Hypothetically, science proves free will isn't real

[Ignorant]

It's very simple. Compatabilism is the view that free will is compatible with determinism by defining free will in such a way that it is.

Right. It's not that I misunderstand that. I am trying to show that the categories and terminology offered by that sort of discussion are ultimately inadequately equipped to describe reality. If you adopt the language and terminology of that debate along with its reluctance to adequately distinguish, then you handicap yourself from the beginning.

The only potential within a deterministic universe is one physically possible future . . .  In determinism there is only one physically possible future at any given moment. You may imagine alternative possible futures, but within determinism there are no alternative possible futures there is only one possible future at any given moment . . . In determinism everything happens necessarily, and alternative possibilities are just within the imagination. It's all cause and effect . . . I defined determinism as the view that there is only one possible future. So there are no alternative futures, the one future that exists is necessary and determined. Have you not agreed to that definition?

Remember when I said that this debate fails to distinguish well, and I specifically mentioned necessity and determined as two different concepts which are readily conflated? Allow me to offer a 'higher resolution' view of the discussion.

Necessary thing/act: This thing/act exists/obtains in any and every possible world. In any and every possible world, it cannot NOT exist/obtain. Its not existing/occurring is NOT a real possibility.

Determined thing/act: Only this thing/act exists/obtains according to the relevant determining factors of its particular world. In some possible worlds it exists/obtains while in other possible worlds it does not exist/obtain. Its not existing/obtaining is a real possibility, and its actual existing/obtaining is determined relevant causal factors.

Determinism:

If each moment in a cosmic causal history is determined by the cosmic moment immediately preceding it, then that cosmic history is a determined one. 

a) If some other/different cosmic causal history impossible, then this determined cosmic history is also a necessary cosmic history.

b) If some other/different cosmic causal history is possible, then this determined cosmic history is also a contingent cosmic history.

Do you think the causal history of our cosmos is the only possible one, or is it one actualized possibility out of several?

The agent is capable [1] of engaging in any of those options but only one of the options will be taken. [2]

The agent is both capable [1] of different options, but is determined to only one of them [2]. 

So when someone asks, "Could the agent have taken a different option?"

How do you choose which sense to answer the question? 1 or 2? If you go with (1), then the answer to the question is 'yes'. If you go with (2), then the answer is 'no'. Unless you distinguish between contingency (the sense of 1) and determination (the sense of 2), then you will enter into a fruitless back and forth based on equivocation like you recorded in a previous post (notice how necessity can't enter a discussion unless the answer to the sense of (1) is 'no').

If an agent is capable of different action in the sense that said agent could be determined to that action given the requisite circumstances, then self-determination and freedom may still be on the table (if they could be shown to play a part in the determination of action). 

If, however, an agent is NOT capable of different action in the sense that said agent could not be determined to that action given the requisite circumstances, then any determination at all, much less self-determination have ceased to be factors in the action itself, and with them, freedom.

So until you can adequately speak about those distinctions, you can't even begin to talk about self-determination, will, freedom, or whatever else.

In determinism there is one future Y. And that future is caused by the one past X. Everything is contingent upon that. [1] What do you mean both a determined and contingent manner? [2] There is no in-between here, either determinism is true or it is false, either we are determined like the rest of the universe or we are not. [3] 

1) Yes, but if it is contingent on that, then the future Y does not happen by necessity (necessity being the contradiction of contingent). If it is contingent upon that, then that means other possibilities are REAL and not illusory.

2) See above (b).

3) I agree, but like I said, your reluctance to distinguish between "determined" and "necessary" and "contingent" is preventing you from accounting for all of the details. Determinism is true, i.e. the conditions of the present(X) determine the future(Y). Different conditions in present(X) would determine a different future(D). If that is the case, X => Y does not happen necessarily, instead, X => Y is contingent upon a particular set of conditions in present(X).