Statelessness is one of the main limitations of the REST architecture, which can be read in the original publication:
5.1.3 stateless
Then we add a restriction on client-server interaction: the connection must be inactive by nature, as in the client-stateless server (CSS) style of section 3.4.3 (Figure 5-3), so that each request from the client to the server should contain all the information required to understand the request, and cannot use any stored context on the server. Therefore, the state of the session is completely saved on the client.
So, for the credentials you mentioned, you must provide them in each call separately (for example, Basic Auth + SSL). Of course, this was the "real world", and applications are starting to vary. You can also use OAuth, fixed tokens, etc., but remember that then you weaken the "RESTfulness" of your API.
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