Here is a free updated version from 2022. https://arxiv.org/pdf/1502.04573 https://arxiv.org/pdf/1502.04573 Edit: Alright, I'm back after skimming the paper. T

Here is a free updated version from 2022. https://arxiv.org/pdf/1502.04573 https://arxiv.org/pdf/1502.04573 Edit: Alright, I'm back after skimming the paper. This is a halting oracle. Here is what I understand, with my limited knowledge of QM. There are two ingredients (Theorem 3: Main Theorem, page 6). 1. For each integer n, the authors construct a spin lattice model H(n). 2. There is a specific Universal Turing Machine, that halts on n iff H(n) is gapped. Here is how to construct the oracle. For any Turing machine, find out what integer n it corresponds to for the specific Universal Turing Machine of the paper. Then physically construct H(n) and see if it's gapped. However, this H(n) cannot be physically realized. First, it is an idealized model in which lattice points only interact with their neighbors. Second, it actually a family of lattices, and the result is about the thermodynamic limit as the lattice becomes infinite. Interestingly, Seth Lloyd appears to have previously proved this result in 1993. https://arxiv.org/pdf/1602.05924 https://arxiv.org/pdf/1602.05924