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In addition, we prove its stability whenever $2m \\geq 14$. Saddle-shaped solutions are odd with respect to the Simons cone ${\\mathcal C} = \\{(x^1,x^2) \\in \\mathbb{R}^m \\times \\mathbb{R}^m : |x^1|=|x^2| \\}$ and exist in all even dimensions. Their uniqueness was only known when $2m=2$. On the other hand, they are known to be unstable in dimensions 2, 4, and 6. 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