{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AMLY3SMLWEL5SQICKYOK3OBEID","short_pith_number":"pith:AMLY3SML","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"},"canonical_sha256":"03178dc98bb117d94102561cadb82440f9e11b457bca99463b3f81d242a41134","source":{"kind":"arxiv","id":"2405.05464","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.05464","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"arxiv_version","alias_value":"2405.05464v1","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05464","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"pith_short_12","alias_value":"AMLY3SMLWEL5","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"pith_short_16","alias_value":"AMLY3SMLWEL5SQIC","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"pith_short_8","alias_value":"AMLY3SML","created_at":"2026-07-05T08:17:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AMLY3SMLWEL5SQICKYOK3OBEID","target":"record","payload":{"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"},"canonical_sha256":"03178dc98bb117d94102561cadb82440f9e11b457bca99463b3f81d242a41134","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"},"source_kind":"arxiv","source_id":"2405.05464","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:17:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ly0a+2wOzH3e6X/GrDVBqRjdYPKdNtND21SKw5wPhtQ8KCTt2iJ0JlxtHX6Fckwz/UKQal3MZ17np7r3lXCBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T20:41:52.707720Z"},"content_sha256":"bea5185090daf4fd328cae5b4e112ae76de2b7b4eeac47c7a93c1b063ffd337d","schema_version":"1.0","event_id":"sha256:bea5185090daf4fd328cae5b4e112ae76de2b7b4eeac47c7a93c1b063ffd337d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AMLY3SMLWEL5SQICKYOK3OBEID","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:17:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZFbMWPEw5UCwn7z2PJwJPVYk7Co+9Z3xGNWEcclnbKLXunyv5nDrRqIlQW11anDQRstAHI8HDpGWB3PVo3uLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T20:41:52.708719Z"},"content_sha256":"01ab079f11040b82ab31de865d5c77ece00801f93fdece9d2cc5e123cdc3b853","schema_version":"1.0","event_id":"sha256:01ab079f11040b82ab31de865d5c77ece00801f93fdece9d2cc5e123cdc3b853"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/bundle.json","state_url":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMLY3SMLWEL5SQICKYOK3OBEID/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T20:41:52Z","links":{"resolver":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID","bundle":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/bundle.json","state":"https://pith.science/pith/AMLY3SMLWEL5SQICKYOK3OBEID/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMLY3SMLWEL5SQICKYOK3OBEID/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AMLY3SMLWEL5SQICKYOK3OBEID","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1be43647129b2bafbe3c086736d6033cf2c32d6e9d9eed2510aeacfc479610e1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-05-08T23:41:32Z","title_canon_sha256":"1fdec95593f80b4bedcb9fe02897831baa8fe5d573c135ff09fc2c094c7bdfe0"},"schema_version":"1.0","source":{"id":"2405.05464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.05464","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"arxiv_version","alias_value":"2405.05464v1","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05464","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"pith_short_12","alias_value":"AMLY3SMLWEL5","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"pith_short_16","alias_value":"AMLY3SMLWEL5SQIC","created_at":"2026-07-05T08:17:18Z"},{"alias_kind":"pith_short_8","alias_value":"AMLY3SML","created_at":"2026-07-05T08:17:18Z"}],"graph_snapshots":[{"event_id":"sha256:01ab079f11040b82ab31de865d5c77ece00801f93fdece9d2cc5e123cdc3b853","target":"graph","created_at":"2026-07-05T08:17:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.05464/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 $","authors_text":"Samir Bedrouni","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-05-08T23:41:32Z","title":"Platitude des tissus duaux de certains pr\\'e-feuilletages convexes du plan projectif complexe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05464","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bea5185090daf4fd328cae5b4e112ae76de2b7b4eeac47c7a93c1b063ffd337d","target":"record","created_at":"2026-07-05T08:17:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1be43647129b2bafbe3c086736d6033cf2c32d6e9d9eed2510aeacfc479610e1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-05-08T23:41:32Z","title_canon_sha256":"1fdec95593f80b4bedcb9fe02897831baa8fe5d573c135ff09fc2c094c7bdfe0"},"schema_version":"1.0","source":{"id":"2405.05464","kind":"arxiv","version":1}},"canonical_sha256":"03178dc98bb117d94102561cadb82440f9e11b457bca99463b3f81d242a41134","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03178dc98bb117d94102561cadb82440f9e11b457bca99463b3f81d242a41134","first_computed_at":"2026-07-05T08:17:18.676653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:17:18.676653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HNPxtwHgYCmGh0Q2vo/Qf6PWE7kpaTCqbxBwHQ6mvY0QaypwIsEbYZ2Kj0Wz2yJHEQqZ5sheFTTts05g8i7NBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:17:18.677009Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.05464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bea5185090daf4fd328cae5b4e112ae76de2b7b4eeac47c7a93c1b063ffd337d","sha256:01ab079f11040b82ab31de865d5c77ece00801f93fdece9d2cc5e123cdc3b853"],"state_sha256":"53236b62dff664f26e49376e4bcf3352e9a128e0816ab0da09b49ae6c8c63709"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbhQMpNq8qmeyblICpkJ4nRlPT5hd3ceJ/2XK0v4l7pp+RHG1dCpsXss4Lfey5cYxfTb9vzUe/rrZmpMiW0ABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T20:41:52.770876Z","bundle_sha256":"27ffa5fd7669cc8dd47c28370122a453816dd5f95380908da2e2f529d44a631e"}}