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Using the leafwise Poincar\\'e metric, we show that H is integrable with respect to T.\n  Consequently, we infer the existence of the Lyapunov exponent functio"},"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":"1403.7688","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-30T01:38:26Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"2b3225f95c37c61efe12d7c1ccbeeeb08d0efc26c01f9a4118034dc7765e18f3","abstract_canon_sha256":"4c91a2b1091f858c9773c1d61c7b77520d3d9ec3746d42a41c1d802b478c05f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:22.758006Z","signature_b64":"6Eyhge4ISoE/kDQ/HRb9bFZsM5dC+w3/5Wv/n8XAK48wJy8wlCeR/Ja8Vmz5YzTyMwvDca91AjP7AasxktxgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e379a210bb5e5019ef802a1098c4b47af01ce61a3cc79e4a6c863ae6d85b14c","last_reissued_at":"2026-05-18T00:27:22.757523Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:22.757523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular holomorphic foliations by curves I: Integrability of holonomy cocycle in dimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.DS","authors_text":"Viet-Anh Nguyen","submitted_at":"2014-03-30T01:38:26Z","abstract_excerpt":"We study the holonomy cocycle H of a holomorphic foliation \\Fc by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions:\n  1) its singularities E are all hyperbolic;\n  2) there is no holomorphic non-constant map \\C\\to X such that out of E the image of \\C is locally contained in a leaf.\n  Let T be a harmonic current tangent to \\Fc which does not give mass to any invariant analytic curve. Using the leafwise Poincar\\'e metric, we show that H is integrable with respect to T.\n  Consequently, we infer the existence of the Lyapunov exponent functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7688","kind":"arxiv","version":4},"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":"1403.7688","created_at":"2026-05-18T00:27:22.757596+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.7688v4","created_at":"2026-05-18T00:27:22.757596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7688","created_at":"2026-05-18T00:27:22.757596+00:00"},{"alias_kind":"pith_short_12","alias_value":"FY3ZUIILWXSQ","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FY3ZUIILWXSQDHXY","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FY3ZUIIL","created_at":"2026-05-18T12:28:28.263976+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/FY3ZUIILWXSQDHXYAKQQTDCLI6","json":"https://pith.science/pith/FY3ZUIILWXSQDHXYAKQQTDCLI6.json","graph_json":"https://pith.science/api/pith-number/FY3ZUIILWXSQDHXYAKQQTDCLI6/graph.json","events_json":"https://pith.science/api/pith-number/FY3ZUIILWXSQDHXYAKQQTDCLI6/events.json","paper":"https://pith.science/paper/FY3ZUIIL"},"agent_actions":{"view_html":"https://pith.science/pith/FY3ZUIILWXSQDHXYAKQQTDCLI6","download_json":"https://pith.science/pith/FY3ZUIILWXSQDHXYAKQQTDCLI6.json","view_paper":"https://pith.science/paper/FY3ZUIIL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.7688&json=true","fetch_graph":"https://pith.science/api/pith-number/FY3ZUIILWXSQDHXYAKQQTDCLI6/graph.json","fetch_events":"https://pith.science/api/pith-number/FY3ZUIILWXSQDHXYAKQQTDCLI6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FY3ZUIILWXSQDHXYAKQQTDCLI6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FY3ZUIILWXSQDHXYAKQQTDCLI6/action/storage_attestation","attest_author":"https://pith.science/pith/FY3ZUIILWXSQDHXYAKQQTDCLI6/action/author_attestation","sign_citation":"https://pith.science/pith/FY3ZUIILWXSQDHXYAKQQTDCLI6/action/citation_signature","submit_replication":"https://pith.science/pith/FY3ZUIILWXSQDHXYAKQQTDCLI6/action/replication_record"}},"created_at":"2026-05-18T00:27:22.757596+00:00","updated_at":"2026-05-18T00:27:22.757596+00:00"}