A catalytic machine is a space-bounded Turing machine with additional access to a second, much larger work tape, with the caveat that this tape is full, and its contents must be preserved by the computation. Catalytic machines were defined by Buhrman et al. (STOC 2014), who, alongside many follow-up works, exhibited the power of catalytic space ($CSPACE$) and in particular catalytic logspace machines ($CL$) beyond that of traditional space-bounded machines.

Several variants of $CL$ have been proposed, including non-deterministic and co-non-deterministic catalytic computation by Buhrman et al. (STACS 2016) and randomized catalytic computation by Datta et. al. (CSR 2020). These and other works proposed several questions, such as catalytic analogues of the theorems of Savitch and Immerman and Szelepcs\'{e}nyi. Catalytic computation was recently derandomized by Cook et al. (STOC 2025), but only in certain parameter regimes.

We settle almost all questions regarding randomized and non-deterministic catalytic computation, by giving an optimal reduction from catalytic space with additional resources to the corresponding non-catalytic space classes. One main consequence of this is
\[
CL = CNL
\]
i.e. with access to a large filled hard-drive, non-determinism provides no additional power.

Our results build on the compress-or-compute framework of Cook et al. (STOC 2025). Despite proving broader and stronger results, our framework is simpler and more modular.