B.5.QD:4.1 - Recover the contribution of the earlier work

State the earlier question and what the work actually obtained. Identify the part that matters now: a counterexample, an unresolved inference, a constructed object, a computational operation or a distinction the earlier description omitted.

For a failure, locate its scope. A counterexample to a lemma can expose a defect in one argument while leaving the main conjecture undecided. A counterexample satisfying the main conjecture’s premises refutes that conjecture. A program’s failure on a case may instead concern its implementation. Recover the relevant reasoning under B.5.RA or B.5.RR when this difference is unclear.

For a success, recover what can now be done with the result. Explain its inputs, output and application conditions. A computation that produces cumulative totals, for example, may provide a way to answer many interval questions. Its reusable contribution is the relation between those totals and the intervals.

Keep independently supported results available. They can supply the construction, limiting case or partial answer for the next question.