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Cellular automata on the Eisenstein integers?

Yes, such cellular automata have been studied. However, you're unlikely to find much about them using terms like "Eisenstein integers", since the convention in the field is to describe ...
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Is there a TM that halts on all inputs but that property is not provable?

The halting of one TM can be encoded by constructing another TM and asking whether it halts. That is, given TM $T_1$ and input $I_0$, we can construct a TM $T_2$ with inputs indexed by the natural ...
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