{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3WXQ7TWG7DPVCG5W6IFKOJIC5S","short_pith_number":"pith:3WXQ7TWG","canonical_record":{"source":{"id":"1006.1262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-07T14:17:46Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"7d03083873562f678364872b0b17d6975c98bb854a036427a50282882f5d4734","abstract_canon_sha256":"3793e888c408eb9166966f5a0af05b79d26d3a2684586f756f11f51c7182cf57"},"schema_version":"1.0"},"canonical_sha256":"ddaf0fcec6f8df511bb6f20aa72502eca69e2bce17fc041e3e6a67cb5eef3ba4","source":{"kind":"arxiv","id":"1006.1262","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1262","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1262v1","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1262","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"3WXQ7TWG7DPV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3WXQ7TWG7DPVCG5W","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3WXQ7TWG","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3WXQ7TWG7DPVCG5W6IFKOJIC5S","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-07T14:17:46Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"7d03083873562f678364872b0b17d6975c98bb854a036427a50282882f5d4734","abstract_canon_sha256":"3793e888c408eb9166966f5a0af05b79d26d3a2684586f756f11f51c7182cf57"},"schema_version":"1.0"},"canonical_sha256":"ddaf0fcec6f8df511bb6f20aa72502eca69e2bce17fc041e3e6a67cb5eef3ba4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.717238Z","signature_b64":"M1bVo0oCZdt1de8ZUsaxG23D0DR4F6Uvqu3jtKANNegbwUWdJ3GI+bf3DpVTolat36Ri5d5KXq9igC0BNm15Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddaf0fcec6f8df511bb6f20aa72502eca69e2bce17fc041e3e6a67cb5eef3ba4","last_reissued_at":"2026-05-17T23:53:19.716630Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.716630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1262","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7P4JTY/G8W4oTGtt2S23V0GrZGa1P7WKT+biyGo7fvRKuWsX/JSSD7enA7+gO52Jz6ZktpBDRq/D2+Ww7sr/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:31:17.698979Z"},"content_sha256":"076d7dd10779776a3baf16cba250118b5fbc67f01e29978c0d66dd9dd4e7d737","schema_version":"1.0","event_id":"sha256:076d7dd10779776a3baf16cba250118b5fbc67f01e29978c0d66dd9dd4e7d737"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3WXQ7TWG7DPVCG5W6IFKOJIC5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strictification of etale stacky Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.DG","authors_text":"Chenchang Zhu, Giorgio Trentinaglia","submitted_at":"2010-06-07T14:17:46Z","abstract_excerpt":"We define stacky Lie groups to be group objects in the 2-category of differentiable stacks. We show that every connected and etale stacky Lie group is equivalent to a crossed module of the form (H,G) where H is the fundamental group of the given stacky Lie group and G is the connected and simply connected Lie group integrating the Lie algebra of the stacky group. Our result is closely related to a strictification result of Baez and Lauda."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1262","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17i1sZ2rbx4T4ngbH0XMnTI0FrE8IGRsnxMHSV6y5cuaoQ9pJMLPhsRNkh9ajHYZkYabNCrH7GMq/fcXPyAYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:31:17.699740Z"},"content_sha256":"a2887e0a7410f80885d1fab265344b87af892f008e9af5790ad69b3ccf378d81","schema_version":"1.0","event_id":"sha256:a2887e0a7410f80885d1fab265344b87af892f008e9af5790ad69b3ccf378d81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WXQ7TWG7DPVCG5W6IFKOJIC5S/bundle.json","state_url":"https://pith.science/pith/3WXQ7TWG7DPVCG5W6IFKOJIC5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WXQ7TWG7DPVCG5W6IFKOJIC5S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T04:31:17Z","links":{"resolver":"https://pith.science/pith/3WXQ7TWG7DPVCG5W6IFKOJIC5S","bundle":"https://pith.science/pith/3WXQ7TWG7DPVCG5W6IFKOJIC5S/bundle.json","state":"https://pith.science/pith/3WXQ7TWG7DPVCG5W6IFKOJIC5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WXQ7TWG7DPVCG5W6IFKOJIC5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3WXQ7TWG7DPVCG5W6IFKOJIC5S","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":"3793e888c408eb9166966f5a0af05b79d26d3a2684586f756f11f51c7182cf57","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-07T14:17:46Z","title_canon_sha256":"7d03083873562f678364872b0b17d6975c98bb854a036427a50282882f5d4734"},"schema_version":"1.0","source":{"id":"1006.1262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1262","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1262v1","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1262","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"3WXQ7TWG7DPV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3WXQ7TWG7DPVCG5W","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3WXQ7TWG","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:a2887e0a7410f80885d1fab265344b87af892f008e9af5790ad69b3ccf378d81","target":"graph","created_at":"2026-05-17T23:53:19Z","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 define stacky Lie groups to be group objects in the 2-category of differentiable stacks. We show that every connected and etale stacky Lie group is equivalent to a crossed module of the form (H,G) where H is the fundamental group of the given stacky Lie group and G is the connected and simply connected Lie group integrating the Lie algebra of the stacky group. Our result is closely related to a strictification result of Baez and Lauda.","authors_text":"Chenchang Zhu, Giorgio Trentinaglia","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-07T14:17:46Z","title":"Strictification of etale stacky Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1262","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":"sha256:076d7dd10779776a3baf16cba250118b5fbc67f01e29978c0d66dd9dd4e7d737","target":"record","created_at":"2026-05-17T23:53:19Z","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":"3793e888c408eb9166966f5a0af05b79d26d3a2684586f756f11f51c7182cf57","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-06-07T14:17:46Z","title_canon_sha256":"7d03083873562f678364872b0b17d6975c98bb854a036427a50282882f5d4734"},"schema_version":"1.0","source":{"id":"1006.1262","kind":"arxiv","version":1}},"canonical_sha256":"ddaf0fcec6f8df511bb6f20aa72502eca69e2bce17fc041e3e6a67cb5eef3ba4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddaf0fcec6f8df511bb6f20aa72502eca69e2bce17fc041e3e6a67cb5eef3ba4","first_computed_at":"2026-05-17T23:53:19.716630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:19.716630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M1bVo0oCZdt1de8ZUsaxG23D0DR4F6Uvqu3jtKANNegbwUWdJ3GI+bf3DpVTolat36Ri5d5KXq9igC0BNm15Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:19.717238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:076d7dd10779776a3baf16cba250118b5fbc67f01e29978c0d66dd9dd4e7d737","sha256:a2887e0a7410f80885d1fab265344b87af892f008e9af5790ad69b3ccf378d81"],"state_sha256":"3e08032a16d7cd39e9053a68e17fafe21c524de85dd119de16f0be3ebe58ba47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gjz+W4T0bNDYggpIfMsS1hybOzgeelSq1eEkrn3upWTMtK8MXUdp0TWpwZT9Q39uOzTO2jP0J5pSBArh1bajBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:31:17.703687Z","bundle_sha256":"7cca4afbdbad93fddb657e6db677e122bba271537ba4ae79e534cadbc4a8c654"}}