MMP.17:4.5 - Refine, combine or return where the difference matters

Choose the next change from the unresolved receiving result. With piecewise interpolation and a bound on curvature, subdivide intervals whose error bound can change that result. With an empirical construction, inspect informative new source cases, a different family or a local correction. Adding cases everywhere can cost more than repairing the affected region.

For adaptive case selection, make a finite candidate set in the allowed region, compare its points by the expected relevance of their unresolved responses and an error or disagreement indicator, and query the chosen source cases. Retain coverage of plausible unexplored regimes; a confident but misspecified replacement can otherwise prevent its own correction. Refit after adding the cases and assess the changed replacement under the conditions needed for the claim. The indicator is a reason to investigate a point, not evidence that the source response there has already been obtained.

A useful combination may keep the source near a threshold or regime boundary and use the surrogate elsewhere. It may keep a cheap model with a learned correction, or different replacements for different response questions. Make the selection condition usable by the caller. When a query is outside the supported region or the needed error control is unavailable, call the source if it can answer, restrict the claim, or return the unresolved response.

Compare total effort: case generation, fitting, checking, each later evaluation, and repairs after relevant changes. A source call can finish a single difficult query more cheaply than improving a reusable approximation. Stop when the receiving question has sufficient support at acceptable cost. Use the existing FPF choice and improvement methods when several worthwhile replacements or refinements remain; this construction does not require one universal best surrogate.