But you confirm that you are using some sort of relativity principle/postulate when you say that a factor is the only possible solution for this extension of the Galilean transfomation, don't you?It's the other way around. We don't know there was a max speed. So the starting point was just an extension of the Galiliean transformation. Then as I showed, we actually have two choices. In one choice, the space-time transformation is symmetric. In such a universe, we find there is a max speed, as shown by the velocity addition formula derived from the transformations. With the other choice, one would have no such properties. The speed can be infinite.