{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CTBM6OWOJ5CANEP35H44OEWSTG","short_pith_number":"pith:CTBM6OWO","schema_version":"1.0","canonical_sha256":"14c2cf3ace4f440691fbe9f9c712d29991d669d4107589910870579a347f3028","source":{"kind":"arxiv","id":"1605.05679","version":1},"attestation_state":"computed","paper":{"title":"Integrable deformations of local analytic fibrations with singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Bruno Scardua, Dominique Cerveau","submitted_at":"2016-05-18T18:21:28Z","abstract_excerpt":"We study analytic integrable deformations of the germ of a holomorphic foliation given by $df=0$ at the origin $0 \\in \\mathbb C^n, n \\geq 3$. We consider the case where $f$ is a germ of an irreducible and reduced holomorphic function. Our central hypotheses is that, {\\em outside of a dimension $\\leq n-3$ analytic subset $Y\\subset X$, the analytic hypersurface $X_f : (f=0)$ has only normal crossings singularities}. We then prove that, as germs, such deformations also exhibit a holomorphic first integral, depending analytically on the parameter of the deformation. This applies to the study of in"},"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":"1605.05679","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-18T18:21:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"8400e2cb5cfa7ebcb4745d7b7cc6b311fa1ef0947e09e6c5df0e8c3114237bdf","abstract_canon_sha256":"496d014073464d150d2552bc8fd08c7dd1ceedd2075860dbb07d730d0d67dca0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:30.041115Z","signature_b64":"4YiMYe5JqkJu5SQuCLEGGAm0B/rRB8rOyxJDZ6qNvwbZoMQUtqL8HOKroXZSRajjQRSJkkqn3Aezy2JeD3c9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14c2cf3ace4f440691fbe9f9c712d29991d669d4107589910870579a347f3028","last_reissued_at":"2026-05-18T01:14:30.040645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:30.040645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrable deformations of local analytic fibrations with singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Bruno Scardua, Dominique Cerveau","submitted_at":"2016-05-18T18:21:28Z","abstract_excerpt":"We study analytic integrable deformations of the germ of a holomorphic foliation given by $df=0$ at the origin $0 \\in \\mathbb C^n, n \\geq 3$. We consider the case where $f$ is a germ of an irreducible and reduced holomorphic function. Our central hypotheses is that, {\\em outside of a dimension $\\leq n-3$ analytic subset $Y\\subset X$, the analytic hypersurface $X_f : (f=0)$ has only normal crossings singularities}. We then prove that, as germs, such deformations also exhibit a holomorphic first integral, depending analytically on the parameter of the deformation. This applies to the study of in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05679","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":"1605.05679","created_at":"2026-05-18T01:14:30.040709+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05679v1","created_at":"2026-05-18T01:14:30.040709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05679","created_at":"2026-05-18T01:14:30.040709+00:00"},{"alias_kind":"pith_short_12","alias_value":"CTBM6OWOJ5CA","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CTBM6OWOJ5CANEP3","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CTBM6OWO","created_at":"2026-05-18T12:30:09.641336+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/CTBM6OWOJ5CANEP35H44OEWSTG","json":"https://pith.science/pith/CTBM6OWOJ5CANEP35H44OEWSTG.json","graph_json":"https://pith.science/api/pith-number/CTBM6OWOJ5CANEP35H44OEWSTG/graph.json","events_json":"https://pith.science/api/pith-number/CTBM6OWOJ5CANEP35H44OEWSTG/events.json","paper":"https://pith.science/paper/CTBM6OWO"},"agent_actions":{"view_html":"https://pith.science/pith/CTBM6OWOJ5CANEP35H44OEWSTG","download_json":"https://pith.science/pith/CTBM6OWOJ5CANEP35H44OEWSTG.json","view_paper":"https://pith.science/paper/CTBM6OWO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05679&json=true","fetch_graph":"https://pith.science/api/pith-number/CTBM6OWOJ5CANEP35H44OEWSTG/graph.json","fetch_events":"https://pith.science/api/pith-number/CTBM6OWOJ5CANEP35H44OEWSTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CTBM6OWOJ5CANEP35H44OEWSTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CTBM6OWOJ5CANEP35H44OEWSTG/action/storage_attestation","attest_author":"https://pith.science/pith/CTBM6OWOJ5CANEP35H44OEWSTG/action/author_attestation","sign_citation":"https://pith.science/pith/CTBM6OWOJ5CANEP35H44OEWSTG/action/citation_signature","submit_replication":"https://pith.science/pith/CTBM6OWOJ5CANEP35H44OEWSTG/action/replication_record"}},"created_at":"2026-05-18T01:14:30.040709+00:00","updated_at":"2026-05-18T01:14:30.040709+00:00"}