> You can “compress all of the three-dimensional world into two dimensions.”

That sounds a little like the sophons in the novel Three Body Problem. IIRC, aliens took a photon, unfolded it to a flat surface to etch circuitry on, then folded it back up and fired the photon at earth where it unfolded again and did the bidding of the aliens.

> you can decipher the entire contents of the box just by repeatedly measuring points on the surface

So if the box is both inside and outside of a black hole, is that a path for information to leave a black hole?