Compared to the mathematical rigor that gets usually thrown at such problems, this is all pretty vague, but maybe this is just the informal version. I admittedly did not completely understand the idea, but I of course have thoughts about it.
Instead of “equality at all times” we should be asking “alignment whenever someone actually looks”, because this is all we can promise about someone else’s state.
It seems to me that we generally do not know when and where someone will look, so we will still have to be consistent at all times and all places because all times and all places is when and where someone could look. If the idea is to delay consensus from the write to reads, then I do not see how this makes things any easier. Instead of ensuring that everyone receives a write when it happens, you now have to ensure that you can gather all the writes that happened when a read occurs.
I completely read the first half of it, hoping that everything would eventually make sense, that the pieces would fall into place, but that never happened. I only skimmed the second half and everything seems to just become more and more incoherent. There are some recognizable underlying themes but nothing of it makes really any sense. If I would have to guess, I would guess that ChatGPT generated that gibberish. For large section I could at least imagine that the ideas are just way over my head, especially since I have never heard anything about promise theory and did not read the references. But page 16 really convinced me, that it all is just nonsense - how on earth do we suddenly and out of nowhere end up with differentials, Fourier series, and Heisenberg's uncertainty relation? And while the paper superficially looks sophisticated and scientific with all the symbols and notation, there is no substance behind it. The symbols are really only used for providing short labels for all kinds of things but they are [essentially] never used to relate anythings, let alone to derive or prove something.
Instead of “equality at all times” we should be asking “alignment whenever someone actually looks”, because this is all we can promise about someone else’s state.
It seems to me that we generally do not know when and where someone will look, so we will still have to be consistent at all times and all places because all times and all places is when and where someone could look. If the idea is to delay consensus from the write to reads, then I do not see how this makes things any easier. Instead of ensuring that everyone receives a write when it happens, you now have to ensure that you can gather all the writes that happened when a read occurs.