When do we cease to exist?

We can change form and retain some elements and even change to energy altogether...become part of something else..do we have proof we can exist as we are again?

I mean you can freeze that water again to form a piece of ice...would that be the same piece of ice even though the mass elements are the same? Same molecular pattern perhaps but not the same piece of ice my dog ate.

Proof is mathematical and base on a few assumptions as anything else is. I am not a mathematician nor a theoretical physicist but I will give you my current layman understanding of it:
Given an infinite amount of time and given an non infinite amount of possible configurations within a discrete amount of space there must be a finite amount of possible states for matter that have a chance greater then zero of occurring.

As I said all you have to do is let it run for enough time that by chance alone one such repeating configuration would occur.

Sameness requires the same arrangement of information given the elementary constituents are the same, it doesn't matter if Y particle of hydrogen is not X particle of hydrogen, so long they have the same state, spin, momentum energy, etc.. What is important to retain here is sameness of information.

Are you referring to the context of time continuum?

Yes but then, you are only referring to mass duplication.

I don't think we cease to exist. Again it doesn't "make sense" to begin from no where (ex nihilo, problems in.)

This is one of the most interesting sentences I have read so far on A2K. Thank you. (no I am not joking)

Its a philosophical web spiral of madness to go down that road....
Who's to say sameness of information is not enough for full identity ?
A perfect atomic twin of you would only stop being you from the moment on you follow different paths. One can argue that up to that point both of you are on a "quantum superposition" and are the same.

I don't either...I think we can transform into something else. From the standpoint of energy and matter.

From where we came or on what we transform to is irrelevant for the problem.
So long what we are can be repeated, then what we were is not ever lost.

I don't mind spirals. Let's say I'm cloned today ..twice. Perhaps in the time loop of eternity I could encounter myself (selves) in exact situations I've lived through...replicate instances in my life. Still...there's a difference between me and the clones.

You can bring the hypothesis up but its highly difficult to clarify why those copies wouldn't be "you"...
Let me give you an example, if you are predicating identity not only in information states but also in having the same exact particles then as you lose some millions of atoms every second you would be dying from instant to instant. If we consider energy states, then every nano second or worse.

Like I said before in terms of energy and matter, I'm on board.

clones aren't going to be the same person though. It's not the same prima mater (like a soul.) How would they be in the same situation or time loop, similar time loop?

To put it in a far more dramatic way consider the following absurd mental experiment:
In a Universe where you would transform from a human to an elephant n back every second, you would still consider yourself the same you, prevented such causal change of information states was fully integrated within your perceptual experience and conscience as time passed by. For self identity purposes what is important is not on what you become but rather the understanding the witnessing the experiencing of the process being integrated within your consciousness. As every second passes you aren't X any more as you lose and gain some different matter. Even the amount of transformation is irrelevant if you consider it natural within the rules of the Universe you live in. Self Identity is constructed within motion and in relation to other things around you. Is the patterns in the change process itself that make you and not any particular state per se. A particular state without reference points informs nothing from you to you.

So regarding not identity, but self identity, we can go as far as to say that aside matter itself not even any information state is crucial to define what you are but rather the cohesion of the transforming process itself making sense within your perceptual frame of reference is what is bottom line essential. Unity in change, equals logos, self understanding. You pay attention to the regularities in the change process itself no matter how crazy those regularities could be in different universes with different rules of nature and different causal change processes.

If time is an element in the equation, then that changes the perspective For instance, if A is created at 0730and B at 0830 then A cannot be B. B didn't exist when A first appeared.

So to make it less confusing:
Self identity is predicated in the regularities of the changing processes. Regularities in change being "familiar"patterns are themselves sameness at a greater level of resolution. When your consciousness unites these patterns in your "experiencing" then all of it is yourself.
If you really want go down the rabbit hole with this we could even speculate that the dimension of self is not fixed as you acquire and lose some perceptual points of view about your own "experiencing"...your self, expands and contracts into and from the world at large depending on different levels of awareness on what "your" consciousness of the world can encompass.

Very well but then you have to take seriously the hypothesis that as every second passes you yourself change and then you are not you any more...but this is not what you experience as you maintain your sense of identity through change so I think bottom line that is a weak argument.
Remember we are not talking about identity of objects alone, but self identity which is a dynamic process.