MMP.16:1 - Problem frame

Use this pattern when several mathematical accounts remain possible and the next useful answer depends on a difference between them. You can choose which cases to observe, under which conditions, or how to record them. The difficulty is to find an attainable observation that exposes the relevant difference.

The desired result may be a better decision, a supported prediction, a distinction between proposed mechanisms, or a new research direction. For example, two response laws agree at all previously tried inputs but imply different behavior in the intended use. Repeating those inputs more accurately may leave the disagreement untouched.

This pattern constructs the mathematical design of an observation. It returns what to observe, what records the alternatives would produce, and how those records would change the answer. It can instead return a useful limitation: the available observation choices leave the needed distinction unresolved. The subject practice supplies feasible access and performs the observation; PHY.9 and PHY.10 do that work for a physical readout and test.

Start with the receiving question, the alternative models and the observation law from MMP.7. Set-valued reasoning needs functions and sets. Probabilistic design also needs conditional probability and the inferential meaning chosen in MMP.13. An analyst can supply that mathematics while another participant supplies the observing conditions and interprets the result.

Use the present answer directly when the remaining alternatives make no consequential difference. A new observation is only one possible response to uncertainty. C.11.DUA supplies the comparison with using what is already known, changing the claim or taking another feasible step. A routine prescribed measurement with an already sufficient design needs no new design study.