It seems to me that we can claim the existence of things, without restricting the nature of that existence. A river exists. That can be true whether we consider the river to be a physical object, or merely an abstract concept, or an amalgamation of an infinitude of physical objects. It still exists. Therefore I propose a statement of an existence axiom which allows for multiple interpretations of the physical world, all without actually denying existence.

Something like this:
- The world around us does, in fact, exist external from our minds.

- Everything in the world has a specific nature. That nature need not be static, nor observable, yet it does exist.

I'm not thoroughly satisfied with that, but it's what I came up with on the spot. Please feel free to adjust it.