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Given everywhere positive global sections f of L^{\\otimes2} and g of M^{\\otimes2}, where L, M are invertible sheaves on X and M is ample, fg^N is a sum of squares of sections of L\\otimes M^{\\otimes N} for all large N >= 0. In fact we prove a much more general version with semi-algebraic"},"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":"1104.1772","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-10T14:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"e6744ee02eb857a13a49872f15e1d6479fccddfffe1ec015d599c896672d7fc8","abstract_canon_sha256":"99cf75576876a4239fe2d7a463ddc54266b46d802fc1dc2ec076c83ed3be5fa2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:43.240531Z","signature_b64":"greUL5t0oS5vao2EDmM568PZamvtzafiYzorJyypMIIB54lo4bI8PGGineFItsvYWsAOsWXNfQQi1/GTLrm6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"542829b7f5f71430d3fb284867e8c869c0e375e170dd0d60c14ab072d6fbb48a","last_reissued_at":"2026-05-18T04:24:43.240115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:43.240115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Positivstellensatz for projective real varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claus Scheiderer","submitted_at":"2011-04-10T14:49:00Z","abstract_excerpt":"Given two positive definite forms f, g in R[x_0,...,x_n], we prove that fg^N is a sum of squares of forms for all sufficiently large N >= 0. 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