I have some good opinions in this area of thinking.
I don't know if you got the ideas from me, but I have said in my work over a year ago at age ~21/22 that too that:
1) you can make a copy w same thoughts running on another exact Earth while you're alive and so if did it when you're dead it again is "another". But maybe we all are the same one, I know we all can slowly turn into the same body w same memories technically. Etc etc.
2) You change yourself slowly, and the way it was done is fine and still you. In contrast I also said in my work we get arms chopped off etc instantly and are still you, so, idk, I guess that's not the answer? I mean 'you' are your thoughts/feelings in ur brain, and those change all the time, slowly. But again, all day long we don't remember all our memories (or can get a chunk of brain extracted)...so why not they just all get erased and we are still the same? But does our neural net process input/thoughts using the net derived/made up from all those experiences we've had? Yes, but only the nodes being accessed...Right now I can clear my mind and just see my hand...on my keyboard.....where is all that "me" anyway? I'm not using my knowledge or attitude at that moment...just a quite sad moment of wasting time looking at my hand on my keyboard, maybe I am the recognition net simply
But then how slow is OK? Why is there a difference? Either you are still you or suddenly not cus happen too fast/hard? I agree maybe waking and fixed in cryonics thawing you'll be "u". Another thing I say is photons move so many locations each second that each second there is a huge number of "ticks", about 135million or thousand years each second, and that during all that slow mo (well, real time) time we DONT sense/comput dude! We are so damn slow. Lightspeed optical computing would solve all problems if all the soil was thinking nanobots running at lightspeed thinking etc. Again, our brain registers so, so, slowly, we only have a "register" between thousands of years in the real real-time of lightspeed. Thats ind boggling.
I also thought recently our bodies can be repaired by nanobot advanced creatures one day soon, like a car, all parts can. We can already add peoples limbs, organs, etc, push nose back in better, add skin....and sow it up and it looks better! Yet we do it so poorly too! Nanobots would push it all to a "better" state. We just can't and think its magic feats of stupendidness! Of course, the faster more unmoral way to save humans is to access and remove right-on-site in the AIR the thinking neocortex waiting at top, how easy you nanoswarms have it.
You, if we want you to stay existing, may be recogniizing stuff, and a own knowledge net, often used, a history of these mental actions...a pattern...the way we act, get up, do something, a sequence, we try to protect ourselves, that one moment staring at a wall is just one moment of a bigger sequence....longer time! ?
Of course if you mean us machines, is my friend Joe still Joe if he morphed too fast? Well, no. But if you age or do stuff slowly humans dont recognize it (you as being "woah different!!")....But that is a different subject - the body.....above I was talking about consciousnesses that sense senses that we do