The traditional view of cancer evolution states that a cancer genome accumulates a sequential ordering of mutations over a long period of time. However, in recent years it has been suggested that a cancer genome may instead undergo a one-time catastrophic event, such as chromothripsis, where a large number of mutations instead occur simultaneously. A number of potential signatures of chromothripsis have been proposed. In this work we provide a rigorous formulation and analysis of the ability to walk the derivative chromosome signature originally proposed by Korbel and Campbell (2013). In particular, we show that this signature, as originally envisioned, may not always be present in a chromothripsis genome and we provide a precise quantification of under what circumstances it would be present. We also propose a variation on this signature, the H/T alternating fraction, which allows us to overcome some of the limitations of the original signature.