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Then for every point $p\\in M$, for every real-algebraic subset $S'\\subset \\C^N\\times\\C^{N'}$ and every positive integer $\\ell$, if $f\\colon (\\C^N,p)\\to \\C^{N'}$ is a germ of a holomorphic map such that ${\\rm Graph}\\, f \\cap (M\\times \\C^{N'})\\subset S'$, then there exists a germ of a complex-algebraic map $f^\\ell \\colon (\\C^N,p)\\to \\C^{N'}$ such that ${\\rm Gr"},"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":"1202.2463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-02-11T19:53:51Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"43cb517240f6ed252f788adb5d836b2a58ebc97c3395e8fc929dc128a724da16","abstract_canon_sha256":"776a26c3d05a7fd7a22e48694db66c78c0ab98d4ff72c2de80adb58077dbed11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:19.944470Z","signature_b64":"LJxEh/7oA+z0BMFwf7g8qBiDuw28vbZNIN+C6g0Kfh+Exk1C+mssqOFyCQE9VNyzbb8o8Z+ounAZAzCu7jNSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7540d8379c7e5e6d396d52fc8e3cc3f26d8628f8d51277768a5cd41c54072815","last_reissued_at":"2026-05-18T03:53:19.943765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:19.943765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic approximation in CR geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Nordine Mir","submitted_at":"2012-02-11T19:53:51Z","abstract_excerpt":"We prove the following CR version of Artin's approximation theorem for holomorphic mappings between real-algebraic sets in complex space. 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Then for every point $p\\in M$, for every real-algebraic subset $S'\\subset \\C^N\\times\\C^{N'}$ and every positive integer $\\ell$, if $f\\colon (\\C^N,p)\\to \\C^{N'}$ is a germ of a holomorphic map such that ${\\rm Graph}\\, f \\cap (M\\times \\C^{N'})\\subset S'$, then there exists a germ of a complex-algebraic map $f^\\ell \\colon (\\C^N,p)\\to \\C^{N'}$ such that ${\\rm Gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2463","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":"1202.2463","created_at":"2026-05-18T03:53:19.943871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.2463v1","created_at":"2026-05-18T03:53:19.943871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2463","created_at":"2026-05-18T03:53:19.943871+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVANQN44PZPG","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVANQN44PZPG2OLN","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVANQN44","created_at":"2026-05-18T12:27:16.716162+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/OVANQN44PZPG2OLNKL6I4PGD6J","json":"https://pith.science/pith/OVANQN44PZPG2OLNKL6I4PGD6J.json","graph_json":"https://pith.science/api/pith-number/OVANQN44PZPG2OLNKL6I4PGD6J/graph.json","events_json":"https://pith.science/api/pith-number/OVANQN44PZPG2OLNKL6I4PGD6J/events.json","paper":"https://pith.science/paper/OVANQN44"},"agent_actions":{"view_html":"https://pith.science/pith/OVANQN44PZPG2OLNKL6I4PGD6J","download_json":"https://pith.science/pith/OVANQN44PZPG2OLNKL6I4PGD6J.json","view_paper":"https://pith.science/paper/OVANQN44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.2463&json=true","fetch_graph":"https://pith.science/api/pith-number/OVANQN44PZPG2OLNKL6I4PGD6J/graph.json","fetch_events":"https://pith.science/api/pith-number/OVANQN44PZPG2OLNKL6I4PGD6J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVANQN44PZPG2OLNKL6I4PGD6J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVANQN44PZPG2OLNKL6I4PGD6J/action/storage_attestation","attest_author":"https://pith.science/pith/OVANQN44PZPG2OLNKL6I4PGD6J/action/author_attestation","sign_citation":"https://pith.science/pith/OVANQN44PZPG2OLNKL6I4PGD6J/action/citation_signature","submit_replication":"https://pith.science/pith/OVANQN44PZPG2OLNKL6I4PGD6J/action/replication_record"}},"created_at":"2026-05-18T03:53:19.943871+00:00","updated_at":"2026-05-18T03:53:19.943871+00:00"}