Before KNOT

Why independent pools for the same pair can expose incompatible quotes.

Without KNOT, each Uniswap pool prices a swap from its own reserves. Two pools can hold the same token pair while remaining completely independent: they do not share liquidity, reserve state, or a price boundary.

The independent-pool path

For a five-token exact-input swap through Pool B, its isolated curve returns 18.993189 token1. Pool A does not participate in that calculation, even though both pools trade the same pair.

Reserve divergence is not proof of manipulation. It can result from legitimate flow, shallow liquidity, or a newly created pool. KNOT does not classify why a pool is skewed.

What changes with KNOT

Participating pools keep separate custody and liquidity-provider (LP) ownership. The hook adds one shared accounting boundary: every swap is quoted once against the local reserves and once against the sum of all member reserves.

The aggregate curve is virtual. A swap still settles against one pool, and the federation never custodies tokens or creates a cross-pool route.

Before and after

Property	Before KNOT	With KNOT
Quote source	Selected pool only	Local pool and federation aggregate
Exact-input result	Local output	min(local output, aggregate output)
Exact-output result	Local input	max(local input, aggregate input)
Pool custody	Independent	Independent
LP ownership and fees	Independent	Independent
Shared price boundary	None	Deterministic reserve-aware bound
Oracle or classifier	None	None

KNOT changes the enforceable quote, not the ownership model. If the local pool already gives the taker the less favourable result, the hook is inert.

See the rule

Follow the exact-input and exact-output decision branches.

Follow a swap

Trace one transaction from the trader through settlement.