Most of classical physics needs classical (not constructionist) mathematics, because it deals with emergent layers of description (like classical mechanics or GR) that are often not computable. But foundational physics must break with this and be constructionist, I think.
What happens when you try to measure something that does not exist, like a position in spacetime when your universe is not in space but in a graph, and a particular location is underconstrained to be projected into 3space?
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Building a measurer with that specification is impossible, but I'm not sure what you mean by "underconstrained": what kind of constraints logically allow a given location to exist in the graph model?
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If information is stored in a lattice and moves only along lattice links, you may project it into a space. But if you remove links from the lattice, you get superposition, if you add links, you get nonlocality.
End of conversation
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