And then one year Baba Yaga agreed to teach Battle Magic at Hogwarts, under an old and respected truce." Professor Quirrell looked... angry, a look such as Harry had rarely seen on him. "But she was not trusted, and so there was invoked a curse.

And although Perenelle was new-come into the beauty of her youth, her heart was already blacker than Baba Yaga's own -"

Ah, yes, Perenelle, the beautiful and covetous. Perenelle seduced the Dark Lady over the months, with gentle touches and flirtations and the shy pretense of innocence. The Dark Lady's heart was captured, and they became lovers. And then one night Perenelle whispered how she had heard of Baba Yaga's shape-changing power and how this thought had enflamed her desires; thus Perenelle swayed Baba Yaga to come to her with the Stone in hand, to assume many guises in a single night, for their pleasures. Among other forms Perenelle bid Baba Yaga take the form of a man; and they lay together in the fashion of a man and a woman.

Does anyone else think this reads like Quirrel has an awful lot of emotional connection to and personal memories about this story, almost as if it were Baba Yaga speaking about herself in the 3rd person? Could Riddle or Quirrel have come across a Baba Yaga horcrux? The resurrection stone, perhaps? Earlier than that? Why would Perenelle share these secrets? How would anyone know these details if Baba Yaga was dead and Perenelle had not shared them? No one else would have been present for those private moments.

And what are the odds that a Dark Lady like Baba Yaga did not have a horcrux?

In Ch. 70 Quirrel makes a point during the S.P.H.E.W. confrontation with the headmaster that Dark Ladies are also underrepresented, and that few could name one except Baba Yaga. Self-reference?

She would probably need to be faking the map labelling her (and Harry?) as Tom Riddle, but a sorceress as powerful as Baba Yaga combined with the secrets of Salazar, who created the Hogwarts security system in the first place, could probably accomplish that.

Notice what Quirrel does and doesn't say in parseltongue:

"None of it iss known to me to be falsse," said Professor Quirrell. "Telling a tale implies filling in certain gaps; I was not present to observe when Perenelle seduced Baba Yaga. The bassicss sshould be mosstly correct, I think."