Why is that when your first upload a paper onto ArXiv, Google Search shows that it has been uploaded to "https://128.84.21.199" Has anyone else noticed this? 

When I uploaded a paper onto ArXiv, and after two days when it finally shows up on Google (in Google Search, of course), Google says the paper can be found via the link https://128.84.21.199/pdf/arxiv_ID_of_your_paper

This wouldn't have been a problem if wasn't for my browser issuing a warning before clicking on it



Can anyone explain what is going on here?
That number is the IP address for arxiv. Typing "arxiv.org" into your browser is effectively the same as typing that number (the domain name will get converted for you).

Why the error? The HTTPS certificate is assigned to a domain name, not to the IP address (which is good, because IP addresses may change). Even though in this case, the domain name would result in this IP address, your browser thinks it is trying to use a false certificate.

To avoid this error message, just replace that number in the URL with "arxiv.org" and the error will go away. A worse workaround would be to replace "HTTPS" with "HTTP".