{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DJ3C6SNQZMFJLSQUBPO22HKAES","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":"ee370ddc64b0dabf91aa2f3ba5acdd71b00d893aef2d8f4df3d1c9f0b0b188d1","cross_cats_sorted":["math.CT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-09-28T13:13:24Z","title_canon_sha256":"7046a97dd4c97846492edd449c89a2e857e496ff4ae520cebed18471ea3a7330"},"schema_version":"1.0","source":{"id":"2109.13702","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.13702","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2109.13702v3","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.13702","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"DJ3C6SNQZMFJ","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"DJ3C6SNQZMFJLSQU","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"DJ3C6SNQ","created_at":"2026-07-05T06:04:32Z"}],"graph_snapshots":[{"event_id":"sha256:046f5698440569e5671338f83eb7237e642f6a1521b16c9ef7a6f63d3c46f2da","target":"graph","created_at":"2026-07-05T06:04:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.13702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corresponding categories enriched in the homotopy category of topological spaces are equivalent. This can also be interpreted as an equivalence of infinity categories.","authors_text":"Adam Thomas, Dmitriy Rumynin, John Jones","cross_cats":["math.CT","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-09-28T13:13:24Z","title":"Compact Lie Groups and Complex Reductive Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.13702","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":"sha256:04ce3f4949d4185cad01b055188c24a5577bc435c1513d4f2170627fea26e667","target":"record","created_at":"2026-07-05T06:04:32Z","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":"ee370ddc64b0dabf91aa2f3ba5acdd71b00d893aef2d8f4df3d1c9f0b0b188d1","cross_cats_sorted":["math.CT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-09-28T13:13:24Z","title_canon_sha256":"7046a97dd4c97846492edd449c89a2e857e496ff4ae520cebed18471ea3a7330"},"schema_version":"1.0","source":{"id":"2109.13702","kind":"arxiv","version":3}},"canonical_sha256":"1a762f49b0cb0a95ca140bddad1d40249895967dfc4cf49298c6eb49cefcfab3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a762f49b0cb0a95ca140bddad1d40249895967dfc4cf49298c6eb49cefcfab3","first_computed_at":"2026-07-05T06:04:32.376108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:04:32.376108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+fCJ6QEktiKD7WUKqsylU4cWeAQWFEZ6vhvlrbX8397Qg0Y0ETwhNp/fCyDHSyVSJ/20OsuDaN9+rrI2Gpf8Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:04:32.376491Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.13702","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04ce3f4949d4185cad01b055188c24a5577bc435c1513d4f2170627fea26e667","sha256:046f5698440569e5671338f83eb7237e642f6a1521b16c9ef7a6f63d3c46f2da"],"state_sha256":"85d28c185bec73730089e1fc45041b79a4e7a7c7ddb273078f52094096ca8335"}