Automatic market-making with dynamic peg

01 Claim ledger

What the paper is allowed to say

Each row is a sentence already in the study. The status is the same on every row: a model claim, not a live measurement.

1. Claim 01 · Paper model

   The peg is a price, not one

   Stableswap assumes assets should trade near 1. This paper repeats the idea around a vector of prices that can change, so volatile pairs can use a similar invariant.

2. Claim 02 · Paper model

   The pool updates its own price

   Trades move an internal price. The transformation is specified in the paper. An outside market is visible to the pool only when arbitrageurs trade.

3. Claim 03 · Paper model

   Concentration without a range order

   Liquidity providers do not set a tick range, as in Uniswap v3. The invariant concentrates liquidity near the current internal price, and the price creeps as the pool is used.

4. Claim 04 · Paper model

   Fees are a function

   The paper allows the fee to rise as the pool leaves balance. That is a protection for liquidity, not a quoted yield.

02 Three cuts

Observation, model, falsifier

A desk does not stop at the summary. Each claim is cut three ways, using only this study's own assumptions and checks. Nothing here is a new figure.

1. 01 The peg is a price, not one

   Observation

   What the study says

   Stableswap assumes assets should trade near 1. This paper repeats the idea around a vector of prices that can change, so volatile pairs can use a similar invariant.

   Model

   What has to hold

   The assets are the ones the invariant expects. A rebasing or fee-on-transfer token is outside the paper.

   Falsifier

   What would retire it

   How fast can a trade move the internal price?

2. 02 The pool updates its own price

   Observation

   What the study says

   Trades move an internal price. The transformation is specified in the paper. An outside market is visible to the pool only when arbitrageurs trade.

   Model

   What has to hold

   The assets are the ones the invariant expects. A rebasing or fee-on-transfer token is outside the paper.

   Falsifier

   What would retire it

   How fast can a trade move the internal price?

3. 03 Concentration without a range order

   Observation

   What the study says

   Liquidity providers do not set a tick range, as in Uniswap v3. The invariant concentrates liquidity near the current internal price, and the price creeps as the pool is used.

   Model

   What has to hold

   Parameters, including how fast the price moves, are the ones in the pool you are looking at. The PDF is a design. Deployments set numbers.

   Falsifier

   What would retire it

   How fast can a trade move the internal price?

4. 04 Fees are a function

   Observation

   What the study says

   The paper allows the fee to rise as the pool leaves balance. That is a protection for liquidity, not a quoted yield.

   Model

   What has to hold

   The assets are the ones the invariant expects. A rebasing or fee-on-transfer token is outside the paper.

   Falsifier

   What would retire it

   Is a fee being presented as a yield? The paper does not.

03 Sequence

One action, as an operating tape

1. 01Liquidity is deposited against the invariant.
2. 02A trader swaps. The balances move and the trader pays a fee that depends on how far the pool is from balance.
3. 03The internal price updates from that imbalance, with the paper's dampening.
4. 04Arbitrageurs who disagree with the internal price trade against it.
5. 05A large trade can move the internal price before that arbitrage arrives.

04 Load-bearing

The argument, and where a pitch drops it

1. Self-reference is the risk

   The cut

   A price computed from the pool's own trades can be pushed by the trades. The paper is a curve design, not a claim that the resulting price is a safe oracle for liquidations.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   A self-referential price can be pushed. The paper's transformation is not a manipulation-proof oracle.

2. Passive is not riskless

   The cut

   Liquidity providers do not manage a range. They still hold inventory of volatile assets, and they still lose to toxic flow. The invariant changes the shape of that loss. It does not repeal it.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   The invariant does not pay liquidity providers a fixed rate. Fees depend on volume and on the parameters.

05 Register

What has to be true

• Model · Not re-measured

  Parameters, including how fast the price moves, are the ones in the pool you are looking at. The PDF is a design. Deployments set numbers.

• Model · Not re-measured

  The assets are the ones the invariant expects. A rebasing or fee-on-transfer token is outside the paper.

• Model · Not re-measured

  Arbitrage is possible. A pool in a market with no arbitrageurs does not track anything.

• Model · Not re-measured

  Later NG contracts may differ. Check the code if the question is a live pool.

06 Divergence

What happened after the paper

Curve's volatile pools are the deployment of this idea. The 2021 PDF remains the design reading. Stableswap is the earlier paper for pegged assets. Uniswap v3 is the alternative where the liquidity provider, not the invariant, chooses the range.

A later client, parameter set, or reward formula is a different object. Cite this paper for the mechanism. Cite a primary release for the network. This desk has not re-run the proof.

07 Pre-mortem

What to check before you use the idea

1. Kill test 1Does the quoted price come from an oracle or from the pool?
2. Kill test 2How fast can a trade move the internal price?
3. Kill test 3Who chooses the concentration, the LP or the invariant?
4. Kill test 4Is a fee being presented as a yield? The paper does not.
5. 0 of 4 marked on this browser. A mark is a reading note, not a pass, a rating, or a recommendation.

08 Anatomy

The paper, in the order a builder needs

09 Lexicon

Terms, opened into the record

Dynamic peg

An internal price the invariant concentrates around, updated from trading imbalance rather than fixed at one.

Amplification

The parameter that decides how tightly liquidity sits near the peg, inherited from the stableswap family.

10 Repository

Every linked record on this page

Underlined words open a page that already exists: a concept, a protocol profile, a failure record, or another paper. If a word is not underlined, this desk does not have a record for it.

11 Related

The next papers, as theses

• Curve · 2019

  StableSwap — efficient mechanism for Stablecoin liquidity

  Egorov's 2019 invariant for pools of assets that should trade near parity. The curve is flat around the peg, where most stablecoin trades happen, and bends toward a constant-product tail when the pool is pushed off parity.

• Uniswap · 2021

  Uniswap v3 Core

  The 2021 paper that replaces the uniform reserve curve with concentrated liquidity. A provider chooses a price range. Inside the range their capital acts like a constant-product pool. Outside it, their position is entirely in one asset.

• Balancer · 2019

  Balancer: A non-custodial portfolio manager, liquidity provider, and price sensor

  The Balancer paper generalises the two-asset constant-product pool to a weighted basket of several tokens. Traders rebalance the basket. Liquidity providers define target weights. The pool is both an index and a market.