{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NVZUNFML5N72IXKUHZFKQFMAXS","short_pith_number":"pith:NVZUNFML","schema_version":"1.0","canonical_sha256":"6d7346958beb7fa45d543e4aa81580bcb3de9136581c1fce4679b6d5b97b2e72","source":{"kind":"arxiv","id":"1111.2364","version":1},"attestation_state":"computed","paper":{"title":"Generic Pseudogroups on (C,0) and the Topology of Leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Helena Reis, Jean-Fran\\c{c}ois Mattei, Julio C. Rebelo","submitted_at":"2011-11-09T23:27:20Z","abstract_excerpt":"We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about $0 \\in \\mathbb{C}$ is free in the sense of pseudogroups even if the class of conjugacy of the generators is fixed. This result has a number of consequences on the topology of leaves for a (singular) holomorphic foliation defined on a neighborhood of an invariant curve. In particular in the classical and simplest case arising from local foliations possessing a unique separatrix that is given by a cusp of the form $\\{y^2-x^{2k+1}=0\\}$, our results allow us to settle the problem of showing that a generic"},"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":"1111.2364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-09T23:27:20Z","cross_cats_sorted":[],"title_canon_sha256":"6f89f81584763b1d11bd30ec22a09d6af828d8366044c0d8969a836b5350cf85","abstract_canon_sha256":"9360bc210de3eb380e22e88f771a37fb790f2f07ebce576ba173c5a739d3659b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:34.350581Z","signature_b64":"cJ8UwKOL9RsdgCKomo1cM71iR8Ov37NKmGgE/P9c0O6F+QMN/jEFvs4cLcXdetrLa9EDA2l17CqxVh08B6t+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d7346958beb7fa45d543e4aa81580bcb3de9136581c1fce4679b6d5b97b2e72","last_reissued_at":"2026-05-18T04:08:34.349949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:34.349949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generic Pseudogroups on (C,0) and the Topology of Leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Helena Reis, Jean-Fran\\c{c}ois Mattei, Julio C. Rebelo","submitted_at":"2011-11-09T23:27:20Z","abstract_excerpt":"We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about $0 \\in \\mathbb{C}$ is free in the sense of pseudogroups even if the class of conjugacy of the generators is fixed. This result has a number of consequences on the topology of leaves for a (singular) holomorphic foliation defined on a neighborhood of an invariant curve. In particular in the classical and simplest case arising from local foliations possessing a unique separatrix that is given by a cusp of the form $\\{y^2-x^{2k+1}=0\\}$, our results allow us to settle the problem of showing that a generic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2364","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":"1111.2364","created_at":"2026-05-18T04:08:34.350029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.2364v1","created_at":"2026-05-18T04:08:34.350029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2364","created_at":"2026-05-18T04:08:34.350029+00:00"},{"alias_kind":"pith_short_12","alias_value":"NVZUNFML5N72","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NVZUNFML5N72IXKU","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NVZUNFML","created_at":"2026-05-18T12:26:37.096874+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/NVZUNFML5N72IXKUHZFKQFMAXS","json":"https://pith.science/pith/NVZUNFML5N72IXKUHZFKQFMAXS.json","graph_json":"https://pith.science/api/pith-number/NVZUNFML5N72IXKUHZFKQFMAXS/graph.json","events_json":"https://pith.science/api/pith-number/NVZUNFML5N72IXKUHZFKQFMAXS/events.json","paper":"https://pith.science/paper/NVZUNFML"},"agent_actions":{"view_html":"https://pith.science/pith/NVZUNFML5N72IXKUHZFKQFMAXS","download_json":"https://pith.science/pith/NVZUNFML5N72IXKUHZFKQFMAXS.json","view_paper":"https://pith.science/paper/NVZUNFML","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.2364&json=true","fetch_graph":"https://pith.science/api/pith-number/NVZUNFML5N72IXKUHZFKQFMAXS/graph.json","fetch_events":"https://pith.science/api/pith-number/NVZUNFML5N72IXKUHZFKQFMAXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NVZUNFML5N72IXKUHZFKQFMAXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NVZUNFML5N72IXKUHZFKQFMAXS/action/storage_attestation","attest_author":"https://pith.science/pith/NVZUNFML5N72IXKUHZFKQFMAXS/action/author_attestation","sign_citation":"https://pith.science/pith/NVZUNFML5N72IXKUHZFKQFMAXS/action/citation_signature","submit_replication":"https://pith.science/pith/NVZUNFML5N72IXKUHZFKQFMAXS/action/replication_record"}},"created_at":"2026-05-18T04:08:34.350029+00:00","updated_at":"2026-05-18T04:08:34.350029+00:00"}