Even if we could assess all the possible input-output conversions for each neuron, this would not lead to any definative proof, because there is no way of showing that our apparent free will decisions are entirely defined by neuron activity.
Is there anything missing - is the explanation sufficient to explain the observed phenomena? No, there's nothing missing.
Is there any evidence of phenomena unexplained by the current scientific paradigm? No.
Is there any explanation of the concept of 'free will' that explains how something could be both free and will? No.
This is merely an assumtion based upon the observation that human scientific endeavors have not yet discovered any other sources of influence.
It is not 'merely' an assumption; it's a deductive explanation from the available evidence. It's not 'proof', scientific explanations are always provisional. However, the logical problem with the concept of free will remains, regardless of how overwhelming the evidence for a purely physical explanation of consciousness and will might currently or potentially be.
The influence of the human soul on our neuron activity may not be detectable yet by scientific investigation, but this is no proof that it does not exist.
No, there isn't. What there isn't, more importantly, is any reason to think that it does. I dismiss the idea of a soul being required for exactly the same reason I dismiss the possibility that I'm a puppet being controlled by a highly-qualified pixie or the possibility that I'm just a slug-brain in a jar being fed artificial-reality inputs by an alien minimum-wage lab assistant - there is no evidence for any of them, and nothing lacking in the available explanation that requires something more.
I can't prove that waves aren't actually caused by magical, invisible, intangible dolphins that abhor the straight lines of a flat sea, but I don't need to prove that they aren't because there's no need to think they are.
I don't need to disprove souls because there's no reason to think they exist. The onus remains on you, as the claimant, to justify your claim; I don't believe the science isn't a good enough reason, nor is I don't like the implications of the evidence.
O.