Fixed-scale inner simulation

The transported-support bound in the source also retains a fixed coarse error of order ${\epsilon }_j$ at fixed $j$. It does not place a simulation in every $O$ merely because $\mathrm{dist}(K,\partial O)>0$; that margin can be smaller than the coarse error.

Thus the claim that every compact coarse local operation gives a constant exact tail in the same local algebra is not established. Nor does equality of its channel imply equality of a chosen list of Kraus operators.