So I know there's a billion threads about this by now, but I think it's finally time that we sat down as a whole community and finally solve this one.
This thread is by no means a complete theory, and will be updated as people add more information.
I'm going to lay down Madame X's basic known information, that will serve as the base for this speculation and we will build it up from there.
Madame X's known information.
So let's begin with Madame X:
Real name: N/A.
Eye color (current): Red.
Hair color (current): Dark blue / Black.
Skin color: A very light brown.
Allies: Comet, Cosmia, Freya, Kieran.
What do we know: Madame X is a persona that existed for quite some time, according to what we gathered from the Goomidra's side-quest that is. She is the leader of the mysterious team Xen, and is after Melia's 'light' also known now as the archetype. She seems to be able to move freely between time and space with no constraints, clearly demonstrated at the intro of the game where she asks Marianette how many times Vitus (Indirad) is going to put her through 'this', implying that she has experienced this timeline multiple times already, she interferes with time yet again to save the interceptor and set him on the right course to stop the bomb from exploding at Kugearen city, when confronted she says: 'You don't know the countless problems you have created for me, yet... I find myself saving you each time, because you're important to everything. Why are you so important? Who are you exactly? Why are you interfering? You weren't here the first time. Who put you here?'. Later she finally understands that we are the interceptor.
Going by this information alone, I have arrived at my speculation, which is Madame X is Griselda, I'm basing this one solely on her hair and skin color. Stupid right? Yeah that's what I thought until I examined both sprites and realized that the skin color is a perfect match and the hair is just slightly darker, another thing to note is that both characters are presumed to be after the archetype. This would also explain how Madame X is familiar with Spacea and Tiempa, and also how she is able to freely move through time and space.
But Acedy, there are way too many holes in this theory! What about Comet and Cosmia? Why and how would she come in contact with Freya and Kieran?
Well yeah, you're totally right, I just said I'm basing this theory just off of her physical attributes lol.
That's it for now, I'm going to be constructing a complete timeline that will serve as a guide for us to better understand the events and then confirm information according to it.
Be sure to contribute your theories and information down below in the comments.