Thank you for that clarification, Tach. Understood.
You managed to understand? I pretty much doubt it.
How does your abstract mathematical "result" agree with the actual fixed distance between the mirrors?
I explained that as well. Though the distance between the mirrors if fixed, the path described by the photon is variable, longer for the photon deeper in the gravity well. The photon follows an arc of spiral, not a straight line. This explains why the clock deeper in the gravity well ticks slower.
Can you demonstrate empirically rather than theoretically that the distance between the mirrors has changed between upper and lower frame positions?
So, you understood nothing.
Unless you can demonstrate empirically that the already fixed relation distance between the mirrors has changed as you assume for your equations, then it remains abstraction and conjecture on your part, yes?
Nope, it remains an ingrained inability to understand physics on your part.