It's not been explicitly confirmed, but given the similarity in forms to later notes signed Santa (and confirmed to be Dumbledore), the note's writer claiming the Cloak was freely given by Harry's father, and the explicit warning against letting Dumbledore see the Cloak, it's very likely that Dumbledore gave Harry the Cloak as in canon.
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 114, and also, as a special case due to the exceptionally close posting times, chapter 115.
There is a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)