The REST API follows a collection/entity model, which just means it has a bunch of collections (search jobs, saved searches, apps, users, views, etc) and each one of those collections is just a list of entities (a single search job, a single saved searches).
For example, the endpoint for all saved searches:
/saved/searches
And the endpoint to get a particular saved search:
/saved/searches/{name}
And in particular for saved searches, if you want to get a list of their running history, you can do:
/saved/searches/{name}/history
Which will give you back job information for that particular saved search. You can read more about collections/entities here and specifically about /history here
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