This is based on a discussion that has been recurring on #mtgrules and #mtgjudge, and intended to be an end to this debate.

If Grafdigger's Cage is on the battlefield, and I manifest the top card of my Library (with Soul Summons, or similar).
While we know it doesn't enter the battlefield, what is the status of the card in the library, and how does it react to the following:

• what does the manifested creature look like face down
  
• Vizier of the Menagerie (whether or not the card would otherwise be a creature)
  
• After being shuffled - for effects that search your library for a creature
  

Edited Chaim Weinberg (July 12, 2017 10:00:25 PM)

If you attempt to manifest the top card of your library while Grafdigger's Cage is on the battlefield, nothing happens. At all. The top card of your library is completely unaffected in any way by the attempt to manifest it.