Proof of Dittert's conjecture for dimensions \texorpdfstring{$n\ge 17$}{n >= 17}

Dittert’s conjecture gives a sharp upper bound for the Dittert functional on nonnegative matrices whose entries sum to $n$. It extends the van der Waerden permanent problem from the doubly stochastic polytope to a larger simplex in which row and column sums are allowed to vary. We prove the conjecture for every dimension $n\ge 17$. The proof combines the Knopp–Sinkhorn lower bound for boundary points of the doubly stochastic polytope with a refined scaling step in the Cheon–Wanless method. The main improvement is a sharper subset-sum estimate for the row and column sums of a near maximizer, which reduces the scalar dilation needed to obtain a doubly superstochastic matrix. This strengthened comparison is sufficient to exclude boundary maximizers in all dimensions $n\ge 17$, and the known positive-support characterization then identifies the unique maximizer as $n^{-1}{J}_n$.