MMP.17:4.2 - Obtain construction cases that can distinguish useful replacements

Reuse source results whose inputs, output meanings and computation are compatible with the target. Choose further cases to expose consequential variation: the region the receiver will visit, boundaries or changes of regime, and places where plausible replacements disagree about the receiving answer.

For a scalar interval, an initial set of endpoints and interior points may suffice. For many inputs, a full grid can be unaffordable; use known structure to reduce the varying inputs, or distribute a finite set across the relevant region before concentrating additional cases. A design concentrated near one operating point supports a local construction unless another argument supports wider use.

Each case supplies an input and the selected source response. If the source response is itself approximate, carry its error into the construction. For a stochastic source, use MMP.7 to identify how the runs were obtained: repetitions, dependence, shared random inputs and selection can change what their averages or fitted probabilities estimate. MMP.13 supplies the uncertainty result needed from those runs.

Choose case placement and assessment together. Cases used to fit, select or repeatedly tune the replacement are construction cases. If the further-use claim depends on held-out performance, retain assessment cases suited to that use and do not count their later reuse for tuning as untouched assessment. For trajectories, repeated runs or grouped inputs, the unit that must be held out follows the claim; randomly separating nearby points does not by itself test a new trajectory or regime.

A query to the source model adds information about that model’s response. An observation of the world may also challenge the model. Keep those contributions separate. Use existing bounds or observations when they already answer the question; another experiment is not an entry condition for constructing a surrogate.