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Thank you both for your replies!

I certainly agree with you, Quark, on the importance of symmetries regarding inversion of coordinates in geometric physics!

This whole sidebar could have been nipped in the bud were it not for RWP hypothesizing a single spatial dimension universe. IOW, a physical universe – not just a dimensional hypothetical. Perhaps that was not his intent, for he says in post 674:

There are one dimensional problems in our universe, too. There are systems with 1D inversion symmetry. You don't need the second or third dimension, or time, to deal with them.

Certainly, we can perform inverse geometry on single dimensional objects in our four dimensional space/time. And mathematics empowers us to hypothesize seemingly without end.

In this case we can hypothesize about a single dimensional universe and perform inverse geometry on it because it is not physically real.

But when we test it with a thought experiment – as though the single spatial dimension universe is physically real and we are the observer “in” it (the line) – then we run into the causal problem of “were it not for time, events could not be.” The inversion becomes physically impossible because the “creator” RWP did not provide a temporal dimension and an additional spatial dimension (template, zero point, direction, etc.) for context.

As "creator" of his universe though RWP could perform an inversion "in" it because he would be the context and not be bound by the spatial/temporal limitations of his own "created" universe.

As betty boop observed, this is a compelling demonstration of a number of issues which intersect in philosophy, theology, mathematics and physics.

This whole sidebar could have been nipped in the bud were it not for RWP hypothesizing a single spatial dimension universe

Which I didn't, as you admit. So why is your misreading of my words my problem?

The inversion becomes physically impossible because the “creator” RWP did not provide a temporal dimension and an additional spatial dimension (template, zero point, direction, etc.) for context.

I've answered this over and over again. I've also asked you, over and over again, to identify where time enters the problem. You are either unable or unwilling to do so.

Go learn some math, AG. That's the kindest thing I can say to you right now.