I’m currently working on Causality with Deterministic Relationships (Finite Factored Sets put differently and more).
Currently, this is mainly extending the framework to the infinite setting, decidability of finite temporal inference, and efficient finite temporal inference.
I think your arguments in Section 3 to rule out Graph 3 can’t be correct if you accept Graph 2.
To see this, note that there is a symmetry between X and Z. Namely, if we use FFS temporal inference, then we know that X and Z are both before Y (and ¬Y ).(here we even have P(X=x,Z=z)=P(X=z,Z=x), so they are entirely exchangeable).
Therefore, if you accept Graph 2 then we can clearly switch X and Z in Graph 2 and obtain a solution for Graph 3. Also, note that in these solutions X=¬W or Z=¬W, so if we see variables as their information content, as in FFS, this is Graph 1 in disguise.
Also in Graph 2 there is a typo P(W=0|Z=0) instead of P(Z=0|W=0)