This is article about Bondi K-Calculus.
What I learned from that article (for example when determining who was old in twin paradox) was when staying twin determining what time in traveling twin frame that simultaneous to him, he used radar methodology, but when traveling twin determining what time in staying twin that simultaneous to him, he used angle between coordinate. For me it is not fair, why traveling twin did not use radar methodology too?
Second, if we switch between who was sending the signal with who was replying, then the situation become alter too. So this method does not make a symmetrical treatment to explain time dilation. If traveling twin sending a signal, then staying twin that younger.
Third, kT was the time for traveling twin when he receiving the signal and then send replying signal. But why this kT become time for traveling twin to reach that point (spatial location when he replying the signal) and it is attributed to time dilation effect. I think it is just because the signal itself have a delayed time to reach traveling twin, not because time in his reference frame that dilated, isn't?