{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:25C3DA4D2JMXZY2HR76XO6QNDB","short_pith_number":"pith:25C3DA4D","schema_version":"1.0","canonical_sha256":"d745b18383d2597ce3478ffd777a0d186a5cdc210c35f3fbf60e8fc14703c77e","source":{"kind":"arxiv","id":"1706.09306","version":2},"attestation_state":"computed","paper":{"title":"Exotic holomorphic Engel structures on C4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Nicola Pia, Rui Coelho","submitted_at":"2017-06-28T14:10:48Z","abstract_excerpt":"A holomorphic Engel structure determines a flag of distributions $\\mathcal{W}\\subset \\mathcal{D}\\subset \\mathcal{E}$. We construct examples of Engel structures on $\\mathbf{C}^4$ such that each of these distributions is hyperbolic in the sense that it has no tangent copies of $\\mathbf{C}$. We also construct two infinite families of pairwise non-isomorphic Engel structures on $\\mathbf{C}^4$ by controlling the curves $f:\\mathbf{C}\\to \\mathbf{C}^4$ tangent to $\\mathcal{W}$. The first is characterised by the topology of the set of points in $\\mathbf{C}^4$ admitting $\\mathcal{W}$-lines, and the seco"},"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":"1706.09306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-28T14:10:48Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6f196bc66864e6bd221bb269ed87a3f73b8bb5f237c8f4dda20d45596e7fa3c9","abstract_canon_sha256":"2ee3fcb1b49b1f1c1335e2d7fa113f0adb59c6db0a48b72bb21992fb9d28c59c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:02.913833Z","signature_b64":"IjcmZBiUMdjpLSQ5Rghj3WBwN6cy3PLniiB0+lClbH4CncuEOPb8l/I2DY+RLos4rrw0QMIHDB5PTGZfiFYMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d745b18383d2597ce3478ffd777a0d186a5cdc210c35f3fbf60e8fc14703c77e","last_reissued_at":"2026-05-18T00:40:02.913159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:02.913159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exotic holomorphic Engel structures on C4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Nicola Pia, Rui Coelho","submitted_at":"2017-06-28T14:10:48Z","abstract_excerpt":"A holomorphic Engel structure determines a flag of distributions $\\mathcal{W}\\subset \\mathcal{D}\\subset \\mathcal{E}$. We construct examples of Engel structures on $\\mathbf{C}^4$ such that each of these distributions is hyperbolic in the sense that it has no tangent copies of $\\mathbf{C}$. We also construct two infinite families of pairwise non-isomorphic Engel structures on $\\mathbf{C}^4$ by controlling the curves $f:\\mathbf{C}\\to \\mathbf{C}^4$ tangent to $\\mathcal{W}$. The first is characterised by the topology of the set of points in $\\mathbf{C}^4$ admitting $\\mathcal{W}$-lines, and the seco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09306","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":"1706.09306","created_at":"2026-05-18T00:40:02.913290+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09306v2","created_at":"2026-05-18T00:40:02.913290+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09306","created_at":"2026-05-18T00:40:02.913290+00:00"},{"alias_kind":"pith_short_12","alias_value":"25C3DA4D2JMX","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"25C3DA4D2JMXZY2H","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"25C3DA4D","created_at":"2026-05-18T12:30:55.937587+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/25C3DA4D2JMXZY2HR76XO6QNDB","json":"https://pith.science/pith/25C3DA4D2JMXZY2HR76XO6QNDB.json","graph_json":"https://pith.science/api/pith-number/25C3DA4D2JMXZY2HR76XO6QNDB/graph.json","events_json":"https://pith.science/api/pith-number/25C3DA4D2JMXZY2HR76XO6QNDB/events.json","paper":"https://pith.science/paper/25C3DA4D"},"agent_actions":{"view_html":"https://pith.science/pith/25C3DA4D2JMXZY2HR76XO6QNDB","download_json":"https://pith.science/pith/25C3DA4D2JMXZY2HR76XO6QNDB.json","view_paper":"https://pith.science/paper/25C3DA4D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09306&json=true","fetch_graph":"https://pith.science/api/pith-number/25C3DA4D2JMXZY2HR76XO6QNDB/graph.json","fetch_events":"https://pith.science/api/pith-number/25C3DA4D2JMXZY2HR76XO6QNDB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/25C3DA4D2JMXZY2HR76XO6QNDB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/25C3DA4D2JMXZY2HR76XO6QNDB/action/storage_attestation","attest_author":"https://pith.science/pith/25C3DA4D2JMXZY2HR76XO6QNDB/action/author_attestation","sign_citation":"https://pith.science/pith/25C3DA4D2JMXZY2HR76XO6QNDB/action/citation_signature","submit_replication":"https://pith.science/pith/25C3DA4D2JMXZY2HR76XO6QNDB/action/replication_record"}},"created_at":"2026-05-18T00:40:02.913290+00:00","updated_at":"2026-05-18T00:40:02.913290+00:00"}