Cartesi (CTSI) is an operating system token for the development and deployment of scalable decentralized applications using both blockchain components and external ones. Allows you to perform complex and intensive calculations in a Linux environment. Another feature of the project is that it has the ability to run your own code written in any programming languages, with any libraries and services.

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They're both provable! 
Risc0's is geared towards ZK, which makes it great for privacy applications and apps with low computation requirements.

Cartesis's VM is provable through fraud proofs. It's geared towards programmability (boots an unmodified ubuntu) and complex…

They're both provable.