Decoder outputs and the external archive

Let $O$ be the decoder's scored output, taking values in

The complete attempted-run record may also contain

where $H_{\mathrm{ext}}$ includes preparation, storage, and diagnostic records kept by the experimenter.

The external archive need not factor through the memory: it deliberately contains the scoring copy of $X$. The capacity bound concerns the decoder marginal $p(O\mid x,j)$, whose access must satisfy (eq:classicalfactor). Any archived record returned to the decoder ceases to be an external spectator.

Define the predeclared score

Every attempted run receives a score. Timeouts and unavailable outputs have a declared outcome, not a retrospective deletion rule.