the metric fluctuates in the infinitely small, then why its principal characteristic, its signature, should remain fixed?
If you're asking why quantum fluctuations don't affect the visible characteristics it's because they are too small to be observed. We only see the average.
This question is completely incomprehensible to me! I suggest that it be re-written in understandable terms and re-submitted.
There are no fluctuations in the infinitely small.
The basic structure remains fixed but a tolerable and inevitable quantum effect allows the universe to evolve into what we experience and see to-day.
Well it`s like this, to ask a question such a yours implys that you know the answer. I will therefore ignore le question.