B737-800

[B2N2]

At least in the US, the rule is that you cannot descend below the assigned altitude until established on a published segment of the approach. And the ATC phraseology to back this up on every approach is "maintain XXXX feet until established, cleared for the..." I assume that the rest of the developed world is the same. (Am I right or wrong in this?) In your scenario, what segment are you established on?

"Established" doesn't mean LOC centered indication in FAA world.
First movement of the needle inbound is considered established as you have lateral guidance.

So GS capture with 1/2 scale deflection (or more) in APP logic would be perfectly feasible.

[Vessbot]

There is no official definition of "established" in the FAA world, but lots of people come up with their own to fill the void.

Nevertheless, regardless of what threshold one uses to consider themselves established and therefore ready to descend, I'm not catching on to the meaning of your post as it relates to mine. I was replying to a post that asked why you can't operate with a glideslope alone. Without a localizer, you could never become established no matter what fraction of a scale width satisfies your definition.

[B2N2]

In FAA world ‘established’ is determined by positive course guidance.
Which is first indication of inward movement of the deviation indicator.
Years ago I have gone through the trouble of finding a reference.