I read enough to get the gist of the paper, That being speed of angular change and how that relates to positive comp/OBT and other tuning "theories." I can summarize where I've found the flaw to be, through my own vibration analysis testing. They are, and so did I for a long while, assume this is all about frequency. It's not. It's PHASE TIME. Essentially, the frequency is a constant(reasonably true) and we are changing phase time...working with as little as a single wave form and manipulating its position relative to bullet exit. And yes, that has a lot to do with why I constantly scream to move tuners in very small increments. Those sine wave targets that I and others have posted show us how far it is between wave forms, err in tune to completely out of tune, as well as the respective group shapes along that wave form. That's the key and no, it's not a secret or voodoo. It's a methodical test(my tuner test that some call a sine wave test) that lets you see and quantify each adjustment, how many between... and group shapes along a single standing wave. The test is simple. It shows ON THE TARGET, 3 very important things. It shows top and bottom of the bbl swing(sine wave), it shows many marks between top and bottom, as well as top and middle, which is technically the node, and it shows repeatable group shapes along that standing wave. IOW, it shows you all we need to make a tuner work. It doesn't explain the science to the nth degree but it shows much of it, literally in a picture that you drew with your own rifle...yourself. Our common use of the term node is incorrect in the context of a shooting forum. We talk about being in a node and such but the node is technically where the bbl moves the fastest and shoots worst. Anti-nodes are the top and bottom spike or trough, where the bbl "stops" and changes directions. Positive compensation can only happen at the top, to my understanding on that point, and it stands to reason, even in my little brain.
There are many, many smarter people than I, even on here, but there may not be anyone that has worked harder, done more research and testing, than little old me, on this one narrow subject.
Aside from pc, I believe I have enough understanding of the subject of what's going on with tuners specifically, to explain it in terms that most anyone can understand and SEE for themselves....or I try my best to. I have every customer shoot a test that shows these things. Not me, but them. It's a light bulb kinda moment when you see the things I describe and predict seeing from my test, for yourself and by yourself. It's remarkable how predictable the group shapes are and how little tuner travel is needed. Many top shooters see the same thing when doing seating depth and powder charge development. That's not a coincidence because ultimately, tuner do the same as load work does. That being, optimizing bullet exit with optimal muzzle position. The load changes exit timing but the tuner changes muzzle timing(position)...phase time.
My first experience with tuners on cf rifles was in 2007. I went to a match in 2008 in which I didn't have one, I was pre-loaded and the tune left me. I don't think I've shot without a tuner since then or very near. I started testing and developing my own tuner in 2014, as soon as the patent on the Browning Boss expired. Actually, that's when I started selling them. I had done a ton of work prior to it, waiting for it to expire.