One complete joint pointer model

This construction includes common preparation and correlated assignment noise explicitly. It assumes fresh apparatus state, not unknown memory carried between trials. Finite-channel and instrument terminology follows the standard framework Watrous; the particular equalities above have their own proofs.

Figure fig:pointer is one complete instrument. The measured register is absent from the output. Assignment noise may be correlated across the two words. Failure labels stay in the alphabet; a reset failure is a visible record, not a discarded trial.