Why two quotes
A pool’s own reserves produce one constant-product quote. The federation’s aggregate reserves produce another. KNOT treats the less favourable quote as a deterministic policy boundary; the aggregate is not an oracle or an external fair-price claim. Those arepreview() outputs from the documented deployment state for a five-token trade.
1
Local pool quotes
Constant product against this pool’s own reserves.
2
Federation quotes
The same maths against the sum of every member’s reserves.
3
Take the worse one
min for exact input, max for exact output.4
The difference stays
The taker never receives the surplus. It remains in the local pool.
Worked example
The shallow member holds 100 token0 and 400 token1. The deep member holds 1,000 and 1,000, so the aggregate is 1,100 / 1,400. Alone, the shallow member offers far more token1 for a new token0 trade. For five token0 in, the local curve pays 18.993189 token1 and the virtual aggregate curve quotes 6.315922. The trader receives 6.315922. The remaining 12.677266 stays in the shallow member, and both reserve books update atomically. The aggregate quote is a policy reference, not a claim that one route can execute against pooled custody from every member.What binds, and when
The bound only bites when the local quote is better for the taker than the aggregate quote. Across 1,000 fuzz cases plus one concrete regression case, the implementation selected exactly that direction. It does not inspect divergence magnitude or trader intent.
A proportional member is untouched. The other rows are one controlled skew sweep; they are not a
claim about realised flow or LP returns.