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BoLD: Fast and Cheap Dispute Resolution

Mario M. Alvarez, Henry Arneson, Ben Berger, Lee Bousfield, Chris Buckland, Yafah Edelman, Edward W. Felten, Daniel Goldman, Raul Jordan, Mahimna Kelkar, Akaki Mamageishvili, Harry Ng, Aman Sanghi, Victor Shoup, Terence Tsao

TL;DR

BoLD introduces a delay-resistant dispute resolution protocol that supersedes Arbitrum Classic by organizing conflicting state assertions into a dynamic protocol graph with local timers. It achieves bounded termination (approximately two challenge periods) while reducing on-chain and staking costs, and it supports a multi-level refinement approach to cut off-chain hashing work. The framework relies on trustless cooperation via Merkle-tree histories and a novel timer-based winner determination, with formal attack models ensuring liveness and safety under censorship. The work also situates BoLD relative to Cartesi and Optimism, proposes a hybridization possibility, and discusses gas, staking, and reimbursement models to sustain secure, scalable operation. Together, these elements provide a practical path toward fast, cheap, and robust dispute resolution in Layer 2 systems.

Abstract

BoLD is a new dispute resolution protocol that is designed to replace the originally deployed Arbitrum dispute resolution protocol. Unlike that protocol, BoLD is resistant to delay attacks. It achieves this resistance without a significant increase in onchain computation costs and with reduced staking costs.

BoLD: Fast and Cheap Dispute Resolution

TL;DR

BoLD introduces a delay-resistant dispute resolution protocol that supersedes Arbitrum Classic by organizing conflicting state assertions into a dynamic protocol graph with local timers. It achieves bounded termination (approximately two challenge periods) while reducing on-chain and staking costs, and it supports a multi-level refinement approach to cut off-chain hashing work. The framework relies on trustless cooperation via Merkle-tree histories and a novel timer-based winner determination, with formal attack models ensuring liveness and safety under censorship. The work also situates BoLD relative to Cartesi and Optimism, proposes a hybridization possibility, and discusses gas, staking, and reimbursement models to sustain secure, scalable operation. Together, these elements provide a practical path toward fast, cheap, and robust dispute resolution in Layer 2 systems.

Abstract

BoLD is a new dispute resolution protocol that is designed to replace the originally deployed Arbitrum dispute resolution protocol. Unlike that protocol, BoLD is resistant to delay attacks. It achieves this resistance without a significant increase in onchain computation costs and with reduced staking costs.
Paper Structure (116 sections, 14 theorems, 104 equations, 1 figure)

This paper contains 116 sections, 14 theorems, 104 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The rest of the paper.
  3. Comparison to other approaches
  4. Arbitrum Classic
  5. The two-party challenge subprotocol
  6. Optimizations.
  7. Orchestrating the challenge subprotocol instances
  8. Full concurrency.
  9. Partial concurrency.
  10. From Arbitrum Classic to BoLD
  11. Trustless cooperation
  12. A streamlined protocol
  13. Multi-level refinement
  14. Relationship between Cartesi and BoLD
  15. Relationship to Optimism's protocol
  16. ...and 101 more sections

Key Result

Lemma 1

Assume the hash function $H$ used to build Merkle trees is collision resistant. Consider an unconstrained execution of the L1 protocol. In the resulting protocol graph $\mathcal{G}$, suppose $v$ is a correctly constructed nonterminal node with children $v_{\text{\rm L}}$ and $v_{\text{\rm R}}$. Then

Figures (1)

  • Figure 1: An example execution

Theorems & Definitions (27)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • ...and 17 more