Caveat - I've never seen one of these hulls in action ...
The pictures in the paper are reasonably consistent with the claim, but video would be nice.
I suspect that if you work out the curve of cross-sectional areas, and built another hull with the same curve it would have the same wave making characteristics
Assuming the draft at the bow is half the width at the stern (which is what the picture of the allegedly theoretically optimal hole in the water looks like) circumference is constant, and draft decreases as beam increases. The curve of areas is then a parabola because the area of each cross section is draft * beam and draft + beam = constant. Set the constant to 1, and the cross sectional area becomes b*(1-b), with b proportional to the position of each station.
I also realised that my speculation is nonsense. Right at the bow, all the water that is moved goes sideways, and possibly up. When beam approaches 0, the total amount of water being sucked under the hull must also approach 0.
Instead, I suppose what the shape does is that it always sucks a constant amount of water across the chine and under the hull bottom. Why that might reduce surface waves I don't know.
I write "single hull" quite deliberately, as if you have two or more hulls you can arrange them so the waves from one are reduced by the waves from others at certain speeds.
Can, to some extent and for a limited range of speed, also be done with a single hull: http://www.duckworksmagazine.com/04/s/excerpts/yachtreport/01/index.cfm
I have been wondering what would happen to drag when the boat heels. Or if you took the lines, and rotated the hull bottoms up by 15 degrees, would it then work well at that angle of heel?