No, on the contrary: it IS an ontological difference, if one "part of our
reality" has an influence on our sensory apparatus, or that we are able to
detect them with machinery, and on the other hand there are "parts of our
reality", where at most the material of their symbols are accessible to
such methods.

What you're doing here, is, creating things by thought. That's ok,
everybody needs to do that, however not to the extent, that by
externalizing them they're given the status of an independent entity.

So I think, for you (natural) numbers are something like "holy things",
i.e. just another variant of Kronecker's "God's work", more valueable than
other mathematical objects, and that this conviction must somehow express
in the mathematical structures. At least this is the impression I got from
your previous postings.

However contemporary mathematicians don't like to let philosophical
pretexts influcence their math and narrow their intellectual freedom.
They prefer to rely on proofs with rigourously defined notions.

This might make today's math smell platonistic at times, but I don't care.
The existence of an unique decimal expansion for pi is so much better than
your belief, that such a thing does not exist.

Call it invention, physically impossible, whatever you like, the
conceptual progress of Dedekind, Cantor and others have made math much
better, and eventually this is what counts. Your philosphical setting is
far from being able to achieve a similiar quality of the theory of
numbers.