Assumption: Fresh current-run bottleneck

Conditional on each past history:

1. the next $X_i$ is uniform on $\{0,1{\}}^2$;

2. the next query is chosen after encoding, uniformly and independently of the current input and retained state;

3. all current-input-dependent retained information at the query still factors through at most two classical values;

4. the actual complete-law discrepancy has a predictable allowance $e_{C,i}$.

Pre-existing device state may be arbitrarily history dependent, but must be independent of the new inputs before they are drawn. Any modification of that state carrying current input information across the boundary is subject to the same storage accounting.