Capacity oracles

What it claims

A protocol can learn the exact total capacity of a permissionless, Sybil-prone supplier set by randomly auditing bids. It does this with three pieces: full slashing of a per-identity stake, a convex reward r(x) = x^p, and the cost of the audits themselves. With stake S = 8 and p = 2, the protocol pays 0.2 units of cost per unit of capacity. That is about 20% of what running the network at full capacity would cost, even with no organic demand. The authors say it falls further when real user demand covers part of the audit work.

How it works

• Bidding. Each supplier (or each identity) stakes S and bids a claimed capacity b.
• Auditing. Each bid is independently selected with probability ε. A selected supplier is allocated its full bid as work. Organic demand can fill this allocation, and synthetic work tops it up when demand is low.
• Payment. Full delivery earns production cost plus r(b). Any shortfall loses the entire stake. This "maximally aggressive" slashing is chosen on purpose to deter splitting.
• Tuning. With S and p fixed, search numerically for the smallest ε at which bidding once at true capacity (N = 1, α = 1) beats every Sybil strategy. The strategies tested are N identities each bidding α, with α ∈ {1, 1/2, 1/3, …}. The authors state that utility is unimodal in N for fixed α, which makes the search cheap. They omit the proof.

Several simpler designs fail:

• Audit without stake. Sybils multiply their chance of being selected, and the oracle becomes arbitrarily bad.
• Fully correlated payment (everyone is paid or no one is). This gives a perfect oracle at any price, but a single non-deliverer can stop all payments, and payouts are highly variable.
• Linear reward with any finite stake. This is still exploitable. An attacker splits into many tiny bids with total overreport α, where 1 < α < 1/ε. The binomial allocation concentrates near αε < 1, so the slashing tail becomes negligible.

Evidence

All results are numerical, for a unit-capacity supplier:

• At ε = 0.017, using 44 Sybils bidding 1/5 each yields utility 0.0245, against an honest utility of 0.017.
• At ε = 0.034, honest bidding is optimal.
• Protocol cost is 2ε at unit capacity and scales linearly with ε otherwise.

Heatmap takeaways for protocol cost:

Stake is measured in multiples of the cost of one unit of work.

How to use it

These are design levers the authors recommend, not code:

• Require roughly 10× unit cost as stake.
• Use mild convexity, around p ≈ 1.5–2.
• Enforce a minimum bid size. The authors call this a sufficient pragmatic fix for splitting but leave out its math.
• Optionally correlate allocations but not payments. Audit everyone at the same time, then pay those who deliver and slash those who don't. This removes the griefing vector, at the cost of bursty throughput and high reward variance.
• Treat the protocol as a controller. It only injects synthetic work when organic demand is too low for a good oracle. Semi-useful jobs such as Ritual's scheduled transactions are a cheaper middle ground, but they are not modelled.

Limits

• The model assumes:
• one homogeneous resource;
• a common, public, linear per-unit cost;
• free verification of delivered work;
• an attacker with enough capital to stake every identity.
• Only one reward family (monomials) and homogeneous Sybil strategies are analysed. Mixed bid sizes are assumed to matter only "up to small rounding errors."
• Only perfect oracles are costed. How quality degrades with lower spend is left open.
• Higher stake and curvature favour well-capitalised, high-capacity suppliers, which raises a centralization concern the authors flag themselves.
• The authors name heterogeneous resources as the most important open problem for practitioners, for example LLM inference versus ZK proving, or TPUs versus FPGAs. They note that capacity estimation becomes "much less tractable" in that setting.