Until recently, I've been an avid proponent of the "co-moving inertial frames" (CMIF) simultaneity method (previously called the "CADO" method by me). I had claimed to have proven that the CMIF method is the ONLY method that agrees with the accelerated observer's own elementary observations and elementary calculations. But I recently concluded that there was a loophole in that proof, and therefore I had failed to prove what I thought I had proven. I decided to take a fresh look at the whole issue of simultaneity for an accelerated observer. In the course of doing that, I discovered a new simultaneity method that shows, with a very simple proof, that the CMIF method isn't correct. My new method says that when the accelerating observer instantaneously changes his velocity, the current age of the home twin DOESN'T instantaneously change. Instead, the slope of the age correspondence curve instantaneously changes its slope from a constant less than one to a constant greater than one. And then after a well-defined passage of time, the slope instantaneously switches back to the same constant less than one that occurs in the first segment. So the "curve" in the age correspondence diagram is always a continuous, piecewise-linear line of three straight line segments. Unlike the Dolby and Gull simultaneity method, and the Minguzzi simultaneity method, my method is causal, i.e., effects are always PRECEDED by causes. My new method is explained in detail on my webpage referenced below (in front of the old information on my webpage, which I now know to be incorrect). Michael Leon Fontenot -- https://sites.google.com/site/cadoequation/cado-reference-frame All you ever need to know about the twin "paradox".