Manuscript Hawk01-A@1 · Hawk01-A.tex · remark · 11979653
Remark: Strength and limitation of the counterexample
An explicit Hawking-mode completion and its nonidentifiability › Paired occupation sectors and the early resource · lines 1645–1660
The ambiguity is stronger than equality of single-particle spectra: the complete late density operator is identical in the two completions. The difference lies in the joint correlations. No measurement on the late radiation alone can distinguish the messages.
The isometries nevertheless differ from the identity-action semiclassical null. They expressly introduce an internal-to-outgoing transfer interaction. Matching an outgoing thermal marginal does not make that interaction a consequence of local semiclassical evolution, nor does it preserve a near-horizon pair state. Thus the example does not evade small-correction theorems by merely changing a thermal diagonal Mathur2009.