Arnold's Seminar 13 April V.Zakalyukin On Ricardo Uribe's paper "Bifurcation diagram of vanishing flattenings" To a germ of function on a plane one associate a (vanishing) family of space curves being the graphs of the restrictions of the functions to the plane circles around the origin. The flattening points of these curve are considered. The problem of Arnold to study the stability of corresponding bifurcation diagrams will be discussed (as well as some other relevent problems of singularity theory).