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Modern mathematics is built on the idea that proofs should be translatableinto formal proofs, whose validity is an objective question, decidable by acomputer. Yet, in practice, proofs are informal and may omit many details. Anagent considers a proof valid if they trust that it could be expanded into amachine-verifiable proof. A proof's validity can thus become a subjectivematter and lead to a debate, which may be difficult to settle. Hence, while theconcept of valid proof is well-defined, the process to establish validity isitself a complex multi-agent problem.  We introduce the SPRIG protocol. SPRIG allows agents to propose and verifysuccinct and informative proofs in a decentralized fashion; the trust isestablished by agents being able to request more details in the proof steps;debates, if they arise, must isolate details of proofs and, if they persist, godown to machine-level details, where they are automatically settled. Astructure of bounties and stakes is set to incentivize agents to act in goodfaith.  We propose a game-theoretic discussion of SPRIG, showing how agents withvarious types of information interact, leading to a proof tree with anappropriate level of detail and to the invalidation of wrong proofs, and wediscuss resilience against various attacks. We then analyze a simplified model,characterize its equilibria and compute the agents' level of trust.  SPRIG is designed to run as a smart contract on a blockchain platform. Thisallows anonymous agents to participate in the verification debate, and tocontribute with their information. The smart contract mediates theinteractions, settles debates, and guarantees that bounties and stakes are paidas specified.  SPRIG enables new applications, such as the issuance of bounties for openproblems, and the creation of derivatives markets, allowing agents to injectmore information pertaining to proofs.

Smart Proofs via Smart Contracts: Succinct and Informative Mathematical Derivations via Decentralized Markets