Proposition: No retrospective query-conditioned encoding

Under Assumption ass:fresh, the encoding state and every pre-query accessible record have a law independent of the realized $J$. Any pre-query prediction of $J$ succeeds with probability $1/2$.

Proof. The complete encoding subnetwork has no query-value input. Its operations depend only on the admitted preceding inputs and resources. Composition therefore supplies one encoding law for each $x,\lambda$, not a family selected by $j$.

Freshness makes $J$ independent of that law. For any pre-query predictor $\hat{J}$,

The same argument applies to predictions produced by a quantum instrument on a pre-query state.