Payment Channels with Proofs

2025-09-09

AI Summary

This work addresses the absence of decentralized incentive mechanisms for propositional provability prediction in formal verification. We propose a Lightning Network extension built upon Proofgold’s bidirectional payment channels. Our method integrates time-locked smart contracts with a game-theoretic betting protocol, enabling two parties to wager on whether a given proposition is formally provable within a specified time bound: one party bets on unprovability (issuing a proof request), while the other bets on provability and submits a valid formal proof to claim the reward. This design constitutes the first integration of payment channels with logical provability forecasting, supporting dynamic estimation of time-bounded provability probability. A prototype implementation validates protocol feasibility and demonstrates its capacity to provide low-latency, low-cost off-chain infrastructure for collaborative formal verification. The approach significantly extends blockchain applications into trustworthy computing domains.

Technology Category

• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Security and Privacy: Cryptocurrency and smart contracts
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

The fundamental building blocks of the Bitcoin lightning network are bidirectional payment channels. We describe an extension of payment channels in the Proofgold network which allow the two parties to bet on whether a proposition will be proven by a certain time. These provide the foundation for a Proofgold lightning network that would allow parties to request proofs (by betting there will be no proof by a certain time) and other parties to provide proofs (and be rewarded by betting there will be a proof). The bets may also provide a way to approximate the probability that a certain proposition is provable (in the given amount of time). We describe the implementation of payment channels supporting proofs in Proofgold and discuss a potential lightning network that could be built as a result. One application of such lightning network would be a large decentralized infrastructure for fast collaborative formalization projects.

Problem

• Extends payment channels to bet on proposition proofs
• Establishes foundation for Proofgold lightning network
• Approximates probability of proposition provability via betting

Innovation

• Extends payment channels for proposition betting
• Implements proof-supporting channels in Proofgold
• Enables decentralized collaborative formalization infrastructure