{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PMNWNIMTCT2UZU6EPM7VABAKLW","short_pith_number":"pith:PMNWNIMT","schema_version":"1.0","canonical_sha256":"7b1b66a19314f54cd3c47b3f50040a5d8ce371a65d1513b2c7c0f8ada8e41a32","source":{"kind":"arxiv","id":"1104.1893","version":1},"attestation_state":"computed","paper":{"title":"Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into $\\mathbb{C}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Antonio Alarcon, Francisco J. Lopez","submitted_at":"2011-04-11T09:52:17Z","abstract_excerpt":"We prove that given an open Riemann surface $N,$ there exists an open domain $M\\subset N$ homeomorphic to $N$ which properly holomorphically embeds in $\\mathbb{C}^2.$ Furthermore, $M$ can be chosen with hyperbolic conformal type. In particular, any open orientable surface admits a complex structure properly holomorphically embedding into $\\mathbb{C}^2.$"},"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":"1104.1893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-04-11T09:52:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"32f2404764b04c4c14bb2cfb8d3ec38670822cd8094b805482ae04527ccd9abe","abstract_canon_sha256":"07f3c2607d4c3a72dd6b14c9c54441574debb6bc88e72ee0535041b6331b4340"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:10.074004Z","signature_b64":"ReiDh/b8IbMYKhXVXC6MjaBxPz4WMAZKQ5wq9Rd8kQbN387coPdfufRmw9GNN45UmcutkIhAYVcOU/BlC5S/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b1b66a19314f54cd3c47b3f50040a5d8ce371a65d1513b2c7c0f8ada8e41a32","last_reissued_at":"2026-05-18T02:22:10.073486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:10.073486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into $\\mathbb{C}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Antonio Alarcon, Francisco J. Lopez","submitted_at":"2011-04-11T09:52:17Z","abstract_excerpt":"We prove that given an open Riemann surface $N,$ there exists an open domain $M\\subset N$ homeomorphic to $N$ which properly holomorphically embeds in $\\mathbb{C}^2.$ Furthermore, $M$ can be chosen with hyperbolic conformal type. In particular, any open orientable surface admits a complex structure properly holomorphically embedding into $\\mathbb{C}^2.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1893","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":"1104.1893","created_at":"2026-05-18T02:22:10.073566+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.1893v1","created_at":"2026-05-18T02:22:10.073566+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1893","created_at":"2026-05-18T02:22:10.073566+00:00"},{"alias_kind":"pith_short_12","alias_value":"PMNWNIMTCT2U","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PMNWNIMTCT2UZU6E","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PMNWNIMT","created_at":"2026-05-18T12:26:39.201973+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/PMNWNIMTCT2UZU6EPM7VABAKLW","json":"https://pith.science/pith/PMNWNIMTCT2UZU6EPM7VABAKLW.json","graph_json":"https://pith.science/api/pith-number/PMNWNIMTCT2UZU6EPM7VABAKLW/graph.json","events_json":"https://pith.science/api/pith-number/PMNWNIMTCT2UZU6EPM7VABAKLW/events.json","paper":"https://pith.science/paper/PMNWNIMT"},"agent_actions":{"view_html":"https://pith.science/pith/PMNWNIMTCT2UZU6EPM7VABAKLW","download_json":"https://pith.science/pith/PMNWNIMTCT2UZU6EPM7VABAKLW.json","view_paper":"https://pith.science/paper/PMNWNIMT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.1893&json=true","fetch_graph":"https://pith.science/api/pith-number/PMNWNIMTCT2UZU6EPM7VABAKLW/graph.json","fetch_events":"https://pith.science/api/pith-number/PMNWNIMTCT2UZU6EPM7VABAKLW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PMNWNIMTCT2UZU6EPM7VABAKLW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PMNWNIMTCT2UZU6EPM7VABAKLW/action/storage_attestation","attest_author":"https://pith.science/pith/PMNWNIMTCT2UZU6EPM7VABAKLW/action/author_attestation","sign_citation":"https://pith.science/pith/PMNWNIMTCT2UZU6EPM7VABAKLW/action/citation_signature","submit_replication":"https://pith.science/pith/PMNWNIMTCT2UZU6EPM7VABAKLW/action/replication_record"}},"created_at":"2026-05-18T02:22:10.073566+00:00","updated_at":"2026-05-18T02:22:10.073566+00:00"}