Grunkle Stan is Bill Cipher - Gravity Falls theory

Many in the Gravity Falls fandom have speculated that Bill Cipher and Grunkle Stan might be one and the same person. The Axolotl poem usually comes up, as well as very specific choice of words used both by Bill and Stan (Buy gold. Eenie-meenie-minie-you! And so on). We know that Bill has found a way out of certain death in the series finale, by invoking the name of the Axolotl. This, contrasted with the aforementioned poem found in Dipper and Mabel and the Curse of the Time Pirates' Treasure sheds light upon a much deeper connection between the entity that Bill Cipher is and the man who is Mr. Mystery for a reason.

Sixty degrees that come in threes.
Watches from within birch trees.
Saw his own dimension burn.
Misses home and can't return.
Says he's happy. He's a liar.
Blame the arson for the fire.
If he wants to shirk the blame,
He'll have to invoke my name.
One way to absolve his crime.
A different form, a different time.

By deconstructing the poem line-by-line, we can see that, from a certain point of view, this poem represents Stan as much as Bill, at certain points even to a much higher degree.

Sixty degrees that come in threes. – This is obvious for Bill, as he is a triangle. But look at Stan's life: he is a man in his sixties and his life can be divided into three periods. His childhood, his wandering years and the last thirty years he was busy to get Ford back from the other dimension.

Watches from within birch trees. – Of course, we can see that Bill has the ability to spy on us using everything that has eye symbolism, including the characteristic marks found on the trees. Stan, however, lived most of his life in the Mystery Shack, surrounded by the very trees, watching out for tourists to scam.

Saw his own dimension burn. – This is where it gets confusing. It means that Bill was responsible for something, but that might not be entirely his fault. The choice of words is interesting here. He "saw" and not "watched", and for me, it means that whatever Bill did, he did not mean to cause that much of a harm. As for Stan, we saw how he burnt all his bridges because of one big mistake, forcing him to leave his family behind.

Misses home and can't return. – This would mean Bill is not native to the Nightmare Realm, from which he orchestrated Weirdmageddon. As for Stan, it is obvious, not much to analyze from his side here.

Says he's happy. He's a liar. – This makes me to believe that all of Bill's psychopathic antics are a cover for a deeply sad personality. As for Stan, another well-known fact is that while he often appears to be in a joyful mood, he has a deep burden to bear.

Blame the arson for the fire. – I speculate that Bill was the cause of something he didn't understand the consequences of, leading to his homeworld being destroyed. Stan, as we know, destroyed Ford's perpetual motion machine, although he didn't mean to, leading to the chain of events that led to his estrangement from his family and Ford's eventual disappearance into the other dimension.

If he wants to shirk the blame, – Well, we didn't see Bill trying to redeem himself, but just wait. Stan, however, was doing everything to make up for his mistakes.

He'll have to invoke my name. – This is the very thing that Bill did, with his final (known) words. Stan, on the other hand, used to own an Axolotl, we can see one in his aquarium next to his TV couch.

One way to absolve his crime. – Yeah, Bill might be repenting out of necessity, not because he really wants to, but he knows that the only way to survive is atonement. Stan was doing everything in the past thirty years to undo the damage he has caused.

A different form, a different time. – And here is where the two fates meet. The Axolotl re-created Bill as Stan to ensure Bill's final downfall. Stan was living under fake names for decades, with his "Stanford" identity becoming a second skin for him for thirty years, all while working to bring the real Stanford back.

By looking at these lines one by one, we can see how these two characters are mirroring each other. Of course, we don't know much of Bill's backstory, but there are certain hints, and more provided by the Axolotl poem. Also, we can speculate that all fit into the multiversal mythology of Gravity Falls:

Bill represents chaos and destruction.

The Axolotl represents order and creation/rebirth.

Time Baby represents time, no argument there.

These entities and the concepts they represent balance each other out. We know that the Axolotl is alive and well, and that Time Baby will be back in a thousand years (and will be really cranky, also, he IS time, so a thousand years is nothing for him). This means that, in order to achieve balance, Bill needs to exist, and as of now, he exists as Stan, trapped in a perpetual loop of being defeated by himself in a different from, at a different time.

Does this mean Stan is evil? Of course not! He is a very flawed human being with a heart of gold deep inside. He managed to overcome both Bill, by literally punching him out of existence inside the Mindscape, and mend the failures of his own life by rescuing Ford and bringing his family together once and again. Yes, he will always make the same mistakes when the loop starts again, but at the end of the loop, he has atoned for his crimes. As for how the loop can be broken? That's a discussion for another time...