Origami — assign a mountain or a valley to every crease and find out whether the paper folds flat. Kawasaki's and Maekawa's theorems are checked live at each vertex and an exact layer-ordering solver decides the rest. Twelve patterns, from a strip of panels to the traditional preliminary base and a square twist. An independent reimplementation of the mathematics of flat folding: theorems by Kawasaki, Justin, Husimi, Maekawa and Murata; counting results by Thomas C. Hull (Ars Combinatoria 67, 2003); NP-hardness by Bern and Hayes (1996). Origami itself is traditional and has no author; only public-domain and purely mathematical crease patterns are used. Runs entirely in the browser, free, no model.

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