Showing me a unicorn example is not proof that unicorns exist. It is evidence towards a hypothesis that they exist. After you present your unicorn, I may discov

Showing me a unicorn example is not proof that unicorns exist. It is evidence towards a hypothesis that they exist. After you present your unicorn, I may discover it is a modified horse. Science can never prove truth or falsity of anything - it only provides evidence for or against hypotheses, but every single thing can be changed subject to future evidence. As such, there is no true/false in science, only degrees of evidence. This article, which you claim uses proof "in the scientific sense," does not prove a hypothesis is false, only that is gets less and less likely and competing ones get more and more likely, which is what your examples are getting at. The article proves (in the mathematical sense) the non-existence of an item, only if a certain conjecture is true. As pointed out above, this is math, not empirical.