The PL surface projection moves conjecture

An isotopy of a surface projection with singularities in a compact subset of the surface can be adjusted so that the moves are the Reidemeister II and III moves for the folds, sliding of folds over or under cusps, or the moves in which cusps appear or disappear in pairs given in the indicated figures.

PL surface projection moves conjecture. The moves for singularities of projection of a PL surface should be the analogues of the moves for the singularities of projection of a smooth surface.

This conjecture is needed to establish invariance of evaluations of standard surface diagrams under isotopies of the projection. The source gives no resolution, so its status remains open.