We continue to study the unbounded \(\mathfrak {sl}_3\) -laminations [16], with a focus on their structures at punctures. A key ingredient is their relation to the root data of \(\mathfrak {sl}_3\) . After giving a classification of signed \(\mathfrak {sl}_3\) -webs around a puncture, we describe the tropicalization of the Goncharov–Shen’s Weyl group action in detail. We also clarify the relationship with several other approaches by Shen–Sun–Weng [28] and Fraser–Pylyavskyy [10]. Finally, we discuss a formulation of unbounded \(\mathfrak {g}\) -laminations for a general semisimple Lie algebra \(\mathfrak {g}\) in brief.
