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We show that every $m \\times n$ sign matrix with approximate sign-rank $d$ contains a monochromatic rectangle of size $d^{-O(d)}m \\times d^{-O(d^2)}n$, paralleling classical results for exact sign-rank. As an application, we establish a lower bound of $\\Omega(\\sqrt{d/\\log d})$ on the $\\epsilon$-approximate sign-rank of large-margin $d$-dimensional half-spaces. 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