Dependence of the limiting straight-segment complex on the direction of approach

Consider a sequence, or a subsequence, of domains approaching a boundary point of a higher-dimensional moduli space, and suppose its images converge under a topology such as the one cited as [MS1]. The limit image consists of surface parts together with a complex of straight line segments.

Direction-of-approach conjecture. The surface parts of the limit image should depend only on the boundary point of moduli space approached, whereas the complex of straight line segments can also depend on the direction of approach of the sequence or subsequence.

This claim refines the description of degenerating harmonic-map images by distinguishing data determined by the boundary point from data determined by the approach direction. The source presents it as an expected dependence statement and gives no resolution.