C4: input information and reference limitations

This theorem requires constancy on all message inputs, not merely on a chosen set of classical basis states.

The A–B stationary preparation is a fixed state, not a microstate-dependent evaporation channel. A successor claiming microscopic recovery must specify a message space, a preparation or encoding map, evolution, radiation access, and a referenced recovery criterion. Adding tomography or a decoder cannot supply those dynamics.

Figure fig:information is the information limitation. Identical accessible inputs cannot reveal a label, even if some unaccessed environment still carries it. A channel that ignores the message is a replacement channel, and a radiation-only decoder then has entanglement fidelity ${D_M}^{-2}$.