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In turn, the strip extends to a variety with boundary $M$ (Rothstein-Sperling Theorem); in case $M$ is contained in a pseudoconvex boundary with no complex tangencies, the variety is embedded in $\\C^n$. Altogether we get: $M$ is the boundary of a variety (Harvey-Lawson Theorem); if $M$ is pseudoconvex oriented the singularities of the variety are isolated in the interior;"},"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":"1211.0787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-11-05T08:24:17Z","cross_cats_sorted":[],"title_canon_sha256":"b84ff8f04e7f0947b99bc562d9e0fd4f47026db5f528faf57cd1f98032b201df","abstract_canon_sha256":"df60dd419a8f1fa6bf2df2ec1e53b7f1bf31238a568b050d96eda38fb7f2a509"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:31.568500Z","signature_b64":"BcEbYHnBb+qYSO1Ar1e3bM1HNzUHNPKJ800k24vTbHz2DfNKpzcAIZYmN/OvQlRnXQB0C5DP0RVIQHphzWk6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d72b2f0830268c5d9c706c48681a4a1d945e6434e74881fca304698cb957c494","last_reissued_at":"2026-05-18T03:41:31.567938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:31.567938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundaries of analytic varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Luca Baracco","submitted_at":"2012-11-05T08:24:17Z","abstract_excerpt":"We prove that every smooth CR manifold $M\\subset\\subset \\C^n$, of hypersurface type, has a complex strip-manifold extension in $\\C^n$. 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