In a recent paper [1] we used a computer assisted proof to show the existence of a highest cusped wave to the Burgers-Hilbert equation in fluid dynamics. We are now working on proving a similar result for a larger class of equations, the fractional KdV equations. In the project which this is a continuation of we developed the code as well as the machinery to run it in scale on the cluster. With this continuation of the project all that remains is to run one final computation. [1]: https://arxiv.org/abs/2205.00802