I read and brainstormed a bunch of different theories and came up with my own – it will be similar to others in many ways, but will be different in some ways.

The theory that Comstock is Booker, who “beat the game” and came back, was baptized/went crazy, is dispelled by the fact that Comstock, whom GG kills, does not have the AD brand on his hand, which Booker burned..
This means, after all, the beginning of the formation of alternative realities – the moment of baptism, so “Comstock” did not sell his daughter, or rather, he did not have her, because he atone for his sins for Wounded Knee and took his current name.

The daughter appeared in the reality of the alcoholic and Tunian Booker 1-2 years after he refused baptism (the situation with Wounded Knee in 1890 was, and Booker said that he was baptized immediately after that. The events of the game exactly 20 years later begin in 1912, respectively, Elizabeth is now just 17/18 years old, and to be precise, the date of the “sale” of the girl is October 8, 1893) At the same moment, Rosalind Lutzs invents her own machine, which allows you to “jump between worlds”. (The car appears regardless of which Booker reality they are in, because the car is a constant, not a variable, it was and will always be, just in Booker’s reality, the male interpretation of Lutzs would have done this later)

Probably Comstock at the same time meets Rosalind Lutzs in his reality (most likely he is a patron), a machine is invented, Columbia is launched (I don’t know for sure, but most likely the machine was invented before Columbia, this will be explained by Comstock’s “prophetic” gift, in addition, the entire technology of “maintaining” the city in weight is built on a similar technology of gaps – Elizabeth speaks about this in the game)

And the physicist (Rosalind Lutzs), after https://charlescasino.uk/ conducting experiments, shows an alternative reality to Comstock, where Booker is a drunk and has a daughter. In Comstock’s reality, the “prophet” is infertile due to experiments with the machine, so Comstock decides to take his daughter away from himself in order to have an heiress to his “Divine” cause. As a result of this, the girl receives power over the faults from childhood, due to the fact that she herself is a “paradox” – she is in a reality where she “cannot exist”, because she could not be born there. Immediately after this, what would physics (see.upd2) didn’t do anything and didn’t blurt out too much – Comstock successfully kills them in his reality, but forgets that these physicists exist somewhere else, namely, judging by the audio recordings – they were preserved in many parallel worlds, and as Rosalind Lutz said in the audio diary: “Time is not a river – but a sea”.

And this is where things get interesting.
Don’t forget that time in parallel universes moves in a straight line, that is, all events are still not exactly a cycle, just a lot of parallel universes have formed (it may be out of place, but there is something like that in the full-length anime “The Disappearance of Haruhi Suzumiya”)

So back to the physicists, having successfully completed the experiment, they understand that they made a very big mistake by giving such a formidable weapon to Comstock as Elizabeth..
And this can only be corrected by “pushing” the drunk Booker into reality, where Comstock dragged his daughter and force him to save her without telling Booker about it, but simply saying – return the girl and we’re even.

Here it is unclear why, even though the current Booker has a mark, he does not remember the events of the sale of the girl, although at the end of the “physics” in the boat they told him: “But it is worth noting that you still tried to get away from the deal,” apparently, after all, 20 years of drinking did not benefit his brain and still he “closed” these memories.
Although perhaps physicists chose that reality for the “game”, where Booker simply does not have a daughter, she dies with her mother during childbirth. And AD could mean that his wife died (As Elizabeth says at the end of the game: “Anna is gone”) because his wife’s name was Anna in our Booker’s reality (this is my terrible adjective, but this is just a “crutch” for the theory, what to do. ) But it also becomes clear why it is known that the false prophet has the AD mark – physicists from Comstock’s reality showed him that in 20 years Booker will rush after his daughter into this reality thanks to them – physicists (by the way, this is probably the very moment after which Comstock kills the physicists in his reality)

So this is where the game actually begins. And the physicists started it, And not just a game, but a “Game of Probabilities”. To achieve a result, as is known from probability theory, you need to “flip a coin” as many times as necessary to achieve the result. By the number of “coin tosses” at the very beginning, you can count in how many realities and, accordingly, how many times the “physicists” carried out the experiment – do not forget they constantly talk sarcastically about the outcomes of experiments (once, for example, Booker died during the revolution, or once he was killed by his own “magnetic shield”, in general, they have already seen so many times that the required outcome is doomed to fiasco again, that they got used to it). They were not afraid of the time paradox, and that someone would interfere with them for one simple reason – they are no longer in this reality – they died at the hands of Comstock, and with the rest of their copies – they were already “reunited”.

But, after all, each experiment was different in detail, and as you know, any detail can affect the outcome of the future (namely the outcome of the experiment), which is what happened at the moment when we play. This time the “coin toss” turned out to be successful, everything turned out exactly as it should, figuratively speaking, as a result of the “experiment” the result was not “tails”, but “heads” (it seems that even physicists mention something similar, unfortunately I can’t remember at what moment). Booker will be drowned before baptism, at the same time “remembering everything,” which will correct the situation.

upd: It is also worth noting that the events in realities, in my opinion, did not turn into a loop, the fact is that everything moves parallel to each other, the ending plays in favor of this assumption – namely, when we see many lighthouses. This is a demonstration to Booker from Elizabeth, so that he would do the right thing and just get at least a little bit into what happened. And the “drowning” of Comstock/Booker is only necessary so that in the future Elizabeth does not become a “scourge” for the world’s population and thereby fulfills Comstock’s prophecy. As a result, we are left with one reality, in which we return at the end of the credits – where Booker was not baptized.

upd2: Judging by the audio recordings, in the reality of Colombia, the physicist is a woman, Rosalinda. In Booker’s Reality – Man Robert. Thus, they are “brother and sister, but in principle – one whole” and after that moment with the sale of the girl, “brother” Lutzs goes to the reality of his “sister”

P.S. (Although I still find the post-credits moment very controversial, since his illusions and memories were always in black and white, unlike the moment when Elizabeth and the physicists show him his trashed room).