It may be useful to know that if events all obey the Markov property (they are probability distributions, conditional on some set of causal parents), then the Reichenbach Common Cause Principle follows (by d-separation arguments) as a theorem. So any counterexamples to RCCP must violate the Markov property as well.

There’s also a lot of interesting discussion here.

I don’t mean this as a criticism—you can both be right—but this is extremely correlated to the updates made by the average Bay Area x-risk reduction-enjoyer over the past 5-10 years, to the extent that it almost could serve as a summary.