{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:AMLY3SMLWEL5SQICKYOK3OBEID","short_pith_number":"pith:AMLY3SML","schema_version":"1.0","canonical_sha256":"03178dc98bb117d94102561cadb82440f9e11b457bca99463b3f81d242a41134","source":{"kind":"arxiv","id":"2405.05464","version":1},"attestation_state":"computed","paper":{"title":"Platitude des tissus duaux de certains pr\\'e-feuilletages convexes du plan projectif complexe","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Samir Bedrouni","submitted_at":"2024-05-08T23:41:32Z","abstract_excerpt":"A holomorphic pre-foliation $\\mathscr{F}=\\mathcal{C}\\boxtimes\\mathcal{F}$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$ is the data of a reduced complex projective curve $\\mathcal{C}$ of $\\mathbb{P}^{2}_{\\mathbb{C}}$ and a holomorphic foliation $\\mathcal{F}$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$. When the foliation $\\mathcal{F}$ is convex and the curve $\\mathcal{C}$ is invariant by $\\mathcal{F}$, we speak of convex pre-foliation. In a previous paper, we showed that if a foliation $\\mathcal{F}$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$ is reduced convex or homogeneous convex and if $\\mathcal{C}$ is an invariant line of $"},"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":"2405.05464","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-05-08T23:41:32Z","cross_cats_sorted":[],"title_canon_sha256":"1fdec95593f80b4bedcb9fe02897831baa8fe5d573c135ff09fc2c094c7bdfe0","abstract_canon_sha256":"1be43647129b2bafbe3c086736d6033cf2c32d6e9d9eed2510aeacfc479610e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:18.677009Z","signature_b64":"HNPxtwHgYCmGh0Q2vo/Qf6PWE7kpaTCqbxBwHQ6mvY0QaypwIsEbYZ2Kj0Wz2yJHEQqZ5sheFTTts05g8i7NBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03178dc98bb117d94102561cadb82440f9e11b457bca99463b3f81d242a41134","last_reissued_at":"2026-07-05T08:17:18.676653Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:18.676653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Platitude des tissus duaux de certains pr\\'e-feuilletages convexes du plan projectif complexe","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Samir Bedrouni","submitted_at":"2024-05-08T23:41:32Z","abstract_excerpt":"A holomorphic pre-foliation $\\mathscr{F}=\\mathcal{C}\\boxtimes\\mathcal{F}$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$ is the data of a reduced complex projective curve $\\mathcal{C}$ of $\\mathbb{P}^{2}_{\\mathbb{C}}$ and a holomorphic foliation $\\mathcal{F}$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$. When the foliation $\\mathcal{F}$ is convex and the curve $\\mathcal{C}$ is invariant by $\\mathcal{F}$, we speak of convex pre-foliation. In a previous paper, we showed that if a foliation $\\mathcal{F}$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$ is reduced convex or homogeneous convex and if $\\mathcal{C}$ is an invariant line of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05464","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.05464/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2405.05464","created_at":"2026-07-05T08:17:18.676709+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.05464v1","created_at":"2026-07-05T08:17:18.676709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05464","created_at":"2026-07-05T08:17:18.676709+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMLY3SMLWEL5","created_at":"2026-07-05T08:17:18.676709+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMLY3SMLWEL5SQIC","created_at":"2026-07-05T08:17:18.676709+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMLY3SML","created_at":"2026-07-05T08:17:18.676709+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.07944","citing_title":"Homogeneous pre-foliations of co-degree one and degree four on the projective plane","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID","json":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID.json","graph_json":"https://pith.science/api/pith-number/AMLY3SMLWEL5SQICKYOK3OBEID/graph.json","events_json":"https://pith.science/api/pith-number/AMLY3SMLWEL5SQICKYOK3OBEID/events.json","paper":"https://pith.science/paper/AMLY3SML"},"agent_actions":{"view_html":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID","download_json":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID.json","view_paper":"https://pith.science/paper/AMLY3SML","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.05464&json=true","fetch_graph":"https://pith.science/api/pith-number/AMLY3SMLWEL5SQICKYOK3OBEID/graph.json","fetch_events":"https://pith.science/api/pith-number/AMLY3SMLWEL5SQICKYOK3OBEID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/action/storage_attestation","attest_author":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/action/author_attestation","sign_citation":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/action/citation_signature","submit_replication":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/action/replication_record"}},"created_at":"2026-07-05T08:17:18.676709+00:00","updated_at":"2026-07-05T08:17:18.676709+00:00"}