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If X is contained in an affine chart C^n on P^n, then the affine part of X^ is the set of points x in C^n for which there exists a constant M=M_x so that\n  |p(x)| < M^d sup{|p(y)| : y in X} for all polynomials p of degree less than or equal to d, and any d > 0. Let X^(M) be the set of points x where M_x can be chosen < M. Using an argument of E. Bishop, we show the following. Let G be a compact real analytic curve (not necessarily connected) in C^2. Then for any"},"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":"math/0611482","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2006-11-15T19:41:31Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"d3884f076cf8acfa319be086f7014dfbd01abbc4d8caef7955fd294e55073703","abstract_canon_sha256":"d4bc40e96f6b7637361bfd22ebcaa77aa40eacb7904506e262c0b6f70ab7e247"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:19.387190Z","signature_b64":"gYOz0TS97hopXSQDTNfHcHIyW1iMawHb9pUDXeaFW27ZcMFTZxOCeHO4zJhPtATijjVRhtVOD2cdn6lfVUQeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08fd3b7b87585467aa8c2e30e45f331559c804516fc4e2bbedf0797322a50612","last_reissued_at":"2026-05-18T00:28:19.386392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:19.386392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Projective Hull of Certain Curves in C^2","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"F. 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