Density of Stable Interval Translation Maps

The uploaded paper proves that for every r ≥ 2, the set S(r) of stable interval translation maps (as defined via Hausdorff continuity and locally constant topological type of X(T) and a locally constant number of discontinuities in I \ X(T)) is dense (and open by definition) in ITM(r). This is stated as Main Theorem I and used to deduce the open-and-dense prevalence of finite-type maps; the paper also records that on each component of X(T), the first return map is a circle rotation and that T ↦ X(T) is Hausdorff-continuous (see Definition 1.1, Main Theorem I, and the summary statements). The model’s solution cites precisely this result (Drach–Staresinic–van Strien) and sketches the same core mechanisms (linear independence/transversality for itinerary vectors; ACC + Matching), reaching the same conclusion. Minor presentation quibbles in the paper’s high-level proof chain (the shorthand equalities in the Main Theorem proof outline) do not affect correctness. Overall, the paper’s argument and the model’s solution are aligned in substance. Key support: stability definition and properties , density statement and proof structure via Theorems A–C , and the rotation/continuity refinements .