{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2Y5OY4ZSSDFFTS63QBNNAAXPBC","short_pith_number":"pith:2Y5OY4ZS","schema_version":"1.0","canonical_sha256":"d63aec733290ca59cbdb805ad002ef088fa46afedbdab596240d9179d7531399","source":{"kind":"arxiv","id":"1704.04220","version":3},"attestation_state":"computed","paper":{"title":"Automorphism groups of rigid geometries on leaf spaces of foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Nina I. Zhukova","submitted_at":"2017-04-13T17:39:30Z","abstract_excerpt":"We introduce a category of rigid geometries on singular spaces which are leaf spaces of foliations and are considered as leaf manifolds. We single out a special category $\\mathfrak F_0$ of leaf manifolds containing the orbifold category as a full subcategory. Objects of $\\mathfrak F_0$ may have non-Hausdorff topology unlike the orbifolds. The topology of some objects of $\\mathfrak F_0$ does not satisfy the separation axiom $T_0$. It is shown that for every ${\\mathcal N}\\in Ob(\\mathfrak F_0)$ a rigid geometry $\\zeta$ on $\\mathcal N$ admits a desingularization. Moreover, for every such $\\mathcal"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.04220","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-13T17:39:30Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"987c1e12dbedcaa3ce920dd16fcc44c1d2e01d967f4bf844b7034a74e15f9ceb","abstract_canon_sha256":"5664e5d27435f96210a058613b2c4e4a49c296bd8b0201f193c8ac7d4e14847f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:37.110891Z","signature_b64":"AErAuRDfQGq9Wf3uN+dMR0rgWx2rD3wLXQ3U/KlTWXeusEoPzgZzOPe5zrA4UTqmY0N+zVVuRKEqLia2Qtu3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d63aec733290ca59cbdb805ad002ef088fa46afedbdab596240d9179d7531399","last_reissued_at":"2026-05-18T00:18:37.110217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:37.110217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphism groups of rigid geometries on leaf spaces of foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Nina I. Zhukova","submitted_at":"2017-04-13T17:39:30Z","abstract_excerpt":"We introduce a category of rigid geometries on singular spaces which are leaf spaces of foliations and are considered as leaf manifolds. We single out a special category $\\mathfrak F_0$ of leaf manifolds containing the orbifold category as a full subcategory. Objects of $\\mathfrak F_0$ may have non-Hausdorff topology unlike the orbifolds. The topology of some objects of $\\mathfrak F_0$ does not satisfy the separation axiom $T_0$. It is shown that for every ${\\mathcal N}\\in Ob(\\mathfrak F_0)$ a rigid geometry $\\zeta$ on $\\mathcal N$ admits a desingularization. Moreover, for every such $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04220","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1704.04220","created_at":"2026-05-18T00:18:37.110331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.04220v3","created_at":"2026-05-18T00:18:37.110331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04220","created_at":"2026-05-18T00:18:37.110331+00:00"},{"alias_kind":"pith_short_12","alias_value":"2Y5OY4ZSSDFF","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2Y5OY4ZSSDFFTS63","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2Y5OY4ZS","created_at":"2026-05-18T12:30:55.937587+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC","json":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC.json","graph_json":"https://pith.science/api/pith-number/2Y5OY4ZSSDFFTS63QBNNAAXPBC/graph.json","events_json":"https://pith.science/api/pith-number/2Y5OY4ZSSDFFTS63QBNNAAXPBC/events.json","paper":"https://pith.science/paper/2Y5OY4ZS"},"agent_actions":{"view_html":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC","download_json":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC.json","view_paper":"https://pith.science/paper/2Y5OY4ZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.04220&json=true","fetch_graph":"https://pith.science/api/pith-number/2Y5OY4ZSSDFFTS63QBNNAAXPBC/graph.json","fetch_events":"https://pith.science/api/pith-number/2Y5OY4ZSSDFFTS63QBNNAAXPBC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC/action/storage_attestation","attest_author":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC/action/author_attestation","sign_citation":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC/action/citation_signature","submit_replication":"https://pith.science/pith/2Y5OY4ZSSDFFTS63QBNNAAXPBC/action/replication_record"}},"created_at":"2026-05-18T00:18:37.110331+00:00","updated_at":"2026-05-18T00:18:37.110331+00:00"}