AIMM at a glance

Constant-product pools price from a fixed curve and let the trade move the price. BTR pools do the opposite: an external reference price anchors the quote, and the pool’s own state decides how far trading can push it.

The three inputs

Mark - the external reference price. NX Rates keepers sign marks off-chain and push them on-chain (the oracle page lets you verify one end-to-end). Past its TTL a feed fails closed: reads revert StaleData and the asset freezes rather than quote off a stale anchor (depeg halt). Same-asset withdrawals are not feed-gated, so a dead keeper cannot trap you in the asset you deposited.
Inventory - what the pool actually holds per asset. When inventory drifts from target allocation, the mid skews and spreads widen so flow that restores balance gets the better side.
Coverage - reserves divided by liabilities on a leg. 100% means the pool holds exactly what LPs are owed; coverage shortfalls feed straight into pricing, which is how BTR does impermanent-loss protection without a separate insurance fund.

What the quote is made of

Not weighted heuristics: three additive terms in one spread, each charged for a different risk:

S = \underset{\underset{v o l}{⏟}}{\sum_{i} f_{\min, i} + \frac{σ_{p} ν_{p}}{100 \cdot B P S}} + \underset{\underset{s t a l e}{⏟}}{\sum_{i} \frac{z σ_{i} \sqrt{τ_{i}}}{B P S}} + \underset{\underset{c o n f}{⏟}}{(\sum_{i} u_{i}) \cdot \frac{B}{B P S}}

term	charges for	driven by
volatility	how fast the asset moves	path sigma $σ_{p}$ , endpoint vega $ν_{p}$
staleness	how old the mark is	age past grace $τ_{i}$ , per leg
confidence	how sure the feed is	each leg’s reported 1σ interval $u_{i}$

The two constants are fixed, not dials: $z = 472$ scales the staleness term, and $B / B P S$ is the pbps-to-bps conversion on the confidence term.

Two details matter more than the algebra. Staleness is summed per leg, not coupled across the path: one keeper feeds several spokes, so an outage stales them together, and charging one aggregate age would under-charge two equally stale legs by 29%. And a path inherits every leg’s confidence, not the worst one, so a quiet leg beside a noisy one still pays its own.

Full derivation, integer arithmetic and clamps in spread & fees.

Why not just x·y=k

A fixed curve pays arbitrageurs out of LP pockets every time the market moves (LVR). Anchoring to a keeper mark means the pool re-prices before arbitrage arrives, so the spread compensates flow that takes real inventory risk instead of subsidizing flow that takes none.

design	prices from	re-prices when	who pays the move
constant product	its own reserves	someone trades	the LP
concentrated range	a range set by hand	someone trades, inside the range	the LP
AIMM	a signed external mark	the mark moves, same block	whoever takes the stale side

Per-asset oracle modes

EXTERNAL (recommended) - any IOracle mark: NX Rates push, Chainlink adapter, Uniswap/vault reader, custom on-chain discovery.
INTERNAL - cash-collateral 1.0 peg helper only. Mix allowed; prefer EXTERNAL.

Routing

One pool holds many assets. Each anchors to a correlated parent, not necessarily the base, and a swap prices along the unique tree path between its two endpoints via their lowest common ancestor. Depth is capped at 4, so a path spans at most 9 nodes and 8 legs.

Two assets sharing a parent trade through that parent: stETH to weETH is two legs via WETH, never touching the base. Everything settles inside the one pool, so there is no cross-pool hop and no aggregator leg. Each leg still charges its own fee floor, so a two-leg path pays both.

Spread & fees carries the formal parameter surface; inventory management shows how drift maps to quote skew.