No @structureoftruth. Your claim of the coherence of libertarian free will (LFW) relies on the truth of your claim that “this “brute fact” is within the agent’s control”.
If you want to demonstrate otherwise, then please give us an argument that shows the coherence of LFW, even given the assumption that the claim that “this “brute fact” is within the agent’s control” is false.
(But if your argument works either way, then the issue of agent control would appear to be a non sequitor.)
And I can give a (probably incomplete) list of causal factors that explain my choice. “Choice” is not evidence of LFW. To provide evidence of it you need to find evidence that I ‘could have chosen otherwise’ for reasons that are neither (i) deterministic, nor (ii) random.
That is a lousy argument. If you have experienced LFW then you have not experienced Determinism (or vice versa), so you have nothing to compare it to. So you have no basis for asserting that the 1st-hand experience of LFW differs from the experience of Determinism.
And HOW do they weigh the two and make the choice? Either they do so for a reason (i.e. T), or they do so arbitrarily/randomly. You have not articulated a third option, merely assumed that it must exist.
And you are simply assuming that there is some sort of magical “control” that is neither psychological nor neurophysiological nor deterministic nor random that lets the agent make a decision that is somehow outside of those factors.
Until you can actually articulate what this ‘magic’ entails, let alone convince anybody that there is a reasonable probability that it exists, your whole claim remains utterly incoherent.