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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 $K_4$. 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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 $K_4$. 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