Telling you what I read. I am no authority here. Originally the Roots blower had rotors with two lobes and then three lobes which were linearly parallel to each other. That evolved to our present design, which incorporates the helix is called "the fourth-generation design of the involute, three-lobe Eaton rotor, which has a 60 degree twist and a special acrylic coating." The Lyshholm design, which is called a screw type design, not twin screw like I have seen posted, is different as it has one rotor with concave lobes and the other with convex lobes. The Eaton and the Lyshholm operating principle is nearly opposite the Roots.
Apparently the Lyshholm was designed in a spiral before the Roots ever was and in that sense both phobos and me were confused in thinking that the helix was introduced into the Eaton design emulating the Lyshholm. A bit of research here has enabled me to correct my misinterpretation. In both cases the spiral design has the cuantitative effect of increasing surface area within the same lenght and adds some direction to the air being compressed due to the directional spiral effect. On the other hand, if there was a change in lobe design where one lobe was smaller than the other to allow more twisting and to function with a smaller lobe against a larger lobe of differrent shape then in fact it would have been a Lysholm emulation. I thought that might have been the case because in the photo above the right hand rotor lobe looks different than the left hand rotor lobes. BC has corrected to say that this is just an optical illusion as both rotors are the same.
Seems to me like the M112 HH by having more helical twisting then the lobes may be smaller to accomodate in the same linear space. There might be some gain in surface area due to more spiralling but at the same time some loss due to smaller lobes. How that translates cuantitatively is up to Magnuson to announce. I suspect this is nothing a smaller pulley cannot take care off in each case. My personal and limited perception is not expect a dramatic improvement over our M112's to warrant a costly upgrade to the M112HH.