3.1. Construct an unfamiliar account

Recover the question → choose objects and operations → formulate relations → obtain a consequence → interpret it or revise the failed contribution.

Start with FPF B.5.FM when the mathematical question is missing. MATH.16 chooses a construction from the maps it must support. MATH.1 and MATH.5 can then construct and interpret composable expressions. MMP.10 expresses admissible subject cases; MMP.11 constructs an unknown relation inside supported conditions. Use FPF C.29 to interpret the consequence through the correspondence between the mathematical account and the working situation.

Small use. A cart log records two unit movements. Total distance is two both for forward-then-backward and forward-then-forward. If each entry records an actual signed displacement, assign +1 and -1 and use addition for composition: the final displacements are zero and two. MATH.1/.5 supplies that interpretation. If entries record commands and the cart can slip, the same sum answers a command question. Observation or a movement model must supply the relation to achieved position.

That missing physical account changes what can be concluded. PHY.4 develops physical grounds for restrictions on an unknown law. These restrictions can still leave a physical relation unresolved; use supported subject knowledge, observation or a collaborator for the needed premise. B.5.MPC connects the physical, mathematical and computational contributions. Stop with the qualified consequence, or with the particular relation still needed.

The physical connected-use example follows an unknown response through a balance, a conditional prediction and a distinguishing observation. It shows when an experiment is unnecessary and which premise to revisit after conditions change.