It does not harm me that you are howlingly ignorant about the mathematics of space-time. But, it does bothers me that you have brought your broken understanding to three different forums, in a language which you have not mastered, and sought to convince people by misleading problems that are not...
This is a deceptive problem.
The event O has t = t'.
The starting event is when t = 0 and x' = -7/8 and the ending event is when x = 0 and x' = -7/8.
The starting event is when t' = 0 and x' = -7/8, which is a different event than in the first question. Comparing the two measures of time tells...
I thought it was physically obvious, since you want to talk about an elapsed time you need two events, and since you are talking about the event where a clock at x' = -7/8 light-seconds intersects something else at x = 0, that gives Q as the unique intersection.
Since you insist on calling...
The original poster of this thread originally titled another thread Time dilation is false.
Event P is not well agreed upon. The OP seems to have chosen t = 0 and x' = -7/8 light seconds. While grav-universe prefers t' = 0 and x' = -7/8 light seconds.
Event Q is well agreed upon with x = 0...
This is based on \sigma(n) = \sum_{d|n}d < e^{\gamma} n \log \log n for all n >= 5041 being logically equivalent to the Riemann Hypothesis as shown in
Guy Robin, Grandes valeurs de la fonction somme des diviseurs et hypoth`ese de Riemann,J. Math. Pures Appl. (9) 63 (1984), 187–213.
See also...
I am under the impression that typesetting software, like troff, predated both TeX and the internet. A quick survey of Google supports this clearly.
TeX was born in 1982, which was in the infancy of "The Internet" http://www.tug.org/ftp/historic/systems/unix/TeX2.9/tex82/TeXdoc/history.txt...