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@freemo I feel like you're unnecessarily equating labels with their underlying concepts here.

The concept of two is still two whether we write it as "2" in base-10 or as "10" in base-2.

Likewise, the concept of integer addition is distinct from the addition symbol "+" which is also used to denote many similar-yet-distinct concepts (such as the ones you describe). While those may be referred to as "addition", they aren't the concept of integer addition that I'm specifically referring to.

These are, as you initially described them, effectively "definitions" that prove themselves circularly, but a tiny subset of such definitions describe concepts that would seem to be universally constant, that are independently and repeatably verifiable regardless of perspective. If we don't call those "facts", what do we call them?