The source promise

For a concrete nontrivial example, take one named surviving qubit, with

where $Z=\mathrm{diag}(1,-1)$. A supplied token $m_{\mathrm{src}}\in {\mathcal{T}}_q$ has the promise

Every token has a nonempty promised matter class. For example,

is a density operator because the coefficient has absolute value less than $3/20$. Spectator extensions preserving the source reduction are admitted.

For another fixed source and nonzero $\kappa$, retain only entries whose required expectation $({\mu }_m-{\mu }_0)/\kappa$ is attainable.