Dear Eckard,
Thanks again for the clarifications. It seems that I keep missing your point. So I will ask you to clarify even more, otherwise I will answer you to something else than you meant.
You mentioned
"the non-subjective border between past and future"
and
"I intend to stress that the natural border between past and future is something objective"
What would be the problem if each "slice of spacetime" is at some instant the "natural border between past and future"?
Again, if you say it is objective, please show me that exists and is not mathematical, as you claim. I understand that you imagine it somehow, but for some reason either I don't get it, or you don't get what I said, or both.
You said "anything that already happened for sure is an effect of a preceding causal influence definitely belonging to the past. What happened cannot be changed while future processes are still open to influences except for a closed mathematical model."
If anything that already happened is an effect of preceding causes, then, at that time, would you have said that it have to be free of preceding causes, so that it is still open? Either I don't understand what you said, or it is a contradiction, or perhaps you think that the outside cause that makes the future open becomes inside, so that it is in the past. I mean, you seem to accept that past is determined by its own past, but future not.
Let me try to explain what I said and I think you misunderstood. You claim "you denied unpredictable causal influences from reality outside the models". I don't see how I deny it, and why I should take care not to deny it, and why this would be a problem. The proof that I did not deny it can be found in the same essay I gave you the link. There, you can find how it is possible to have free will even in this context, and how mathematics and even determinism doesn't exclude it.
You say that you want the future to be open. Mathematical structures are not necessarily deterministic, as you seem to imply. So, if you think indeterminism means open future, then it is not excluded. Also, as I explained in that essay, determinism doesn't exclude open future and free choice. The key point here is the idea of delayed initial conditions. Even in a deterministic mathematical structure, if the initial conditions are not fully specified from the beginning, but you add them with each choice of the observable you make, the future is open (of course, because you get to choose now initial conditions which were not specified before, the past is open in a sense too, so long as it doesn't contradict the records of previous observations).
So I don't see what you claim it escapes any mathematical description. If I am missing something, please explain what that thing that escapes is, and the proof that it can't be described mathematically. Maybe it is that thing about which I wrote in my essay "I don't claim we can explain consciousness, with or without mathematics."?
Best wishes,
Cristi