Complete channel and late query

Let $B$ denote the initially inaccessible source degrees of freedom, and let $E$ be a declared stored early-radiation resource. Initially $A$ is independent of $BE$, whose state ${\omega }^{BE}$ may be correlated. A supplied linear physical evolution and access prescription defines a CPTP map

The complete output $Z_u$ contains every accessible quantum system and classical flag surviving to the decoding boundary:

A factor is absent if and only if its exclusion is part of the declared boundary. Initially correlated early radiation is not silently traced out and later restored to the decoder.

Only after that boundary is fixed, a uniform $J\in \{1,2\}$ is generated independently of $X$, all pre-query systems, and all accessible random seeds. The decoder then reports $B_{\mathrm{out}}\in \{0,1\}$. The score is