Run a speculative-decoding round at a time: a cheap drafter proposes γ tokens, the target verifies them in parallel and accepts a prefix plus one free token. Drive α, γ, and drafter cost c; watch the accepted length converge to Leviathan's Ω and the speedup peak, then fade.
A chain commits to a model's 32-byte hash for cents; keeping the gigabytes it points to retrievable is a separate, recurring bill. Pick a model and horizon and watch three rent-charging storage layers race Arweave's pay-once permanence to a crossover — plus the on-chain byte cost and cold-load wall.
Proving an agent's top-k retrieval is real costs a sort over every scanned candidate, unless you prove a boundary instead. Drive top-k and the corpus preset; watch the in-circuit comparison count split into the flat boundary proof and the sort tax you skip, anchored to V3DB's measured 22x.
Under secure two-party inference, a transformer's cost is eaten by Softmax and GELU, not the matrix multiplies. Stacked per-operation communication and interaction rounds for one BERT-base block across Iron, BumbleBee, and Nimbus — the nonlinear activations are 80–95% of the bill.
Cost per million tokens and throughput for Llama 3.3 70B on 8x H100 as the batch fills. A single-tenant node (B=1) runs ~25 tok/s at ~$258/M; a filled batch (B=256) runs ~2,800 tok/s at ~$2.30/M — same silicon, 112x cheaper. Pick a batch; read the tax you pay for the GPU you can't fill.
In decentralized RL the rollout worker acts with a policy several steps behind the trainer. Staleness g = broadcast time / step cadence. Pick a model and link, toggle sparse deltas, and watch g cross INTELLECT-2's demonstrated 4-step budget — full 32B weights blow right past it.
Bittensor's Yuma Consensus scores a miner by the stake-weighted median of validator weights, then clips everything above it. Validators sit on a cumulative-stake axis; the consensus line is read at the κ=50% mark. Push a colluding bloc past 50% and watch the pump go from clipped to unstoppable.
An inspection game between a solver and a verifier. Drag the operating rate and tune the bond, reward, and bounty to find p*, the minimum sampling rate that makes honest AI inference a dominant strategy — and watch it collapse without a bounty.
An on-chain agent is told to pay an invoice, but one MCP tool hides an instruction in its description that redirects the transfer to an attacker. Pick a defense layer — model, tool, client, policy, custody — and run it; alignment alone refused under 3% of these in MCPTox.
Cumulative net carry of a $10k delta-neutral perpetual funding harvest over real Hyperliquid funding regimes. The line starts below zero by the round-trip fee, then climbs at the annualized funding rate; a flip slider rolls it over. Carry, not alpha — until funding inverts.
On-chain cost of a query versus how much history it touches. Re-executing pays a cold SLOAD per value and hits the 60M block-gas wall — or can't reach the data at all. A coprocessor's proof verifies flat at ~300k gas whatever the size. Drag the cursor or pick a real query; the cyan line never moves.
Seven ways to verify what an AI agent claims it did, plotted by latency added against the share of fabricated claims caught. Pick a claim type and watch it route to the cheapest sufficient verifier — a free chain receipt, a 12ms signed receipt, or a zkLLM proof reserved for the inference itself.