2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133289The mapping class group invariant ideal cell decomposition of the Teichmueller space of a punctured surface times an open simplex has been used in a number of computations. This paper answers a question about the asymptotics of this decomposition, namely, in a given cell of the decomposition, which curves can be short? Screens are a new combinatorial structure which provide an answer to this question. The heart of the calculation here involves Ptolemy transformations and the triangle inequalities on lambda lengths.23 pages, 4 figuresGeometric TopologyAlgebraic Geometry32G15; 57M99; 14H10; 14G15; 57N05; 20F99text