I'm trying to understand Lincoln's values for frame C. So I added some values from GrayGhost's Minkowski diagram for essentially the same (ABC) scenario:


With , and :

Lincoln's transformations with Gray's values calculated:

Now to get the time passage of C from 2 to 3, we need to subtract their times:



So the total time experienced by two, inertial observers (as compared to A) is

Lincoln used the reference frame of observer C in 'standard configuration', i.e. frame C's origin is also where A and B's are (Event 1). Gray and me 'resynchronized' the clock of observer C so that it read 2 yrs at event 2, which we called the 'time-handoff', i.e. C sets her clock to momentarily read the same as B's clock, i.e. 2 years.

To show how the C's values on the Minkowski correlate with Lincoln's equations, one can do a Lorentz transform for Event 0 from reference frame A to frame C. Event 0 is where observer C crosses the t=0 line of frame A, so in frame A, Event O sits at (6.928,0) and v= -0.866, i.e. gamma = 2.



This means Gray's clock C is exactly 12 years behind what Lincoln's 'standard configuration' clock would have been, explaining the values for t_C shown on the diagram.