Controlled island comparison without a reconstruction overclaim

Writing (eq:Petz) does not prove that it corrects a given evaporation code. One must evaluate or bound $D_{\diamond }({\mathcal{D}}_{\sigma ,\mathcal{N}}\mathcal{N},{\mathrm{id}}_A)$. A scalar entropy history supplies neither the channel on every matrix unit nor its adjoint, and therefore does not by itself specify this calculation.

The operational gap addressed here is consequently narrow: an entropy history alone is not a code-wide channel certificate. It does not deny reconstruction conclusions derived from entropy together with additional gravitational, algebraic, and code-space structure. Page-curve expectations likewise remain valuable unitary-evaporation diagnostics without being substituted for an arbitrary-input decoder error Page2013.