Stage 3: an implicit limit is not a finite evaluation

The inspected source describes a conditioned edge measure ${\Pi }_g$, a Markov semigroup ${S_t}^g$, and entrance densities ${h_s}^g$. In that notation it represents the proposed quench limit by

and the stationary function by the corresponding expression with density one OAI227Background,OAI227Entrance.

This is a substantive representation, not an absent formula. However, evaluating it requires the edge environment, the conditioned measure, the semigroup, the selected entrance, and control of its infinite tail. A representation of this kind is not:

• a closed elementary formula for the random function;

• a computable error bound at a chosen finite $n$;

• a convergence rate in the random-function topology;

• a finite comparison of stationary and quench curves.

The local theorem in Section sec:certificate supplies the last item for one small finite system. It supplies none of the missing infinite-system verification.