Do you need a certificate to validate your publication? Background:
I got an acceptance at a conference and now need to register for it. They said that only the person who registers, gets the certificate and not all authors (we have 5 but only 2 primary authors).

Question: Is the publication in the proceedings (LNCS) alone sufficient to prove that you published the paper? Or does one need the certificate as well?
If required as to whom I am asking for, you can assume it to be a PhD (CS) admit panel in the US.
I am aware of this question: How to show proof of publication?. But my conference has no admit card associated with it.
Published conference proceedings suffice for proof of publication.