Liftability conditions for multi-strip semi-discrete frameworks with vanishing boundary forces

Determine explicit liftability conditions for planar semi-discrete frameworks composed of n ≥ 2 strips whose boundary forces vanish, i.e., μ_{-1} = μ_n = 0, specifying when such frameworks admit a semi-discrete conjugate surface F = (f, z) in R^3 that orthogonally projects to the framework f.

Background

The paper establishes a semi-discrete analogue of the Maxwell-Cremona lifting property, proving that a planar semi-discrete framework is stressable if and only if it is the orthogonal projection of a semi-discrete conjugate surface built from developable strips.

For frameworks with vanishing boundary forces (μ_{-1} = μ_n = 0), the authors show that boundary curves in the lifting lie in planes and fully characterize liftability in the simplest non-trivial case of a single strip via Equation (1-strip-liftability).

Beyond the one-strip case, the authors explicitly state that determining analogous liftability conditions for frameworks with n ≥ 2 strips and vanishing boundary forces remains unresolved.