Before revision:  As a starting point, open convex codes have a desirable monotonicity property,  but here we show that  closed convex codes do not possess the same property. We additionally show that, even for 3-sparse codes, closed convexity is not equivalent to avoiding local obstructions to convexity .
After revision:  As a starting point, open convex codes have a desirable monotonicity property, but here we show that closed convex codes .