9 · Push the radius into the wall

The negative half of the balanced function has to fit inside a ball. The slider shrinks that ball.

Try this. Shrink the radius past the dashed line. The room left for the negative half collapses, and half of the weight cannot possibly fit.

The collapse drawn here is exponential, which is the shape the proof gives. The rate of that curve is chosen for legibility and is not the constant from the paper.