Proposition: Conditional semantics transfer

Purify the complete finite decoder experiment, including undelivered carriers, inaccessible boundary systems, and its reference. Suppose it is represented inside En02-A's global structural class at capacity $N_{\mathrm{glob}}$, with its admissibility requirements and global diagonal faithfulness.

If every actual readout of $s$ qubits, on a global configuration of $g$ live qubits, satisfies

then the decoder's histories and quantum outputs agree with the specified Born programme.

Proof. En02-A's global diagonal-faithfulness theorem identifies all outcome laws. Its continuation-record corollary identifies positive projective residual rays whenever the displayed record budget fits. Apply these statements at each actual readout. Gates and allocations already have the specified meanings. Induction over the finite instruction tree gives the same branch weights and residuals as the Born execution. Zero branches contribute nothing.