Mathematics and Metaphysics are not one in the same, and your assertion that they are the same does not make them so
Mathematics is the mechanics about physics.
Determinism is a concept under mathematics.
You have attempted to define determinism as what is really radical fatalism and personally, I won't really abide it.
You are writing about Newtonian Determinism, which does fall within the province of physics, which is driven by mathematics. No dispute there.
Determinism (or Causal Determinism) also is the name given to a metaphysical (or philosophical) paradigm (or concept) that is not driven by math or physics, and which is a thought experiment that predates Newton and earlier physicists who may have articulated similar formulations.
I am not attempting to define the metaphysical paradigm of Determinism (or Causal Determinism) in any manner other than it is articulated by philosophers (including philosophers of science) -- as my quotation of Karl Popper demonstrates.
As far as you lack of willingness to abide the fact that the metaphysical paradigm of Determinism (as contrasted with Newtonian Determinism) produces consequences that you characterize as "radical fatalism" is exactly the point I have been making. Once one accepts that consequence of the truth of the metaphysical paradigm of Determinism, it follows that Free Will cannot exist within that paradigm, and Compatibilism is, therefore, illogical within that paradigm. Again, to quote William James, who also was writing about the metaphysical paradigm of Determinism, and not Newtonian physics:
“The issue . . . is a perfectly sharp one, which no eulogistic terminology can smear over or wipe out. The truth
must lie with one side or the other, and its lying with one side makes the other false.”
If you wish to spread this claim about radical fatalism, and that the universe is radically fatalistic, be my guest, but please quit lying and pretending this has anything to do with any concept "determinism" that can be expressed in some rigorous way.
I have not asserted that the metaphysical paradigm of Determinism (or Causal Determinism) truly, entirely, and perfectly describes the actual state of the universe, and I defy you to quote my saying so. Rather, as stated above (and elsewhere), I am just exploring the logical consequences of the truth of the metaphysical paradigm of Determinism (or Causal Determinism) in order to test the validity of the assertion of Compatibilism (which also is a metaphysical paradigm) that some form of Free Will can exist in a universe that is truly, entirely, and perfectly deterministic.
I do happen to believe that the universe is truly, entirely, and perfectly deterministic, but that is neither here nor there for purposes of testing the validity of Compatibilism. Again, I do not claim my belief to accurately describe the state of the universe. Like any belief about the ultimate nature of the universe, there is no way to prove or falsify the belief, which can be held only on faith (unless and until it is no longer held). What I cannot respect is any claim by anyone of certainty about the ultimate nature of the universe, which is beyond the abilities of human beings to know on account of the combined limitations of Heisenberg’s Uncertainty Principle, Godel’s Incompleteness Theorems, the observer effect, and other human and inherent limitations of empirical observation, which acknowledge the theoretical impossibility of obtaining a certain, complete, and precise understanding of the universe — at least from within the universe.
Even at a more mundane level, I believe many things to be true that I lack sufficient evidence to know to be true. I am confident that the same is true of you and everyone else. When you take a drink of tea, you do so under the belief that it is not poisoned. It may be poisoned, in which case your belief will not only fail to correlate with reality, but you will become sick or even die. If your belief is correct, there will be no such consequence (unless, perhaps, you are allergic to tea). Either way, the fact of your belief, including the strength of your conviction, does not alter the fact of the tea being poisoned or not poisoned -- at least not in a universe in which having a belief does not cause the thing that is believed to become a reality.
If you cannot express your "metaphysics" as math, it has no value for me or anyone else, it's just so much PFFFT.
If your willingness to consider something to be of value is limited to the issue of whether it can be expressed as math, I feel sad for you. That sounds like the way a computer operates. Long before Albert Einstein expressed the Theory of Relativity in mathematical terms, he theorized and philosophized that the universe worked that way. Philosophy (which includes logic) also is a valuable tool for testing the validity (but not the truth) of assertions and arguments.
Notably, Albert Einstein also believed that "“Human beings in their thinking, feeling and acting are not free but are as causally bound as the stars in their motions.”
That is the metaphysical paradigm of Determinism, which cannot be proved or falsified -- not by math or otherwise. Instead, it must be accepted or rejected on faith, with respect to which Thomas Aquinas famously wrote: "To one who has faith, no explanation is necessary. To one without it, no explanation is possible."
If you wish to dismiss that as PFFFT, that is your prerogative, but it is extremely disrespectful.
Also, if you truly believe my post is PFFFT, you will not reply -- at least not if you have Free Will. I know I am done with this discourse -- either because I am compelled to be done or because I choose to be so if I have Free Will. Stay Well.