{"paper":{"title":"Singleton Optimality in Standard Quadratic Programs with the GOE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xin Chen","submitted_at":"2026-05-18T16:29:32Z","abstract_excerpt":"We study the standard quadratic optimization problem over the simplex when the objective matrix is drawn from the Gaussian Orthogonal Ensemble (GOE). Let \\(\\kappa_n\\) denote the support size of the almost surely unique global optimizer. We prove \\[ \\Prob(\\kappa_n>1)\\sim 2\\sqrt{2\\pi}\\,\\frac{\\sqrt{\\log n}}{n}. \\] The proof combines an exact two-coordinate condition for edge improvement with a product formula obtained by conditioning on the diagonal order statistics. Boundary-layer estimates identify the leading contribution and show that supports of size at least three are negligible. Consequent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18620","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18620/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.222559Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"04320d06a20cf5265df331d11a30ecfd6abc33e097257408ce4cf85a0371f942"},"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"}