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To clarify, the noisy channel encoding theorem should mean there is a theoretical prohibition on *completely* eliminating side-channels for an AI reading outside information, even if you can mitigate the channels arbitrarily well. (Even a Faraday cage only reduces the bandwidth!)
It might be made cryptographically impossible; you're confidant up to cryptographic assumptions that it won't be able to use side-channels to optimize, due to how they're scrambled.
