One attempted run

Each attempted run has the following order:

1. Independently sample uniform bits

   $$X=(X_1,X_2)\in \{0,1{\}}^2.$$

2. Supply the bits to an encoder, either together or at two distinct encoding times.

3. Enforce a storage boundary after the last encoding operation.

4. Apply a declared delay.

5. Only after encoding and storage, independently sample

   $$J\sim \mathrm{Unif}\{1,2\}.$$

6. Supply $J$ to the decoder and record its answer $B$.

The ideal binary score is

Its population expectation is

The experimenter retains $X,J$ for scoring. That record is inaccessible to the device's decoder. Only one query is scored per independently encoded run.