Also, how did anything that you proposed in your OP, demonstrate that you are both simultaneously on mars and on earth?
The only thing that I've seen researching those links is that they promote a specific brand of wave theory that demonstrates that the center of said wave function is, in actuality, what demonstrates particle like qualities when observed. It also states that space is actually what is vibrating, and therefore what we are perceiving when we see matter, rather than a group of particles.
I will say, it is very interesting stuff, but from what I gathered, it in no way implies that "you" are simultaneously on earth and mars, or conversely absent on Earth and Mars.
I guess I could see that you are trying to imply that since, according to these theories, that all matter is actually vibrations of "empty space" that we in affect "don't exist", but in my opinion, you are missing the entire point of the theories. The "vibrations of empty space" are, in effect, caused by the waves being emitted by different "particles" that are vibrating the aforementioned empty space.
So we are not actually "empty space", but rather we are the result of "particle/waves" vibrating the empty space, which is not necessarily a new idea, and from what I have gathered, is pretty much the common theory amongst quantum physicists for quantum mechanics, although I haven't seen it presented in the way that you presented it, which I will admit was pretty ingenious, although you definitely could have shortened things down without all the philosophical nothingness and non-absolute location nonsense.
But along with that, the holographic universe theories do present an interesting aspect of non-absolute location, although not so much the nothingness in my opinion. Although Hawking once supported the idea of the holographic universe theory, he has since come to oppose the theory due to some experiments that did not confirm the calculations that would promote the holographic universe theory. Even though Hawking no longer supports it, I still believe that the universe is holographic in nature due to the fractal nature of reality, which in a way is representative of a holograph.
In any regard, your presence at more than one location, or none at all, depends on your definition of "self", and according to the information you presented, unless you could prove that your specific "resonant frequency", which implies "yourself" according to these theories, exists simultaneously on Earth and mars, which I personally find would be difficult to prove, then you have no logical stance that you simultaneously exist in both places.
And on the subject of you not existing at all, then you would have no "resonant frequency" to speak of, and you would not be able to type anything at all. If you are arguing that everything is made up of nothing but empty space and waves, then I think a large majority of members on here would agree with you. But along those lines, you have the possible presence of the Higgs Boson/Higgs Field which could throw a wrench in the entire wave vs. particle argument all together.
What do the wave coherence theories that you presented have to say about the wave function vs. the particle attributes of the Higgs?