I don't mean to sound harsh below Alexey. On the whole, I think you've done a wonderful job, but that said, here's my take...

I personally think the question is poorly phrased. Throughout the document, Turchin asks the question "will some future entity be me?" The copy problem, which he takes as one of the central issues at task, demonstrates why this question is so poorly formulated, for it leads us into such troublesome quandaries and paradoxes. I think the future-oriented question (will a future entity be me?) is simply a nonsense question, perhaps best conceptualized by the fact that the future doesn't exist and therefore it violates some fundamental temporal property to speak about things as if they already exist and are available for scrutiny. They don't and it is wrong to do so.

I think the only rational way to pose the question is past-oriented: "was some past entity me?" Notice how simply and totally the copy problem evaporates in this context. Two current people can both give a positive answer to the question via a branching scenario in which one person splits into two, perhaps physically, perhaps psychologically (informationally). Despite both answering "yes", practically all the funny questions and challenges just go away when we phrase the question in a past-oriented manner. Asking which of multiple future people is you paralyzes you with some "choice" to be made from the available future options. Hence the paradox. But asking which past person of you puts no choice on the table. The copy scenario always consists of a single person splitting, and so there is only one ancestor from which a descendant could claim to have derived. No choice from a set of available people enters into the question.

One question claws its way back into the discussion though. If current persons A and B both answer "yes" to identifying with past C, then does that somehow make them identified with one another? That can be a highly problematic notion since they can seem to be so irrefutably different, both in their memories and in their "conscious states" (and also in their physical aspects if one cares about physical or body identity). The solution to this addition problem is simple however: identity is not transitive to begin with. Thus, the fact that A is C and B is C does not imply that A is B in the first place. It never implied that anyway, so why even entertain the question? No, of course A and B aren't the same, and yet they are both still identified as C. No problem.

Draw a straight line segment. At one end, deviate with smooth curvature to bend the line to the left. But also deviate from the same point to the right. As we trace along the line, approaching the branch point, we are faced with the classic question: which of the impending branches is the line? We can follow either branch with smooth curvature, which is one good definition of a line "identity" (with lines switching identity at sharp angles). The question is unanswerable since either branch could be identified as the original, yet we are phrasing the question so as to insist upon one choice. I maintain that the question is literally nonsense. Now, pick an arbitrary point on either of the branches, looking back along its history and ask which set of points along its smooth curvature are the same line as that branch? For each branch we can conclude that points along the segment prior to the split are the same line as the branch itself, yet the branches are not equivalent to one another since that would require turning a sharp corner to switch branches. How is this possible? Simple. It is not a transitive relation. It never was.

Turchin pays very minor attention to branching (or splitting) identity in his map, which I think is disappointing since it is likely the best model of identity available.

And that is why I advocate for branching identity in my book and my various articles and papers. I just genuinely think it is the closest theory of identity available to an actual notion of some fundamental truth, assuming there is any such thing on these matters.