Time is an operation count

Time is the number of calculations the vacuum of a wrist watch and the vacuum of free space need to move the second hand one tick.  It is always a constant. We can scale down and make that operation count meet the limits of the noise induced by kinetic energy. So, in the Lorentz transformation, pick a decent inaccuracy, and where time appears (eight times in one equation!), just replace it with an integer constant.  Within that inaccuracy, time remains the same.

That is all Lorentz is doing, scaling down to make time equivalent.The speed of light appears because there is the Nyquist limit, you cannot  exceed the density of free space in velocity; the vacuum 'multiply' count exceeds the vacuum 'add' count and free space arithmetic no longer works. Wrist watches require many more operations per second than does an atomic clock, they have more vacuum samples involved in their operation. So the vacuum basically starts rounding off to larger units.

So, take the Lorentz equation, replace t everywhere with N, and it all cancels on the right side, and on the left you are left with something like N*prime, where prime is some operator.  All the other ratios, on the right are of the form distance relative to speed of light distance; which is nothing more than the density of your wristwatch, in units of vacuum bubbles, relative to the maximum allowable density of the vacuum.  The prime, then is the position of the decimal point for N operation counts.  The vacuum bubbles are re-arranged to make your wrist watch tick, but some of the operations will end up as fractions, otherwise called kinetic energy, and your wrist watch, by definition, only measures whole numbers of ticks.

Someone with enterprise put the concept into a graph made of hyperbolic lines of equilibrium. What is a hyperbolic?

 Here, a hyperbolic.  In the first form, there are two symmetrical parts, the one has x and the other -x in the exponent.  The -x are the fractions, the x the whole numbers. In the diagram, that Greek looking angle is 1/2 the relative density of your wrist watch to the Plank density of the vacuum. That is directly from the Lorentz transformation where the ratio is converted to angle, and hyperbolic identities work nicely.

 The vacuum always operates to the same Signal to Noise. So it sets the decimal point such that a whole number at light speed =   log2(1+SNR).