Two-slope extremality conjecture for continuous classical DFFs

Let a continuous piecewise linear maximal classical dual-feasible function (DFF) be a function whose derivative, wherever it exists, takes only two values, with one of those slope values equal to $0$. Call an interval component uncovered if it is not covered by the relevant additive structure.

Two-slope extremality conjecture. If the function has no uncovered components, then it is extreme.

This conjecture proposes a sufficient condition for extremality in the continuous two-slope DFF setting. It is motivated by the observation that, unlike the Gomory–Johnson two-slope theorem, two-slope DFFs may have more than two covered components; the source reports a computer-found extreme example with three covered components. The general assertion is not resolved in the supplied text.