Are stake and audits substitutes in trace verification?

What it found

Sampled audits of a committed training trace under capped slashing: cheating payoff is convex in the number of corrupted steps, and deterrence holds iff min(F, f·k) ≥ T·g. Stake and audits are complements, so stake must scale with job length. Exact hypergeometric computation. Stylised.

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Verification games & slashing

• What does secret task assignment buy?Random k-fold replication with slashing against a colluding fraction β: secret assignment makes cheating a coordination game with unique-honesty stake Gβ^{k−1}/(1−β^{k−1}), public assignment leaves β^k corruption at any stake, and assignment leaks leave a λβ^k floor.
• How should a scarce audit budget be spread?Scarce audit budget across heterogeneous jobs: deterrence threshold g/(g+S) makes it a knapsack, greedy with a 1/3 guarantee (within 1% on 91% of instances), uniform audits need up to 1.9× the budget, heterogeneity lowers deterrence cost (Jensen), stake substitutes for audits.
• How many verifiers does deterrence-by-audit need?Staffing the audit pool that stake-based deterrence needs: exact Erlang-C waiting (matches simulation), square-root staffing R+1.06√R (spare capacity 60% at R=5, 1.1% at 10⁴), stake–headcount optimum G+S=√(wsG/(rd₀)) (cost 24 vs 77 at too little stake), and bursty audit demand delays 1.8× what Allen–Cunneen predicts.
• Escalating bonds: cheap challenges, fixed deterrence, a γ-fold capital asymmetryEscalating-bond dispute games: exact deterrence opening bond εV/((1−ε)C−εD) shrinks geometrically in rounds while the attacker's total outlay barely moves, and a sharp capital race where the defender needs γ·max{C(r) ≤ B_C} ≤ γ·B_C.
• How wide should a dispute bisect?K-ary bisection dispute games: optimal arity solves k ln k − k + 1 = a/b (binary only if a/b ≤ 0.386), 1.9–6× cheaper than binary at T=10⁶, adaptive schedules gain ≤1%, leaf-size trade-off, latency as extra round cost.
• Can stake shorten a challenge window when proposers can be bribed?Optimistic-verification challenge windows with bribable proposers: exact gamble-then-bribe attacker recursion, closed-form window, stake cannot shorten it under an exogenous bribe price (63 blocks for S=10…1600), bounty-funded priority fees give S·w ≈ G/((1−ρ)θ).

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Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.