{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:444FKXCMM2MADT2Z46P3RRR62J","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":"369501e771196884bebd286ee5a8d4f3297f3a72116b483af7331d314805d913","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-28T16:51:56Z","title_canon_sha256":"c738b37ec54df420dfa06dbdc70f49aa8c2be7f60fecb7fcf83f61b1edc02817"},"schema_version":"1.0","source":{"id":"1312.7450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7450","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7450v2","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7450","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"pith_short_12","alias_value":"444FKXCMM2MA","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"444FKXCMM2MADT2Z","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"444FKXCM","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:2cd31aa66f73ff0ad105a6da0b6e0c9dfe6cb37df6c695b601986687f5a54e90","target":"graph","created_at":"2026-05-18T01:19:31Z","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 study the classifying space of a twisted loop group $L_{\\sigma}G$ where $G$ is a compact Lie group and $\\sigma$ is an automorphism of $G$ of finite order modulo inner automorphisms. Equivalently, we study the $\\sigma$-twisted adjoint action of $G$ on itself. We derive a formula for the cohomology ring $H^*(BL_{\\sigma}G)$ and explicitly carry out the calculation for all automorphisms of simple Lie groups. More generally, we derive a formula for the equivariant cohomology of compact Lie group actions with constant rank stabilizers.","authors_text":"Thomas Baird","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-28T16:51:56Z","title":"Classifying spaces of twisted loop groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7450","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:a217d7601eeedb670e682d2c585d78be2d6525cefc52bf9a02e55448d5111d97","target":"record","created_at":"2026-05-18T01:19:31Z","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":"369501e771196884bebd286ee5a8d4f3297f3a72116b483af7331d314805d913","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-28T16:51:56Z","title_canon_sha256":"c738b37ec54df420dfa06dbdc70f49aa8c2be7f60fecb7fcf83f61b1edc02817"},"schema_version":"1.0","source":{"id":"1312.7450","kind":"arxiv","version":2}},"canonical_sha256":"e738555c4c669801cf59e79fb8c63ed25339085cec2f145df3cd92906083a4f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e738555c4c669801cf59e79fb8c63ed25339085cec2f145df3cd92906083a4f8","first_computed_at":"2026-05-18T01:19:31.002726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:31.002726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HwSV666K/xTKZqbZbh4WXmYlnDkygoFtnP+JJ1vlt14SCoynkWRCNj3PbHi1lIpUusCA8nrDaPwGS9g1hSD7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:31.003383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a217d7601eeedb670e682d2c585d78be2d6525cefc52bf9a02e55448d5111d97","sha256:2cd31aa66f73ff0ad105a6da0b6e0c9dfe6cb37df6c695b601986687f5a54e90"],"state_sha256":"7402e9aaea52adfdfeeed10abe484f47a87e5e8dc434bc65efa4a70ff66d46fa"}