{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:JLCEAFUN7XL6YG4N2HDRAYA7IJ","short_pith_number":"pith:JLCEAFUN","schema_version":"1.0","canonical_sha256":"4ac440168dfdd7ec1b8dd1c710601f4254183f03ee35739b70c94aef22635a20","source":{"kind":"arxiv","id":"1011.4116","version":1},"attestation_state":"computed","paper":{"title":"A strong Oka principle for embeddings of some planar domains into CxC*","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tyson Ritter","submitted_at":"2010-11-18T01:13:20Z","abstract_excerpt":"Gromov, in his seminal 1989 paper on the Oka principle, introduced the notion of an elliptic manifold and proved that every continuous map from a Stein manifold to an elliptic manifold is homotopic to a holomorphic map. We show that a much stronger Oka principle holds in the special case of maps from certain open Riemann surfaces called circular domains into CxC*, namely that every continuous map is homotopic to a proper holomorphic embedding. An important ingredient is a generalisation to CxC* of recent results of Wold and Forstneric on the long-standing problem of properly embedding open Rie"},"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":"1011.4116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-11-18T01:13:20Z","cross_cats_sorted":[],"title_canon_sha256":"8b161966398ba3386706a4678e6c3a5b9d3abd753114a3bbd6210cee22779b80","abstract_canon_sha256":"b21a7364627b6c3869b52231e1e01e517c139f8bf4a3b01b2a420573f937060e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:46.614572Z","signature_b64":"0j1bBbYL3LqjWlGyW/qAXds2nwCQGSdCQ8n7k5LCoothQ54AZTS5eY98NfJfyCzR6SfTlcQWphauPruRAGubDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ac440168dfdd7ec1b8dd1c710601f4254183f03ee35739b70c94aef22635a20","last_reissued_at":"2026-05-18T04:35:46.613979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:46.613979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A strong Oka principle for embeddings of some planar domains into CxC*","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tyson Ritter","submitted_at":"2010-11-18T01:13:20Z","abstract_excerpt":"Gromov, in his seminal 1989 paper on the Oka principle, introduced the notion of an elliptic manifold and proved that every continuous map from a Stein manifold to an elliptic manifold is homotopic to a holomorphic map. We show that a much stronger Oka principle holds in the special case of maps from certain open Riemann surfaces called circular domains into CxC*, namely that every continuous map is homotopic to a proper holomorphic embedding. An important ingredient is a generalisation to CxC* of recent results of Wold and Forstneric on the long-standing problem of properly embedding open Rie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4116","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":""},"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":"1011.4116","created_at":"2026-05-18T04:35:46.614075+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.4116v1","created_at":"2026-05-18T04:35:46.614075+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4116","created_at":"2026-05-18T04:35:46.614075+00:00"},{"alias_kind":"pith_short_12","alias_value":"JLCEAFUN7XL6","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JLCEAFUN7XL6YG4N","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JLCEAFUN","created_at":"2026-05-18T12:26:09.077623+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/JLCEAFUN7XL6YG4N2HDRAYA7IJ","json":"https://pith.science/pith/JLCEAFUN7XL6YG4N2HDRAYA7IJ.json","graph_json":"https://pith.science/api/pith-number/JLCEAFUN7XL6YG4N2HDRAYA7IJ/graph.json","events_json":"https://pith.science/api/pith-number/JLCEAFUN7XL6YG4N2HDRAYA7IJ/events.json","paper":"https://pith.science/paper/JLCEAFUN"},"agent_actions":{"view_html":"https://pith.science/pith/JLCEAFUN7XL6YG4N2HDRAYA7IJ","download_json":"https://pith.science/pith/JLCEAFUN7XL6YG4N2HDRAYA7IJ.json","view_paper":"https://pith.science/paper/JLCEAFUN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.4116&json=true","fetch_graph":"https://pith.science/api/pith-number/JLCEAFUN7XL6YG4N2HDRAYA7IJ/graph.json","fetch_events":"https://pith.science/api/pith-number/JLCEAFUN7XL6YG4N2HDRAYA7IJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JLCEAFUN7XL6YG4N2HDRAYA7IJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JLCEAFUN7XL6YG4N2HDRAYA7IJ/action/storage_attestation","attest_author":"https://pith.science/pith/JLCEAFUN7XL6YG4N2HDRAYA7IJ/action/author_attestation","sign_citation":"https://pith.science/pith/JLCEAFUN7XL6YG4N2HDRAYA7IJ/action/citation_signature","submit_replication":"https://pith.science/pith/JLCEAFUN7XL6YG4N2HDRAYA7IJ/action/replication_record"}},"created_at":"2026-05-18T04:35:46.614075+00:00","updated_at":"2026-05-18T04:35:46.614075+00:00"}