{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:R5USUYGGIPTXVLBXOZQNUNEAV6","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":"63940525f2922d67691971f26289d645da059fdd2e40e62ace8fc390709d3587","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-24T16:02:56Z","title_canon_sha256":"8f3e2c988eb33ed43ec9c43148e92d3f1cde0f83a3990f30d4ef495367a5c9f9"},"schema_version":"1.0","source":{"id":"0810.4402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.4402","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"arxiv_version","alias_value":"0810.4402v1","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4402","created_at":"2026-05-18T02:15:23Z"},{"alias_kind":"pith_short_12","alias_value":"R5USUYGGIPTX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"R5USUYGGIPTXVLBX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"R5USUYGG","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:b4d4e58e1853f7c651b7d55390f9c2ed5d4a2c5bd2dfb7764f781dcfe8c76d56","target":"graph","created_at":"2026-05-18T02:15:23Z","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 connected Lie group, LG its loop group, and PG->G the principal LG-bundle defined by quasi-periodic paths in G. This paper is devoted to differential geometry of the Atiyah algebroid A=T(PG)/LG of this bundle. Given a symmetric bilinear form on the Lie algebra g and the corresponding central extension of Lg, we consider the lifting problem for A, and show how the cohomology class of the Cartan 3-form on G arises as an obstruction. This involves the construction of a 2-form on PG with differential the pull-back of the Cartan form. In the second part of this paper we obtain similar LG","authors_text":"A. Alekseev, E. Meinrenken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-24T16:02:56Z","title":"The Atiyah algebroid of the path fibration over a Lie group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4402","kind":"arxiv","version":1},"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:b083dd23a132d563f30995695b93d8c1d972f3226f4c37dff9c2841f4a95c4d1","target":"record","created_at":"2026-05-18T02:15:23Z","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":"63940525f2922d67691971f26289d645da059fdd2e40e62ace8fc390709d3587","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-24T16:02:56Z","title_canon_sha256":"8f3e2c988eb33ed43ec9c43148e92d3f1cde0f83a3990f30d4ef495367a5c9f9"},"schema_version":"1.0","source":{"id":"0810.4402","kind":"arxiv","version":1}},"canonical_sha256":"8f692a60c643e77aac377660da3480afaa722cfb91748f6ce6ba9982ec9b178a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f692a60c643e77aac377660da3480afaa722cfb91748f6ce6ba9982ec9b178a","first_computed_at":"2026-05-18T02:15:23.441910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:23.441910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sxv2xmTy5NSpNJhvsHS44dU5H1IXWiQ4vjOAEgj0Qwalqn8VaIXeRspjSMJPjcZ5zaRZbLlkSNwm6wBeom89AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:23.442582Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.4402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b083dd23a132d563f30995695b93d8c1d972f3226f4c37dff9c2841f4a95c4d1","sha256:b4d4e58e1853f7c651b7d55390f9c2ed5d4a2c5bd2dfb7764f781dcfe8c76d56"],"state_sha256":"385a1ae0ae2e5d5ebe583b1089268b1295781b2ef06be36a6199d4f4ea6f95fe"}