CS: Just because you haven’t bothered looking into it doesn’t mean it doesn’t exist. I actually got the pages of a book written with so much info and references I couldn’t read it through to the end. You’re welcome to look them all up yourself. Problem is the book isn’t online. The title is yechi HaMelech HaMoshiach- by Rabbi Wolpo.
Aha! So the proof is something “investigated” by someone who was a known meshichist even before it was at all popular. He dispassionately proved beyong a shadow of a doubt that the LR is descended ben achar ben from Dovid Hamelech. Right. And I’m going to believe him. In non-Lubavich circles he is known as a nutcase. (Mods, if you don’t approve of that term, please alter it to something suitable that retains that meaning.)
Btw thanks for reporting but I’m pretty sure the term Nassi wasn’t out of use for the last 1000 years. If you Google נשיא הדור חבדפדי׳ה you’ll get seforim listed, I don’t think they’re all that old.
I actually went to the site and had a random look at quite a number of the sources quoted. I did not find anything referring to a modern-day Nassi that was not from Lubavich sources. So they simply don’t count for us non-believers.