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  "body": "\n## Summary\n\nThe Morin singularities are the stable [[singularities|1JG3HFWX3T]] of smooth maps whose differential drops rank by exactly one.\nFor maps between manifolds of the same dimension $n$ they form one sequence, with one member for each order $k$ with $1 \\le k \\le n$.\nIt begins with the fold, the cusp and the swallowtail.\nMorin gave their normal forms, and they are exactly the generic corank one singularities.\nTheir [[Thom–Boardman symbol|A9TYDPD5D7]] is $(1, 1, \\ldots, 1, 0)$ with $k$ ones.\n\n## Explanations\n\n### L1 human\n\nThe simplest way a map can degenerate is to crush exactly one direction.\nAmong such degenerations, the fold of a sheet of paper is the mildest.\nThe next is the cusp, where a fold line ends.\nIn more dimensions there are further steps, such as the swallowtail, each one rarer than the last.\nThe Morin singularities are this whole ladder, written in simple coordinates.\n",
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