"It is trivial to demonstrate the validity of the mathematics." - tortoise
Well, since you say that it is "trivial", you'll have no problem producing a demonstration of the mathematics for random noise creating a working version of Abode PhotoShop.
Trivial, indeed...
Perhaps you just don't get it, but proving the validity does not require giving you an example, only proof of all the pertinent concepts. For example, you could state that it is possible to travel at Mach 10 (which it is in a handful of vehicles), and using your reasoning demand that the only proof of human Mach 10 travel is a video of you personally going Mach 10. It would be stupid and ridiculous for me to deny the fact that it is a trivial engineering exercise to travel at Mach 10 despite the fact that you can't do it personally. I'm using "trivial" to mean mundane in an technical sense (i.e. no special or yet undiscovered magic); I am not using it to imply "cheap and easily accessible".