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Wiktionary:Cusp>
Note that the figurative usage and the geometric usage are actually closely connected.
Making a small change near a cusp point can produce a large change in the outcome.
An analogy might be the (American)
continental divide where a drop of water falling on the west side will end up in the Pacific, while a drop of water falling just a
very short distance to the east will end up in the Atlantic.
Thus one might suspect that a cusp electron is one where a tiny "push" (which would be practically negligible for a "normal" electron) would send the cusp electron along dramatically different future paths.