You probably also need at least: - Y does not appear when X does not - We need an overwhelming sample size containing examples of both X and not X - The experiment and data collection and trivially repeatable (so that we don't need to rely on trust) - The experiment, data collection and analysis must be easy to understand and sensible in every way without leaving room for error

And as another commenter already pointed out: You can't really eradicate the existence of an unknown Z