{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LHEUOQDGNPVN3LFHFQ37QZUSR3","short_pith_number":"pith:LHEUOQDG","schema_version":"1.0","canonical_sha256":"59c94740666beaddaca72c37f866928ee6b0afdf86e84671eea2d3fe2f364673","source":{"kind":"arxiv","id":"1608.03925","version":2},"attestation_state":"computed","paper":{"title":"Generating positive geometric entropy from recurrent leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Ponce","submitted_at":"2016-08-12T23:55:19Z","abstract_excerpt":"In this paper we introduce a new $C^r-$perturbation procedure, with respect to the $C^r$-Epstein topology, for $C^r$-foliations by surfaces. Using this perturbation procedure we show how one can use the existence of recurrent leaves of certain $C^r-$foliation $\\mathcal F$ to obtain a foliation $\\mathcal G$, $C^r-$close to $\\mathcal F$ in the $C^r-$Epstein topology, which has a resilient leaf. In particular, one can take advantage of recurrence property to construct examples of $C^r-$foliations by surfaces, $C^r-$close to each other and such that one of them has a resilient leaf while the other"},"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":"1608.03925","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-12T23:55:19Z","cross_cats_sorted":[],"title_canon_sha256":"267b7bcd8f09fc1fba9b633db8d4c4ce943c0d8f41df93e24394101ecdec87e6","abstract_canon_sha256":"4ae50952ea77508952e3270ad638dbfb604e6f2b3935012d174bf31dc1f735dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:33.195625Z","signature_b64":"agGDQ+PGx9mfG8QNOZSUant4UH0RMheRkbNT5udtQS5NNnmb+PtG/1iVnWV6MpllEKmbBss4I/IrANGu3UzBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59c94740666beaddaca72c37f866928ee6b0afdf86e84671eea2d3fe2f364673","last_reissued_at":"2026-05-18T00:36:33.194789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:33.194789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generating positive geometric entropy from recurrent leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Ponce","submitted_at":"2016-08-12T23:55:19Z","abstract_excerpt":"In this paper we introduce a new $C^r-$perturbation procedure, with respect to the $C^r$-Epstein topology, for $C^r$-foliations by surfaces. Using this perturbation procedure we show how one can use the existence of recurrent leaves of certain $C^r-$foliation $\\mathcal F$ to obtain a foliation $\\mathcal G$, $C^r-$close to $\\mathcal F$ in the $C^r-$Epstein topology, which has a resilient leaf. In particular, one can take advantage of recurrence property to construct examples of $C^r-$foliations by surfaces, $C^r-$close to each other and such that one of them has a resilient leaf while the other"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03925","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.03925","created_at":"2026-05-18T00:36:33.194903+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.03925v2","created_at":"2026-05-18T00:36:33.194903+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03925","created_at":"2026-05-18T00:36:33.194903+00:00"},{"alias_kind":"pith_short_12","alias_value":"LHEUOQDGNPVN","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LHEUOQDGNPVN3LFH","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LHEUOQDG","created_at":"2026-05-18T12:30:29.479603+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/LHEUOQDGNPVN3LFHFQ37QZUSR3","json":"https://pith.science/pith/LHEUOQDGNPVN3LFHFQ37QZUSR3.json","graph_json":"https://pith.science/api/pith-number/LHEUOQDGNPVN3LFHFQ37QZUSR3/graph.json","events_json":"https://pith.science/api/pith-number/LHEUOQDGNPVN3LFHFQ37QZUSR3/events.json","paper":"https://pith.science/paper/LHEUOQDG"},"agent_actions":{"view_html":"https://pith.science/pith/LHEUOQDGNPVN3LFHFQ37QZUSR3","download_json":"https://pith.science/pith/LHEUOQDGNPVN3LFHFQ37QZUSR3.json","view_paper":"https://pith.science/paper/LHEUOQDG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.03925&json=true","fetch_graph":"https://pith.science/api/pith-number/LHEUOQDGNPVN3LFHFQ37QZUSR3/graph.json","fetch_events":"https://pith.science/api/pith-number/LHEUOQDGNPVN3LFHFQ37QZUSR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LHEUOQDGNPVN3LFHFQ37QZUSR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LHEUOQDGNPVN3LFHFQ37QZUSR3/action/storage_attestation","attest_author":"https://pith.science/pith/LHEUOQDGNPVN3LFHFQ37QZUSR3/action/author_attestation","sign_citation":"https://pith.science/pith/LHEUOQDGNPVN3LFHFQ37QZUSR3/action/citation_signature","submit_replication":"https://pith.science/pith/LHEUOQDGNPVN3LFHFQ37QZUSR3/action/replication_record"}},"created_at":"2026-05-18T00:36:33.194903+00:00","updated_at":"2026-05-18T00:36:33.194903+00:00"}