wu-lee I think that each registered profile has a page on the index server,
Not exactly. Each node profile has a unique URL (which is registered in the Index) - there are no 'pages' in the index, just links to node profiles
The ID you list is simply the end portion of the unique URL which is registered in the index, for this specific profile.
In the example you use the node profile URL was generated by the Murmurations Profile Generator, because I chose to host that specific profile with the MPG
Other profiles will not have that kind of ID, because they are hosted elsewhere. e.g. https://www.open.coop/open.json
This ID isn't part of the schema, it's assigned to the profile somehow by the index.
No, it's assigned to the node profile, by the MPG, when the user chooses to host their profile via the MPG
So if I have an organisation with a profile, and that's been indexed and an ID assigned, I might want to refer to the index server's page from somewhere else. How do I discover what the correct ID (or URL) is so I can reference it?
The question doesn't really make sense, because it's not how the Index works.
To find a list of profiles which match a certain schema you can search the index (for node profiles which validate against the chosen schema/s), collect the list of their unique URLs, then visit those URLs and download the data.
In Murmurations the node profile URL is the unique ID.
Also, how stable is that ID? For example, will it change if the profile content changes? Or if the profile location changes?
URLs which are generated by MPG do not change when the node profile is updated.