{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CEKBCBD5I7CNKUEPRN4WUNUN6O","short_pith_number":"pith:CEKBCBD5","schema_version":"1.0","canonical_sha256":"111411047d47c4d5508f8b796a368df390fd5ed781b2b29bf4cf9a29667ba249","source":{"kind":"arxiv","id":"1103.3623","version":1},"attestation_state":"computed","paper":{"title":"Correspondence between diffeomorphism groups and singular foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Tomasz Rybicki","submitted_at":"2011-03-18T13:36:28Z","abstract_excerpt":"It is well-known that any isotopically connected diffeomorphism group $G$ of a manifold determines uniquely a singular foliation $\\F_G$. A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup $[G,G]$ of an isotopically connected, factorizable and non-fixing $C^r$-diffeomorphism group $G$ is simple iff the foliation $\\F_{[G,G]}$ defined by $[G,G]$ admits no proper minimal sets. In particular, the compactly supported $e$-component of the leaf pr"},"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":"1103.3623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-18T13:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"26afce3ddc4c03f7b293c0a529c4f882d135f273db7173ab8a1ccbe13a9c38f0","abstract_canon_sha256":"7187663f60825cf92301b0973278844f73d2b1fe1da0955426a896ad04aa4e86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:32.265858Z","signature_b64":"t7O50YNM1FK4UeVdwe9OxHz/LAzk0sFhNLk4WhkQjdVe/h66ueKLp5Rp38GjZ8LzDXLwMCJd9b3mEZ6gaN8tAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"111411047d47c4d5508f8b796a368df390fd5ed781b2b29bf4cf9a29667ba249","last_reissued_at":"2026-05-18T04:26:32.265358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:32.265358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correspondence between diffeomorphism groups and singular foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Tomasz Rybicki","submitted_at":"2011-03-18T13:36:28Z","abstract_excerpt":"It is well-known that any isotopically connected diffeomorphism group $G$ of a manifold determines uniquely a singular foliation $\\F_G$. A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup $[G,G]$ of an isotopically connected, factorizable and non-fixing $C^r$-diffeomorphism group $G$ is simple iff the foliation $\\F_{[G,G]}$ defined by $[G,G]$ admits no proper minimal sets. In particular, the compactly supported $e$-component of the leaf pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3623","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.3623","created_at":"2026-05-18T04:26:32.265430+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.3623v1","created_at":"2026-05-18T04:26:32.265430+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3623","created_at":"2026-05-18T04:26:32.265430+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEKBCBD5I7CN","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEKBCBD5I7CNKUEP","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEKBCBD5","created_at":"2026-05-18T12:26:26.731475+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/CEKBCBD5I7CNKUEPRN4WUNUN6O","json":"https://pith.science/pith/CEKBCBD5I7CNKUEPRN4WUNUN6O.json","graph_json":"https://pith.science/api/pith-number/CEKBCBD5I7CNKUEPRN4WUNUN6O/graph.json","events_json":"https://pith.science/api/pith-number/CEKBCBD5I7CNKUEPRN4WUNUN6O/events.json","paper":"https://pith.science/paper/CEKBCBD5"},"agent_actions":{"view_html":"https://pith.science/pith/CEKBCBD5I7CNKUEPRN4WUNUN6O","download_json":"https://pith.science/pith/CEKBCBD5I7CNKUEPRN4WUNUN6O.json","view_paper":"https://pith.science/paper/CEKBCBD5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.3623&json=true","fetch_graph":"https://pith.science/api/pith-number/CEKBCBD5I7CNKUEPRN4WUNUN6O/graph.json","fetch_events":"https://pith.science/api/pith-number/CEKBCBD5I7CNKUEPRN4WUNUN6O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEKBCBD5I7CNKUEPRN4WUNUN6O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEKBCBD5I7CNKUEPRN4WUNUN6O/action/storage_attestation","attest_author":"https://pith.science/pith/CEKBCBD5I7CNKUEPRN4WUNUN6O/action/author_attestation","sign_citation":"https://pith.science/pith/CEKBCBD5I7CNKUEPRN4WUNUN6O/action/citation_signature","submit_replication":"https://pith.science/pith/CEKBCBD5I7CNKUEPRN4WUNUN6O/action/replication_record"}},"created_at":"2026-05-18T04:26:32.265430+00:00","updated_at":"2026-05-18T04:26:32.265430+00:00"}