Bitcoin’s proof of work consensus consumes energy and requires dedicated, expensive hardware. Therefore, alternatives have been proposed, including proof of stake and proof of space. The latter mines with disk space instead of CPU power. Signum is the only implemented proof of space blockchain with smart contracts, and runs since ten years. But its relatively simple consensus algorithm lacks any formalization. This paper formalizes Signum’s consensus and uses that formalization to show that Signum is free from block-grinding attacks and is largely protected from challenge-grinding attacks. Moreover, this paper proposes a new protection for Signum against newborn attacks.