This isn't really a great system for reporting causation. It's at best OK and is used from time to time (see any literature on Granger Causality). As I linked

This isn't really a great system for reporting causation. It's at best OK and is used from time to time (see any literature on Granger Causality). As I linked elsewhere in this thread, if you really want to prove causality then you need to be making counterfactuality arguments. Judea Pearl's framework of causal networks is a good system for doing this. At the end of the day, your claim of causality rests upon a network of assumptions about causality (and this is a formal description of your point (3), basically) and someone accepts this proof by accepting your assumption network and the strength of your new data.