{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7QMP7ORCO3BXVDLDD7BRON7T7G","short_pith_number":"pith:7QMP7ORC","canonical_record":{"source":{"id":"1711.10174","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-28T08:35:59Z","cross_cats_sorted":[],"title_canon_sha256":"6f8234f77fca566bb715a70015c2b59ff79844d79b17cc94511b95bfca316ed3","abstract_canon_sha256":"61fda8ea5d0f6476d879769ebbbcd110a16c5cc236611fd8b8defe224f99bd8a"},"schema_version":"1.0"},"canonical_sha256":"fc18ffba2276c37a8d631fc31737f3f998d3a7327d57f0cb643aa093e4a5696a","source":{"kind":"arxiv","id":"1711.10174","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10174","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10174v2","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10174","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"7QMP7ORCO3BX","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7QMP7ORCO3BXVDLD","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7QMP7ORC","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7QMP7ORCO3BXVDLDD7BRON7T7G","target":"record","payload":{"canonical_record":{"source":{"id":"1711.10174","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-28T08:35:59Z","cross_cats_sorted":[],"title_canon_sha256":"6f8234f77fca566bb715a70015c2b59ff79844d79b17cc94511b95bfca316ed3","abstract_canon_sha256":"61fda8ea5d0f6476d879769ebbbcd110a16c5cc236611fd8b8defe224f99bd8a"},"schema_version":"1.0"},"canonical_sha256":"fc18ffba2276c37a8d631fc31737f3f998d3a7327d57f0cb643aa093e4a5696a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:30.567578Z","signature_b64":"5tyfxOMhtj/c6KFvQeDBB53gxv2ElfWrVYFFfEL/nmyV1B0gNJS46rqRPgQdimSBIbFbOdBSxdMicKKc6mxmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc18ffba2276c37a8d631fc31737f3f998d3a7327d57f0cb643aa093e4a5696a","last_reissued_at":"2026-05-18T00:17:30.567068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:30.567068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.10174","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hbZLR4dSaikGSKZ50ynnXRYnqHo/156b3s2EW421GWBvT8oIA6YqIqyFqlU+Z6ULoq8JgcO2aANoP8XNRCUfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:59:10.786478Z"},"content_sha256":"0774bcf3a88e5ab55453d206c30e713ea01078ebc196b0f753f4de851c11711b","schema_version":"1.0","event_id":"sha256:0774bcf3a88e5ab55453d206c30e713ea01078ebc196b0f753f4de851c11711b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7QMP7ORCO3BXVDLDD7BRON7T7G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of generic projective space bundles and algebraicity of foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Carolina Araujo, St\\'ephane Druel","submitted_at":"2017-11-28T08:35:59Z","abstract_excerpt":"In this paper we consider various notions of positivity for distributions on complex projective manifolds. We start by analyzing distributions having big slope with respect to curve classes, obtaining characterizations of generic projective space bundles in terms of movable curve classes. We then apply this result to investigate algebraicity of leaves of foliations, providing a lower bound for the algebraic rank of a foliation in terms of invariants measuring positivity. We classify foliations attaining this bound, and describe those whose algebraic rank slightly exceeds this bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10174","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WBa8/ExbfuP73iglBOTzWxmGedRabdUASsCZu8mlirSUXMvyknRxvMfUyE9lbiGcZUV5yAM/utwR3ccZg3mqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:59:10.787125Z"},"content_sha256":"7f1c6694af371f8d1df0645def8a37450affd4f711d5d1c6b493a225d2cc6897","schema_version":"1.0","event_id":"sha256:7f1c6694af371f8d1df0645def8a37450affd4f711d5d1c6b493a225d2cc6897"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QMP7ORCO3BXVDLDD7BRON7T7G/bundle.json","state_url":"https://pith.science/pith/7QMP7ORCO3BXVDLDD7BRON7T7G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QMP7ORCO3BXVDLDD7BRON7T7G/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":"2026-05-27T14:59:10Z","links":{"resolver":"https://pith.science/pith/7QMP7ORCO3BXVDLDD7BRON7T7G","bundle":"https://pith.science/pith/7QMP7ORCO3BXVDLDD7BRON7T7G/bundle.json","state":"https://pith.science/pith/7QMP7ORCO3BXVDLDD7BRON7T7G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QMP7ORCO3BXVDLDD7BRON7T7G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7QMP7ORCO3BXVDLDD7BRON7T7G","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":"61fda8ea5d0f6476d879769ebbbcd110a16c5cc236611fd8b8defe224f99bd8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-28T08:35:59Z","title_canon_sha256":"6f8234f77fca566bb715a70015c2b59ff79844d79b17cc94511b95bfca316ed3"},"schema_version":"1.0","source":{"id":"1711.10174","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10174","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10174v2","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10174","created_at":"2026-05-18T00:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"7QMP7ORCO3BX","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7QMP7ORCO3BXVDLD","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7QMP7ORC","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:7f1c6694af371f8d1df0645def8a37450affd4f711d5d1c6b493a225d2cc6897","target":"graph","created_at":"2026-05-18T00:17:30Z","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"},"paper":{"abstract_excerpt":"In this paper we consider various notions of positivity for distributions on complex projective manifolds. We start by analyzing distributions having big slope with respect to curve classes, obtaining characterizations of generic projective space bundles in terms of movable curve classes. We then apply this result to investigate algebraicity of leaves of foliations, providing a lower bound for the algebraic rank of a foliation in terms of invariants measuring positivity. We classify foliations attaining this bound, and describe those whose algebraic rank slightly exceeds this bound.","authors_text":"Carolina Araujo, St\\'ephane Druel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-28T08:35:59Z","title":"Characterization of generic projective space bundles and algebraicity of foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10174","kind":"arxiv","version":2},"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":"sha256:0774bcf3a88e5ab55453d206c30e713ea01078ebc196b0f753f4de851c11711b","target":"record","created_at":"2026-05-18T00:17:30Z","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":"61fda8ea5d0f6476d879769ebbbcd110a16c5cc236611fd8b8defe224f99bd8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-28T08:35:59Z","title_canon_sha256":"6f8234f77fca566bb715a70015c2b59ff79844d79b17cc94511b95bfca316ed3"},"schema_version":"1.0","source":{"id":"1711.10174","kind":"arxiv","version":2}},"canonical_sha256":"fc18ffba2276c37a8d631fc31737f3f998d3a7327d57f0cb643aa093e4a5696a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc18ffba2276c37a8d631fc31737f3f998d3a7327d57f0cb643aa093e4a5696a","first_computed_at":"2026-05-18T00:17:30.567068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:30.567068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5tyfxOMhtj/c6KFvQeDBB53gxv2ElfWrVYFFfEL/nmyV1B0gNJS46rqRPgQdimSBIbFbOdBSxdMicKKc6mxmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:30.567578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10174","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0774bcf3a88e5ab55453d206c30e713ea01078ebc196b0f753f4de851c11711b","sha256:7f1c6694af371f8d1df0645def8a37450affd4f711d5d1c6b493a225d2cc6897"],"state_sha256":"2879474df9b712b72823c0a585e9e5a08b12ae7ef8742ef49a49e0583664d4cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOwCy7fl+UwECHHwbwcZ26lMs2718ViQ5jy40HZeWjLBdj8bku1n0/RWLXFNhCTQ4PSQFcWtgg2bFs1NxO+iAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:59:10.790723Z","bundle_sha256":"94c0025bddcae0ea620989a9b94b2b9f8b497430c3bbcd0a508601185a2de815"}}