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For any nonzero polynomial $f$ in this ideal, we construct a small depth-three $f$-oracle circuit that approximates the determinant of size $\\Theta(r^{1/3})$ in the sense of border complexity. For many classes of algebraic circuits, this implies that every nonzero polynomial in the ideal generated by $r \\times r$ minors is at least as hard to approximately compute as the determinant of size $\\Theta(r^{1/3})$. 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