{"paper":{"title":"A Gramian Description of the Degree 4 Generalized Elliptope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Afonso S. Bandeira, Dmitriy Kunisky","submitted_at":"2018-12-30T18:32:07Z","abstract_excerpt":"One of the most widely studied convex relaxations in combinatorial optimization is the relaxation of the cut polytope $\\mathscr C^N$ to the elliptope $\\mathscr E^N$, which corresponds to the degree 2 sum-of-squares (SOS) relaxation of optimizing a quadratic form over the hypercube $\\{\\pm 1\\}^N$. We study the extension of this classical idea to degree 4 SOS, which gives an intermediate relaxation we call the degree 4 generalized elliptope $\\mathscr E_4^N$. Our main result is a necessary and sufficient condition for the Gram matrix of a collection of vectors to belong to $\\mathscr E_4^N$. Conseq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11583","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}