{"paper":{"title":"A Proof of the Dittert Conjecture in Dimension 4 via an Agent-Guided Exact Sum-of-Squares Certificate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Beibei Xiong, Jinhui Li, Zhengfeng Yang","submitted_at":"2026-07-31T09:12:45Z","abstract_excerpt":"The Dittert conjecture states that the Dittert functional on nonnegative $n\\times n$ matrices whose entries sum to $n$ is uniquely maximized by the uniform matrix. We prove the conjecture in dimension $4$. More precisely, let $K_4$ be the simplex of nonnegative $4\\times4$ real matrices whose entries sum to $4$, let $U_4$ be the uniform matrix, and let $\\phi$ denote the Dittert functional. We establish $\\frac{61}{32}-\\phi(A)\\geq \\frac{1}{52}\\lVert A-U_4\\rVert_F^2$ for every $A\\in K_4$. Consequently, $U_4$ is the unique maximizer of $\\phi$ on $K_4$. The proof reduces to certifying the nonnegativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29191","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/2607.29191/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}