I quickly looked through the link you gave.
I have been working independently with a small AI sensation team ........ since 1968.
My thoughts are:
All events take place in a "time series".
There is a past time series, which has the probability of "high", as far as the observer-observer is concerned.
There is a predicted future “predicted” time series predicted ahead of the “best” time series model that a reasonable observer can create, and as time series disappear in the future, the likelihood that this time series “becomes past time series” is reduced to zero and may occur in milliseconds or billions of years, depending on the dynamics of the model.
I do not think there is ever a "present."
Unfortunately, after studying Kalman Filters and Predictors and using them in missile targeting, I came to the conclusion that the whole "topic" of the "mathematical representation" of the best algorithms (for example, models) that people could come up with was empty of time, because even the simplest The "program" performs a task that cannot be represented by mathematical symbols ... and therefore I came to the conclusion that the "computer algorithms" "ARE" are mathematical formulas ... i.e. formulas that normal symbolic mathematics do not have tools for describing (i.e. programs outperform complex mathematical notation systems).
Mathematics is great for "proofs" and "great statistical representations", but ... (and I get to the end now) ... I would "trust" your own instincts to create the "model" that predicts the future best. ..that is, perhaps, he should have the concept of "on alternative media in the USA", in it ... as well as thousands of other such non-atomic "states" or various "axioms" ... this is normal!
since you ask if this could be mathematically correct !!!!
Well, the answer is quite simple: the best model - the best model for predicting the future!
And the future continues to appear unexpectedly - and therefore it is easy to test - and continue testing!
All you need to know that you have the best “math” (ie, a program) is to see how much “noise” or “deviation from the prediction” exists in the prediction versus the actual result in the time series.
"State-Space" is the best "math" used for this ... i.e. Suppose that there is a “ground state”, and then suppose that your “observations” are simply erroneous “noisy or just wrong” observations, this is the ground state - that is, the system output signals are “somehow” based on these “invisible” system states.
There is an artificial “artificial language” called MTR, which we created (mainly in the 1980s), which is designed to create such a dynamic model, but for us (people) we see that it is intended for an IA entity to use, not for people, although we are going to soon put the front end of Pascal Like on it to allow normal people to use it. IBM, Intel, GCHQ, MOD, DOD, etc. Everyone had licenses, but then we put it off!
We intend to resume the project in the near future.
In any case, this is what I think - I hope this is not too abstract for your purposes!
We could say ... (and I'm joking about this) .... that programmers who try to use “pure math” to write programs “have bull horns”?
So, I hope, programmers can be much more relaxed when they do not fully understand all the mathematicians !!!
I hope this thought can also help any non-math readers ... of this answer.