A new geometric proof shows that simultaneous binary collisions in the collinear four-body problem are regularisable only up to C^{8/3}, with the obstruction caused by the first coupling term between the two binaries.
Normal forms for manifolds of normally hyperbolic singularities and asymptotic properties of nearby transitions
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On the $ C^{8/3} $-Regularisation of Simultaneous Binary Collisions in the Collinear 4-Body Problem
A new geometric proof shows that simultaneous binary collisions in the collinear four-body problem are regularisable only up to C^{8/3}, with the obstruction caused by the first coupling term between the two binaries.