{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XL6IP3MCHWISVXX46UWXSPK2KA","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":"ff550b5a5705b6e3e5d0a5ca789ab15616d3e093d0d9fa01ca2d41d46ff5416e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-23T19:22:48Z","title_canon_sha256":"4b1593dd5f008d0aff1a8fa1e3560deb6bd0ab5ef00abb860c2aadcbd791365a"},"schema_version":"1.0","source":{"id":"1706.07843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07843","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07843v1","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07843","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"XL6IP3MCHWIS","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XL6IP3MCHWISVXX4","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XL6IP3MC","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d133a76dd06f9458b19bc52944b6beb05159f942a89d9ed943e2d54e6f8f0319","target":"graph","created_at":"2026-05-18T00:41:47Z","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 prove that every proper Lie groupoid admits a desingularization to a regular proper Lie groupoid. When equipped with a Riemannian metric, we show that it admits a desingularization to a regular Riemannian proper Lie groupoid, arbitrarily close to the original one in the Gromov-Hausdorff distance between the quotient spaces. We construct the desingularization via a successive blow-up construction on a proper Lie groupoid. We also prove that our construction of the desingularization is invariant under Morita equivalence of groupoids, showing that it is a desingularization of the","authors_text":"Hessel B. Posthuma, Kirsten J.L. Wang, Xiang Tang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-23T19:22:48Z","title":"Resolutions of proper Riemannian Lie groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07843","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":"sha256:0faeca6e42d89815b3684708234ed71577af9853110e807518d8b8f7fe3e6bd2","target":"record","created_at":"2026-05-18T00:41:47Z","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":"ff550b5a5705b6e3e5d0a5ca789ab15616d3e093d0d9fa01ca2d41d46ff5416e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-23T19:22:48Z","title_canon_sha256":"4b1593dd5f008d0aff1a8fa1e3560deb6bd0ab5ef00abb860c2aadcbd791365a"},"schema_version":"1.0","source":{"id":"1706.07843","kind":"arxiv","version":1}},"canonical_sha256":"bafc87ed823d912adefcf52d793d5a502b8d04f045f003f2d3957a50af4eaa7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bafc87ed823d912adefcf52d793d5a502b8d04f045f003f2d3957a50af4eaa7f","first_computed_at":"2026-05-18T00:41:47.400270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:47.400270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JefTRNCgOgslqaw9zLlla4roUhhl/lLRpjGQ9OGfFD0+d00bgIDctfEkAqcw6dYaTftedjhjg2UOFghARAx7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:47.400705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0faeca6e42d89815b3684708234ed71577af9853110e807518d8b8f7fe3e6bd2","sha256:d133a76dd06f9458b19bc52944b6beb05159f942a89d9ed943e2d54e6f8f0319"],"state_sha256":"f1c6ff3dbcbdb5b46f9e758f683c6c7e3b572478fc3cc1a965f4f9c26f484685"}