Theorem: Neutral output failures preserve the classical bound

Suppose the complete record kernel factors through the $K\le 2$ classical state:

With score (eq:neutralscore),

The decoder's failure or erasure probability may depend on $m,j,\lambda$.

Proof. Replace every neutral record by an independent fair binary answer. Its expected correctness is $1/2$, so the expected score is unchanged. This replacement is another stochastic decoder using the same memory. Apply Theorem thm:classical.