No state law that I’ve ever heard of.I don't think there is a federal requirement to have proof on you at all times - but you do have to produce proof if asked eventually. However, is there not state law that you have to be able to show LE that you have the stamp? IDK I might be wrong.
Also, while an RSO cannot be a rep of the ATF, can't a private entity have a policy that requires NFA owners to have proof?
That being said - if an RSO asks me for my stamp, if there is no range rule for that, yeah, in that case pound sand.
And if the range I’m frequenting demands to see it, I’m leaving and not returning.