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A complete proof of the recursive gradient approach is presented. It gives aconstruction of all the hierarchy structures of N=1 Super KdV, including thenon-local one. A precise definition of the ring of superfields involved in thenon-local construction is given. In particular, new non-local conservedquantities of N=1 Super KdV are found.

New non-local SUSY KdV conservation laws from a recursive gradient algorithm