What is a metric for uniformly moving frame?

[Dale]

This is obvious, because this setup is frame invariant, thus it must be simultaneity convention invariant also.

The mapping between B and events on O's worldline is neither frame invariant nor simultaneity convention invariant.

In that setup we measure a local time duration between two real events, not between two abstract coordinates, which are not a real entities.

I have already shown that this is not true. Event B is not local to observer O.