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To me it looks like they have exponential growth in the number of connections between the memory elements. This would account for having exponential storage while still not violating any physical principles (also, it would not be nearly as useful as they imply).

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That would violate a physical principle (The Holographic Principle[1]), namely that the amount of information in any given volume of space is limited by the volume's surface area. At some point an exponentially growing number of connections is going to overtake the surface area of the volume of space occupied by the supposed physical device.

[1] I understand that this is largely theoretical, but it seems to be pretty much accepted by the Physics community AFAICT.

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