---
title: "Curve presets"
seo_title: "AMM Curve Presets and Liquidity Shaping"
description: "How a BTR pool shapes its liquidity, every curve preset installed on chain with its numbers and charts, and which preset fits which leg."
audience: tech
type: reference
status: live
lang: en
updated: "2026-10-01"
publish: true
---
# Curve presets

A leg's depth curve is not tuned per asset. It is one of a few presets written once at deploy, and the leg points at it with a `curveId`. This page covers what the curve does to a quote, what each installed preset looks like, and how to pick one. The spline mathematics, storage layout and gas are in [Liquidity Shaping](/docs/1-1-2-liquidity-shaping).

---

## 1. How shaping works

The mark comes from the oracle. The curve only answers one question: how far from the mark does the next unit of depth trade?

- **x** is cumulative depth, 0 to 10,000 bps of the leg's depth. The mark sits near 5,000.
- **y(x)** is the price offset at that depth, nondecreasing, stored in pbps. A trade walks x away from the mark and pays the mean of y over the depth it consumes ([traversal](/docs/1-1-2-liquidity-shaping#8-traversal)).
- **Density** is dx/dy: depth per unit of price move. Where y is flat the book is deep and a trade barely moves the price. Where y is steep the book is thin.
- **Scale** is separate: a quote multiplies y by $\kappa / \text{dispRef}$, with $\kappa$ the live [dispersion](/docs/1-1-2-liquidity-shaping#6-dispersion-dynamics). Volatility rescales the curve and never reshapes it.

Two knobs follow, and only one of them is a preset:

| Knob | Sets | Changed by |
|---|---|---|
| Preset (`curveId`) | Shape of the book and its reference scale | `UPDATE_PROFILE`, TUNING tier (1 h) |
| `minDispersionPbps`, vega | Width at quote time | Steward raise, or `UPDATE_PROFILE` for a cut |

Writing a new preset (`UPDATE_CURVE`, LISTING tier, 1 day) is rare and immutable: an id is written once and never renumbered. Moving a leg between existing presets is the routine operation.

Fees and the coverage toll sit on top of the offset: [Spread & Fees](/docs/1-1-4-spread-fees), [Slippage & Price Impact](/docs/1-1-5-slippage-price-impact).

---

## 2. Presets

Every number in this section is generated from the deploy manifests by `gen-curve-presets.ts` in the content repo, so it cannot drift from what the ceremony installs. Preset ids are per deployment: see [deployed instances](/docs/2-1-contract-addresses) for the ids a given pool carries.

### Installed presets

One row per preset family and reference scale. The curve letter names the shape and edge multiple: names that differ in an off-chain flag, in reference scale or by 1 to 2 ULP in the stored weights share a letter, and everything below is computed per letter. Half-swing is the offset at the far edge at the preset's own reference scale; **edge at $\kappa$** is that edge as a multiple of the live dispersion $\kappa$.

| Curve | Preset names | Shape | Weights | Interior knots (bps) | Half-swing @ ref | Ref scale | Edge at $\kappa$ | Used by |
|---|---|---|---:|---|---:|---:|---:|---|
| A | `bell_100`, `cn_w100_d100_flat`, `cn_w100_d100_wall` | bell, depth at the mark | 7 | 1314, 8686 | 1.00 bps | 100 pbps | 1x | stable |
| A | `bell_500`, `cn_w500_d500_flat` | bell, depth at the mark | 7 | 1314, 8686 | 5.00 bps | 500 pbps | 1x | equity, fx, volatile |
| B | `cn_w500_d100_wall` | bell, depth at the mark | 7 | 1314, 8686 | 5.00 bps | 100 pbps | 5x | stable |
| C | `bell_100_inv` | complement of the bell, depth in the wings | 9 | 4012, 4997, 7221, 7853 | 1.00 bps | 100 pbps | 1x | none |
| C | `bell_500_inv` | complement of the bell, depth in the wings | 9 | 4012, 4997, 7221, 7853 | 5.00 bps | 500 pbps | 1x | none |

Offsets, densities and costs below are evaluated at a dispersion of $\kappa$ = 5 bps and scale linearly with it.

### Cost of depth consumed from the mark

Mean offset paid, in bps, by a trade that consumes the given share of the leg's depth above the mark (before fees and the coverage toll), at $\kappa$ = 5 bps.

| Curve | 1% | 5% | 10% | 25% | 50% | Density at mark / mean | Density at edge / mean |
|---|---:|---:|---:|---:|---:|---:|---:|
| A | 0.04 | 0.21 | 0.42 | 1.07 | 2.28 | 1.19x | 0.66x |
| B | 0.21 | 1.05 | 2.11 | 5.36 | 11.42 | 1.19x | 0.66x |
| C | 0.06 | 0.32 | 0.64 | 1.52 | 2.76 | 0.78x | 1.40x |

### Offset curve

Price offset against cumulative depth, normalized to the half-swing so shapes compare directly. Depth runs from 0 to 100% of the leg; the mark sits near 50%. orange: curve A; blue: curve C.

```mermaid
xychart-beta
    title "Normalized offset vs depth"
    x-axis "cumulative depth (%)" [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]
    y-axis "offset / half-swing" -1 --> 1
    line [-1.00, -0.86, -0.75, -0.64, -0.53, -0.44, -0.35, -0.26, -0.17, -0.08, 0.00, 0.08, 0.17, 0.26, 0.35, 0.44, 0.53, 0.64, 0.75, 0.86, 1.00]
    line [-1.00, -0.93, -0.85, -0.76, -0.67, -0.58, -0.47, -0.37, -0.25, -0.13, 0.00, 0.13, 0.25, 0.37, 0.47, 0.58, 0.67, 0.76, 0.85, 0.93, 1.00]
```

### Depth density

Depth per unit of price move, relative to a flat curve of the same half-swing (1.0 = flat). Above 1 the book is deep and a trade moves the price little; below 1 it is thin. orange: curve A; blue: curve C.

```mermaid
xychart-beta
    title "Relative depth density"
    x-axis "cumulative depth (%)" [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]
    y-axis "density / flat" 0 --> 2
    line [0.66, 0.80, 0.89, 0.95, 1.00, 1.05, 1.10, 1.14, 1.17, 1.19, 1.19, 1.19, 1.17, 1.14, 1.10, 1.05, 1.00, 0.95, 0.89, 0.80, 0.66]
    line [1.40, 1.30, 1.22, 1.14, 1.07, 1.01, 0.95, 0.90, 0.85, 0.80, 0.78, 0.79, 0.83, 0.89, 0.96, 1.02, 1.07, 1.14, 1.22, 1.30, 1.40]
```

### Mean offset by trade size

Mean offset paid by a trade that consumes the share of depth on the x axis, at $\kappa$ = 5 bps, in bps. orange: curve A; blue: curve C. Every other curve is a multiple of these (see the edge column).

```mermaid
xychart-beta
    title "Mean offset vs depth consumed"
    x-axis "depth consumed from the mark (%)" [0.5, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25, 27.5, 30, 32.5, 35, 37.5, 40, 42.5, 45, 47.5, 50]
    y-axis "offset (bps)" 0 --> 3
    line [0.02, 0.10, 0.21, 0.32, 0.42, 0.53, 0.63, 0.74, 0.85, 0.96, 1.07, 1.18, 1.30, 1.41, 1.53, 1.65, 1.77, 1.90, 2.02, 2.15, 2.28]
    line [0.03, 0.16, 0.32, 0.48, 0.64, 0.79, 0.94, 1.09, 1.24, 1.38, 1.52, 1.65, 1.78, 1.91, 2.04, 2.17, 2.29, 2.41, 2.53, 2.64, 2.76]
```

Curve key: **A** = `bell_100`, `bell_500`, `cn_w100_d100_flat`, `cn_w100_d100_wall`, `cn_w500_d500_flat`; **B** = `cn_w500_d100_wall`; **C** = `bell_100_inv`, `bell_500_inv`.

---

## 3. Choosing a preset

Pick by the leg's measured trade density, not by its class label: [Width selection](/docs/1-1-2-liquidity-shaping#13-width-selection) has the rule. The **Used by** column above shows where each preset has landed.

### 3.1. Bell (curve A)

Depth peaks at the mark and thins toward the edge. Small trades pay almost nothing beyond the fee and the cost climbs as a trade eats into the shoulders. It is the right shape when flow clusters near the mark and tails are rare.

- **Pegged legs and the hub** take the 1 bp half-swing (`bell_100`), where the book is tight and the edge is the dispersion itself.
- **Floating legs** (volatile, metals, FX, equity) take the 5 bp half-swing (`bell_500`).

The two have the same shape. They differ in the scale they were fitted at (100 against 500 pbps), so point a leg at the one whose reference scale is nearer its dispersion: the scale factor stays near 1 and the integer-pbps truncation stays small against the offset. Never derive one from the other by rescaling ([§4.3](/docs/1-1-2-liquidity-shaping#43-shipped-curves-5-rows)).

### 3.2. Wide bell (curve B)

The same bell with its half-swing at 5x the reference scale: the edge sits at 5 times $\kappa$, so a leg with a 1.6 bp floor reaches 8 bp at the far edge. It is for the widest pegged legs, whose quiet-tape floor is small but whose book has to reach further out. Every figure in the cost table is 5x curve A, so check it before assigning the preset.

### 3.3. Complement (curve C)

The complement inverts the density: thin at the mark, deep in the wings. It is refitted from the bell as $\rho_{inv} = \rho_{max} + \rho_{min} - \rho_{base}$ and constrained monotone to under 2% density error, which is why it carries 9 weights and 4 interior knots instead of 7 and 2. At the same dispersion both reach the same edge, but the complement's mean cost stays above the bell's at every trade size in the table (1.5x at a 10% trade); only the marginal price in the last few percent of depth moves less, where its density is about twice the bell's.

Assign it only when a leg's measured density has its mass in the shoulders rather than at the mark. It is installed so the fit has somewhere to land, never chosen on intuition.

### 3.4. Rules of thumb

| Situation | Preset |
|---|---|
| Pegged leg or hub, flow at the mark | bell at ref 100 |
| Floating leg, flow at the mark | bell at ref 500 |
| Pegged leg whose book must reach several times its floor | wide bell, if installed |
| Measured density has its mass in the shoulders | complement at the matching scale |

A wrong preset is cheap to fix: re-pointing is one TUNING op, and because the curve is anchor-free it can be tried against a leg's live tape without touching the oracle or the reserves.

---

## 4. Reading the curve in the pool risk modal

The risk modal names a leg's preset and its shape (segments, reference scale, wall). Read it with the tables above:

- **Preset** is the codebook entry the leg points at. Two legs on the same name have the same shape and can differ in width.
- **Reference scale** is the dispersion the preset was fitted at. The far edge sits at the curve's edge multiple times the leg's dispersion, so a 4 bp dispersion on a bell quotes at most 4 bps off the mark before the fee and the coverage toll.
- **Min fee** is the leg's path floor, not the one-way fee: the one-way fee is half the sum of the spoke's and the hub's ([Spread & Fees](/docs/1-1-4-spread-fees)).

---

## 5. Related documentation

- [Liquidity Shaping](/docs/1-1-2-liquidity-shaping): spline mathematics, storage, traversal
- [Parametrization](/docs/1-1-7-parametrization): `minDispersionPbps`, vega and the fences
- [Spread & Fees](/docs/1-1-4-spread-fees): the fee on top of the offset
- [Slippage & Price Impact](/docs/1-1-5-slippage-price-impact): the full decomposition