Sounds arbitrary.
I think numbers are more akin to symbols, just like language itself. It is an intellectual abstraction. Your hypo definitely requires application of logic in order to prove. Numbers do not exist without intelligent life abstracting them.
You're splitting hairs here. Nothing truly exists without the concept originating within intelligent life's brain. So you can't have one without the other.
The old tree falling in the forest canard? I knew that was a possible rebuttal, but honestly, I'm pretty phocking sure a tree falling in a forest still creates sound waves even if no one is around.
Or Schrodinger's cat? That puss is either alive or dead. Human knowledge doesn't change that reality.
I don't find those thought experiments very useful, tbh.