df1c5b190c894b8226481","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.AT","submitted_at":"2002-06-24T23:11:22Z","title_canon_sha256":"3c803434aeee62e86255c63bb64331a4c44c0188268ffc288807c747babb61e8"},"schema_version":"1.0","source":{"id":"math/0206257","kind":"arxiv","version":4}},"canonical_sha256":"83ec7c1a5d554bec1dfd94b969f320ba54d0c781dfc953bd915ae8f90a94d088","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83ec7c1a5d554bec1dfd94b969f320ba54d0c781dfc953bd915ae8f90a94d088","first_computed_at":"2026-05-18T02:57:51.158970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:51.158970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N2NXvSJX8PcByGwLXkczm4rBL9eqhnsEjCsYOmF0r6Q8shTOmP4ab1S3pPbG8h7qjsbaRNOZmILbpCbfCQANBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:51.159595Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0206257","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98544234c08225dcfab76b51c225353ceec9a8a939fb745e6e5f3ee5be8d5bb6","sha256:b423d03db587b6aef7adec61a892b175aa1f95073f4578f90e0bef169e9e9a77"],"state_sha256":"f47bd04de730180ab7c7c4641155bd425890253947362a1536d0de9ea54f32a3"}