Thank you! It's arguably a semantic point, but yes, I think mathematics is rooted in experience, because it started with observing thing coming in different quantities.

That aside, you are right to focus on what is and is not imaginable. From a truth units perspective, math is effectively true to the extent that you or anyone cannot imagine anything to the contrary. The analogy of the two glasses of water was meant to get toward this, but reading your comment, I think this needs to be addressed more fulsomely in a follow-up piece on truth as a function of imaginability, so thank you for your thoughts.