One major mistake was pointed out in my work on the Takeno line element from yesterday [6]. When working on a theory that describes the behavior of physical quantities with respect to velocity, (like special relativity), don't decompose the velocity into its components like distance and time, or in my case into angular displacement, and time. Just leave omega, (angular velocity), as omega! Since omega isn't one of the variables that the derivatives are being taken with respect to, the many terms due to chain ruling out the innards of the hyperbolic trig functions disappeared and the phi and time components of the line element as calculated by Takeno fell out pretty simply. I also found out last night while reading through one of the Takeno referencing articles [5] I mentioned a few days ago that Takeno was scooped on his transform by about thirty years. As it turns out, Phillip Franklin [2], (picture 2), a then recent PhD from Princeton, beat Takeno to t...