  Modern mathematics is built on the idea that proofs should be translatable
into formal proofs, whose validity is an objective question, decidable by a
computer. Yet, in practice, proofs are informal and may omit many details. An
agent considers a proof valid if they trust that it could be expanded into a
machine-verifiable proof. A proof's validity can thus become a subjective
matter and lead to a debate, which may be difficult to settle. Hence, while the
concept of valid proof is well-defined, the process to establish validity is
itself a complex multi-agent problem.
  We introduce the SPRIG protocol. SPRIG allows agents to propose and verify
succinct and informative proofs in a decentralized fashion; the trust is
established 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, go
down to machine-level details, where they are automatically settled. A
structure of bounties and stakes is set to incentivize agents to act in good
faith.
  We propose a game-theoretic discussion of SPRIG, showing how agents with
various types of information interact, leading to a proof tree with an
appropriate level of detail and to the invalidation of wrong proofs, and we
discuss 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. This
allows anonymous agents to participate in the verification debate, and to
contribute with their information. The smart contract mediates the
interactions, settles debates, and guarantees that bounties and stakes are paid
as specified.
  SPRIG enables new applications, such as the issuance of bounties for open
problems, and the creation of derivatives markets, allowing agents to inject
more information pertaining to proofs.
