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Combined with known upper bounds they give $p(3,2d)\\in\\{d+1,\\,d+2\\}$ in the ternary case. Assuming a conjecture of Iarrobino-Kanev on dimensions of tangent spaces to catalecticant varieties, we show that $p(n,2d)\\sim const\\cdot d^{(n-1)/2}$ for $d\\to\\infty$ and all $n\\ge3$. For ternary sextics and quaternary quartics we de"},"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":"1603.05430","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T11:19:05Z","cross_cats_sorted":[],"title_canon_sha256":"4447918ff2e92a5c0724c10b6f9d97b1a4d5893f0905218d175fb7450564cc6c","abstract_canon_sha256":"b6b1f7fc4444bf80060f62e46813c9e305b534c852b65ce4451b30589a5a3952"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:56.362899Z","signature_b64":"1Ne7ZsF1UWCslObf/8bYe/9IB1vTt0hsHdypdV4EW17eTampilnlwbmnf2QTM4J8ybOFDOH1ITvS9EEXxcRYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"216b3ccd5da8d9541daa8a80909c962a5db22dea9d3091e33919c6bdb639780b","last_reissued_at":"2026-05-18T01:18:56.362494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:56.362494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sum of squares length of real forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claus Scheiderer","submitted_at":"2016-03-17T11:19:05Z","abstract_excerpt":"For $n,\\,d\\ge1$ let $p(n,2d)$ denote the smallest number $p$ such that every sum of squares of forms of degree $d$ in $\\mathbb{R}[x_1,\\dots,x_n]$ is a sum of $p$ squares. We establish lower bounds for these numbers that are considerably stronger than the bounds known so far. Combined with known upper bounds they give $p(3,2d)\\in\\{d+1,\\,d+2\\}$ in the ternary case. Assuming a conjecture of Iarrobino-Kanev on dimensions of tangent spaces to catalecticant varieties, we show that $p(n,2d)\\sim const\\cdot d^{(n-1)/2}$ for $d\\to\\infty$ and all $n\\ge3$. 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