MMP.18:4.3 - Restore what the receiving scale needs

Apply the receiving operation to the proposed supplied description. If the result still depends on discarded detail, identify that dependency before choosing a closure.

For example, a component supplies only the mean of x over a region, while a neighboring response requires the mean of x^2. The missing contribution is the variance:

mean(x^2) = mean(x)^2 + variance(x).

Two fields with the same mean can therefore yield different received responses. Supplying the squared mean silently sets the variance to zero. Retain the needed statistic, obtain it from the finer model, supply a justified closure or return bounds sufficient for the question. MMP.9 derives reduced evolution and closures; MMP.17 constructs a surrogate when that is the chosen supplier.

A time-scale change can create memory. An interval average need not determine a response at an intermediate instant. A rapidly changing component can also leave an accumulated effect after its local state has relaxed. Recover the information needed by the receiving answer instead of assuming that a small or fast component has no relevant contribution.

Use a coupled approximation only within the conditions supporting it. If feedback drives a surrogate or closure into a different regime, revise that contribution or return to a suitable supplier. Good behavior on isolated component inputs does not establish behavior on inputs generated by the coupled system.