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However, if the degree is sufficiently larger than the number of variables, then the theorem obviously does not provide nontrivial information. Our approach is to look at $(m + 1)$-dimensional subspaces of even symmetric forms of degree 4d, at which nonnegativity can be checked at $(m - 1)$-points, i.e., points with at most $m - 1 \\in \\N$ distinct components, where $m$ is i"},"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":"1303.4241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-18T13:12:13Z","cross_cats_sorted":[],"title_canon_sha256":"9ec555c51b79161e5251906d4d74fde38706c3ce25f2c5f6cda148ba9c2b2cf6","abstract_canon_sha256":"8db5d4d33487029032f9548fff9573b91d6320cd486e8f25d5f70e8deafd8835"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:39.144173Z","signature_b64":"MkvXyMEQMdqVCNHVq9sciiTxlNGCPIBdl0GUDX5iBbWbaUAAjrNsbMxRz31/wDG7mzc6dCwkLYNF/UBZcUHECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d17476032446e5461fef21ae17e2940145367cf802f5c9f39b18a032bf94a525","last_reissued_at":"2026-05-18T03:30:39.143273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:39.143273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low Dimensional Test Sets for Nonnegativity of Even Symmetric Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sadik Iliman, Timo de Wolff","submitted_at":"2013-03-18T13:12:13Z","abstract_excerpt":"An important theorem by Timofte states that nonnegativity of real $n$-variate symmetric polynomials of degree $d$ can be decided at test sets given by all points with at most $\\lfloor\\frac{d}{2}\\rfloor$ distinct components. 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