{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J5PLXXKE2X75D3QMYBRYDJ365H","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":"bc8a87293b7dbf921f932cf5d998216e16d3cb97f0f914868fd5e3beabd59c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-14T17:53:54Z","title_canon_sha256":"466f58a33211e49d782d93aa136a096ab18232e3787ef22aef2978f6b4b7dae2"},"schema_version":"1.0","source":{"id":"1803.05422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05422","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05422v1","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05422","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"J5PLXXKE2X75","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J5PLXXKE2X75D3QM","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J5PLXXKE","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:e562028a4342644edf9cb77aa8f01a9d03d5f9ceaaf1c5f78deb5b84d3632745","target":"graph","created_at":"2026-05-18T00:21:01Z","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":"In this paper we show that topological subgroupoids of Lie groupoids, under special circumstances are Lie subgroupoids. Giving an example, we indicate that having the same topological dimension is a necessary condition for topological subgroupoids to be Lie subgroupoids. Also, we provide some conditions for double subgroupoids to become double Lie subgroupoids. Moreover, we illustrate that having the same conditions as the Cartan's theorem for Lie groups, helps us prove the same theorem for generalized Lie groups.","authors_text":"A. R. Armakan, F. Gorlizkhatami, M. R. Farhangdoost, T. Nasirzadeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-14T17:53:54Z","title":"Cartan's theorem for some topological generalized groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05422","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":"sha256:1b6e549aec3eb43b2760a1470ec9de1f4f53267be737a904721c5732d08f4953","target":"record","created_at":"2026-05-18T00:21:01Z","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":"bc8a87293b7dbf921f932cf5d998216e16d3cb97f0f914868fd5e3beabd59c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-14T17:53:54Z","title_canon_sha256":"466f58a33211e49d782d93aa136a096ab18232e3787ef22aef2978f6b4b7dae2"},"schema_version":"1.0","source":{"id":"1803.05422","kind":"arxiv","version":1}},"canonical_sha256":"4f5ebbdd44d5ffd1ee0cc06381a77ee9da3c2c25045a7b36f38b33086a5ab85b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f5ebbdd44d5ffd1ee0cc06381a77ee9da3c2c25045a7b36f38b33086a5ab85b","first_computed_at":"2026-05-18T00:21:01.266290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:01.266290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CNNxiuRXTMcNJiXBFDi3Jx8ksOgw0o0PifjOX7MkYOMYPfTLrm2Fyd+VPmAGt3tJdTL8dDCDasm4BkHREnmmAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:01.266724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b6e549aec3eb43b2760a1470ec9de1f4f53267be737a904721c5732d08f4953","sha256:e562028a4342644edf9cb77aa8f01a9d03d5f9ceaaf1c5f78deb5b84d3632745"],"state_sha256":"983df7e2d77edaa2bb0d855dae373eb58880f33ba88e6e341b183448d1f5a5ba"}