RSo,
This isnt quite accurate. If you want to actually understand a movement you need to listen to what they claim. David Berger who is considered to be an expert himself acknowledges that this belief was in major part fueled by things the rebbe said. The claim is the rebbe taught it, not that we just want him to be. As for criteria, look you again are watching from far away so u do not know all the various strains of thought in lubavitch, but there are messianists who dont think he is doing any of the criteria. Some hold he will return to fulfill them. Yes there are a great many who hold he matched until the status of chezkas moshiach. The problem with “proving” this is that like anything people have different pshatim and arguments for their pshatim. Much of what lubavitchers say is taken from the rebbes sichas themselves. Perhaps you should check those out before you comment further. I dont know where ur getting the idea that we dont know the rebbe was from king david. He himself testified that his father is from zera dovid in an edited sicha. We have the rebbes family background recorded. He is related to the alter rebbe, who is related to the maharal who is related to dovid hamelech. None of this is disputed by anyone in entire lubavitch.