{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XHMA4EWSPLHH7XZBPKT6X2MVAZ","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":"9e909a2690e386fb3810544cba8b96cc330b7257259e9b7ec5fbfdbf5761f3f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-06T20:15:49Z","title_canon_sha256":"2f69b532150c71f9c8f345bbe6f31cc1c2c63c104fab129604e25b5e166045ab"},"schema_version":"1.0","source":{"id":"1308.1412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1412","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1412v1","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1412","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"XHMA4EWSPLHH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XHMA4EWSPLHH7XZB","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XHMA4EWS","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:4180879527be1ef37e857b1236e7e7212cb0ed8165cebf0ef30a3b8f2dfacf90","target":"graph","created_at":"2026-05-18T03:16:38Z","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 complex Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a trivial bundle over some finite covering space of the base space if and only if each real characteristic class of positive degree of G vanishes. A third equivalent condition is that the derived group of the radical of G is simply connected. As a corollary, the same conditions are equivalent if G is a connected amenable Lie group. In particular, if G is a connected compact Lie group then any flat principal G-bundle over any finite CW-complex pulls back to a trivial bundle ","authors_text":"Christophe Pittet, Guido Mislin, Indira Chatterji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-06T20:15:49Z","title":"Flat bundles with complex analytic holonomy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1412","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:ce1f88d8a2b3bcd1bb9d602c3a6864a84a3f45ea6aaa5b39e40c88aeb4801a9b","target":"record","created_at":"2026-05-18T03:16:38Z","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":"9e909a2690e386fb3810544cba8b96cc330b7257259e9b7ec5fbfdbf5761f3f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-06T20:15:49Z","title_canon_sha256":"2f69b532150c71f9c8f345bbe6f31cc1c2c63c104fab129604e25b5e166045ab"},"schema_version":"1.0","source":{"id":"1308.1412","kind":"arxiv","version":1}},"canonical_sha256":"b9d80e12d27ace7fdf217aa7ebe99506626f7defbc16a3018bbdeb75e13d3061","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9d80e12d27ace7fdf217aa7ebe99506626f7defbc16a3018bbdeb75e13d3061","first_computed_at":"2026-05-18T03:16:38.090444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:38.090444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HH3vk5yMMgt+rXCFROfUKGi8bG1iiy5JnqQOGW77hIU2q2q6ZogC5rmfal7PTljWCVkzFdh7pkjsv0rjPs+gDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:38.090939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce1f88d8a2b3bcd1bb9d602c3a6864a84a3f45ea6aaa5b39e40c88aeb4801a9b","sha256:4180879527be1ef37e857b1236e7e7212cb0ed8165cebf0ef30a3b8f2dfacf90"],"state_sha256":"fd5fc35f5cfdea05f6240ddc2b450fe318b24161f50a608e9bdc7769940f7498"}