λ is the share of the reserves arbitrage can reach in a block. Move it and the iceberg sinks or rises, and the real 21 Sep replay re-runs in your browser with the keeper's own model.
λ: how much is reachable
The keeper's floor is 40%, so ordinary traders always find deep liquidity. Try 100% to get a plain AMM.
Replay 21 Sep 2026
1,440 real Coinbase 1-minute closes. ETH +6.24%.
The keeper's search
Every λ from 100% to the floor on the same day at 5 bps. Green is the λ the keeper would publish. Click a bar to try it.
Best: λ 40%, 19.1% less loss. On 7 days of real prices, the best λ at 30 bps is 100%: partial activity only pays at low fees.
Two seconds in the life of the pool.
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A block opens.
Base mints a block every 2 seconds. Until someone trades, the pool holds R: its total reserves, on both venues.
The first trade splits R.
λ·R becomes the active side. (1 − λ)·R is frozen for the rest of the block: it is not in the curve, so nothing in this block can touch it.
Arbitrage sees only the tip.
Every trade in the block, the arbitrageur's included, is priced by x·y = k on the active reserves, with a 5 bps fee. Quotes never write storage, so quote == swap.
the arbitrageur's reach stops at λ
The frozen part earns.
Idle reserves sit in Morpho vaults and are pulled out mid-swap only if a trade needs them. Next block, the reserves re-split at the keeper's current λ.
What the arbitrageur can take
Within a block and before fees, trading reserves (x, y) to a new price p₁ yields (√(p₁x) − √y)². Only λ·R is in the curve, so the prize scales by λ.
The paper's closed form
The on-chain kernel matches this to within 1e-16. The paper assumes zero fees; the keeper measures the fee instead.