I mean, what proof do I have that the half-life of Polonium-210 is actually 138.376 days? Maybe it's really 139.24 days. Maybe Polonium-210 doesn't EVEN EXIST.
It's not difficult to get access to a scientific paper or a textbook that states the half-life. You don't have to be able to verify that something is true, you need to be able to verify that the source given really says when it's being claimed it says.