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Assume $F$ does not send a neighborhood of $M_\\ell$ in $\\mathbf C^n$ into $H_\\ell^N$. We show that $F$ is necessarily CR transversal to $M_\\ell$ at any point. Equivalently, we show that $F$ is a local CR embedding from $M_\\ell$ into $H_\\ell^N$."},"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":"1410.4116","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-15T16:32:10Z","cross_cats_sorted":[],"title_canon_sha256":"ee59e8cc626b6534ece9fcdd1302433039a96e8c9b51573b581480d5a55f7366","abstract_canon_sha256":"e2cf1c226e2bbe1556dc51216f0552ebc2d6d9fef5dbb92047a244945efd9e28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:55.287548Z","signature_b64":"XMlbWCxVNifS3hua+Z2TvSTkRQYA3YsCeb292m3JZJ4asSvLV0+PMJwxqE7mbbtjFs1wp+08Ia9Wbp9UKnPIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecd53436e94748290da09229c252ba59e9006b651f1d8ced23284b8b7fd842f2","last_reissued_at":"2026-05-18T02:39:55.287119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:55.287119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the CR transversality of holomorphic maps into hyperquadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Xiaojun Huang, Yuan Zhang","submitted_at":"2014-10-15T16:32:10Z","abstract_excerpt":"Let $M_\\ell$ be a smooth Levi-nondegenerate hypersurface of signature $\\ell$ in $\\mathbf C^n$ with $ n\\ge 3$, and write $H_\\ell^N$ for the standard hyperquadric of the same signature in $\\mathbf C^N$ with $N-n< \\frac{n-1}{2}$. Let $F$ be a holomorphic map sending $M_\\ell$ into $H_\\ell^N$. Assume $F$ does not send a neighborhood of $M_\\ell$ in $\\mathbf C^n$ into $H_\\ell^N$. We show that $F$ is necessarily CR transversal to $M_\\ell$ at any point. Equivalently, we show that $F$ is a local CR embedding from $M_\\ell$ into $H_\\ell^N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4116","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":"1410.4116","created_at":"2026-05-18T02:39:55.287184+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.4116v2","created_at":"2026-05-18T02:39:55.287184+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4116","created_at":"2026-05-18T02:39:55.287184+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TKTINXJI5EC","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TKTINXJI5ECSDNA","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TKTINXJ","created_at":"2026-05-18T12:28:16.859392+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/5TKTINXJI5ECSDNASIU4EUV2LH","json":"https://pith.science/pith/5TKTINXJI5ECSDNASIU4EUV2LH.json","graph_json":"https://pith.science/api/pith-number/5TKTINXJI5ECSDNASIU4EUV2LH/graph.json","events_json":"https://pith.science/api/pith-number/5TKTINXJI5ECSDNASIU4EUV2LH/events.json","paper":"https://pith.science/paper/5TKTINXJ"},"agent_actions":{"view_html":"https://pith.science/pith/5TKTINXJI5ECSDNASIU4EUV2LH","download_json":"https://pith.science/pith/5TKTINXJI5ECSDNASIU4EUV2LH.json","view_paper":"https://pith.science/paper/5TKTINXJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.4116&json=true","fetch_graph":"https://pith.science/api/pith-number/5TKTINXJI5ECSDNASIU4EUV2LH/graph.json","fetch_events":"https://pith.science/api/pith-number/5TKTINXJI5ECSDNASIU4EUV2LH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TKTINXJI5ECSDNASIU4EUV2LH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TKTINXJI5ECSDNASIU4EUV2LH/action/storage_attestation","attest_author":"https://pith.science/pith/5TKTINXJI5ECSDNASIU4EUV2LH/action/author_attestation","sign_citation":"https://pith.science/pith/5TKTINXJI5ECSDNASIU4EUV2LH/action/citation_signature","submit_replication":"https://pith.science/pith/5TKTINXJI5ECSDNASIU4EUV2LH/action/replication_record"}},"created_at":"2026-05-18T02:39:55.287184+00:00","updated_at":"2026-05-18T02:39:55.287184+00:00"}