Paper · June 2026

Zero-Bond Deterrence

When verification is cheap, the correctness bond is redundant.

Download PDF ↓Machine-checked: Z3 (SMT), Lean 4, PRISM-games

Abstract

Decentralized compute markets discipline a paid worker in one of two ways. Either the worker posts a slashable bond and a fraud proof burns it (optimistic rollups, refereed delegation), or there is no bond and the system relies on reputation and subjective trust. The first locks up capital proportional to the value at risk; the second is soft. We argue this dichotomy is not fundamental, it is an artifact of verification cost. A bond is what you require when catching a cheat is expensive, so you catch rarely and must punish hard when you do. Make catching cheap and the logic collapses. We make this precise. For a rational worker who cheats only to save compute, honesty is the best response exactly when the detection margin q satisfies q ≥ Δ/(p+Φ), where Δ is the compute saved by cheating, p the fee, and Φ the franchise value of continued participation. A correctness bond b only enters as a substitute for low q: b ≥ Δ/q - (p+Φ), so it is needed only when verification is too sparse. When verification is cheap enough to cover nearly every request, q approaches 1, and because any viable market already prices the service above the cost it saves to cheat (Δ < p), the escrowed fee on the single cheated request deters on its own, at zero bond and zero franchise. We machine-check the result (the deterrence algebra and the martingale false-ejection bound in Z3 and Lean 4; the honesty boundary in PRISM-games) and state its scope honestly. We then observe a second consequence: once verification is the discipline, the Sybil cost can be the verification work itself rather than burned capital, the anti-Sybil proof and the audit are the same computation.

Contributions

  • A precise condition for zero-bond deterrence: honesty is the best response when q ≥ Δ/(p+Φ).
  • The bond is shown to be a substitute for sparse verification (b ≥ Δ/q - (p+Φ)), and so is redundant once verification is cheap enough that q approaches 1.
  • A second consequence: the Sybil cost can be the verification work itself, so the anti-Sybil proof and the audit are the same computation.
  • Machine-checked: the deterrence algebra and the martingale false-ejection bound in Z3 and Lean 4, and the honesty boundary in PRISM-games.