It has been said that "Extraordinary claims require extraordinary evidence" (Sagan) or that "Extraordinary claims require extraordinary proof" (Truzzi). However, is not the assertion that something -- anything -- is extraordinary itself an "arbitrary claim"? After all, the claim is normally made to dismiss something else as extraordinary. But what is the basis of the claim itself claiming something else is extraordinary? The problem is that the history of science is littered with broken paradigms that asserted what whatever replaced the paradigm was "extraordinary" and therefore could be ignored.
I give a single example. Medicine ignored the concept that stomach ulcers could be caused by bacteria because "of course" bacteria could not survive in such a hostile environment as stomach acid. In this case orthodox medicine claimed that only "extraordinary evidence" could satisfy the assertion that ulcers were caused by bacteria. In point of fact, the evidence was not particularly extraordinary -- it was proven that Helicobacter pylori was the main cause by swallowing it, getting ulcers, then using antibiotics to kill the Helicobacter pylori. And since people with ulcers were very motivated to find a resolution, a cure for most stomach ulcers was distributed and a Nobel prize in Medicine was awarded.
I suggest that the assertion that something is "extraordinary" and therefore requires extraordinary evidence (or proof) is itself an arbitrary claim and should not be regarded. And that we should use the same standards of proof or evidence for everything.