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LibraryMarkets2019Design paperCorpus record

StableSwap — efficient mechanism for Stablecoin liquidity

Curve. Michael Egorov.

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.

StableSwap shapes the curve so that similarly priced assets trade near one-to-one with low slippage, and the pool steepens into a normal product curve if the price runs away.
Evidence
Primary paper
Re-measured
No
Assumptions
4
Records linked
4

Code

Source, repository, and what is actually hosted

  • StableSwap paperhttps://curve.fi/files/stableswap-paper.pdf
  • The source URL is not a GitHub repository. No code remote is invented.
  • Full text is not mirrored. Public availability is not a licence to copy the file onto this site.
  • Add to a reading list

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

    Constant product is wasteful for stablecoins

    A dollar-for-dollar pair does not need liquidity at a price of ten. The paper concentrates the curve around one.

  2. Claim 02 · Paper model

    The amplification parameter is the shape

    A higher A makes the pool flatter near the peg and more violent away from it. A is the product decision. It is not a minor constant.

  3. Claim 03 · Paper model

    The invariant blends two curves

    Near equality, the pool behaves like a constant sum, which has no slippage and no rebalancing force. Far away, it behaves like a constant product, so it cannot be drained of one asset for nothing.

  4. Claim 04 · Paper model

    The peg is an assumption the pool does not create

    The mathematics serves assets that ought to be worth the same. If one of them breaks, the pool will sell the good asset for the bad one all the way along that flat region.

  5. Claim 05 · Paper model

    Liquidity providers are betting on the peg

    They earn fees from tight spreads and they warehouse the asset that loses the peg. The paper's efficiency and this warehouse risk are the same design.

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 Constant product is wasteful for stablecoins

    Observation

    What the study says

    A dollar-for-dollar pair does not need liquidity at a price of ten. The paper concentrates the curve around one.

    Model

    What has to hold

    The assets are meant to track the same value most of the time. The curve is a bad fit for uncorrelated coins.

    Falsifier

    What would retire it

    Is the internal price being used as proof that a token is worth a dollar?

  2. 02 The amplification parameter is the shape

    Observation

    What the study says

    A higher A makes the pool flatter near the peg and more violent away from it. A is the product decision. It is not a minor constant.

    Model

    What has to hold

    Arbitrage against a redemption market exists. Without it the internal price is only a ratio of inventory.

    Falsifier

    What would retire it

    Is there a redemption market outside the pool for each asset?

  3. 03 The invariant blends two curves

    Observation

    What the study says

    Near equality, the pool behaves like a constant sum, which has no slippage and no rebalancing force. Far away, it behaves like a constant product, so it cannot be drained of one asset for nothing.

    Model

    What has to hold

    A is set by someone whose incentives a provider understands.

    Falsifier

    What would retire it

    Is there a redemption market outside the pool for each asset?

  4. 04 The peg is an assumption the pool does not create

    Observation

    What the study says

    The mathematics serves assets that ought to be worth the same. If one of them breaks, the pool will sell the good asset for the bad one all the way along that flat region.

    Model

    What has to hold

    The assets are meant to track the same value most of the time. The curve is a bad fit for uncorrelated coins.

    Falsifier

    What would retire it

    Is there a redemption market outside the pool for each asset?

  5. 05 Liquidity providers are betting on the peg

    Observation

    What the study says

    They earn fees from tight spreads and they warehouse the asset that loses the peg. The paper's efficiency and this warehouse risk are the same design.

    Model

    What has to hold

    The assets are meant to track the same value most of the time. The curve is a bad fit for uncorrelated coins.

    Falsifier

    What would retire it

    Is there a redemption market outside the pool for each asset?

03 Sequence

One action, as an operating tape

  1. 01Providers deposit the stable assets in whatever shares the pool allows and receive pool tokens.
  2. 02A trader swapping one dollar token for another moves along the flat part of the curve and pays a small fee, while A is large and balances are close.
  3. 03If one asset's external price falls and traders keep selling it into the pool, balances tilt.
  4. 04As the tilt grows, the invariant steepens. Further sales move the internal price more, which is the pool's way of stopping a complete drain.
  5. 05Providers who withdraw during the tilt receive more of the impaired asset. The fee income is what they hoped would pay for that.

04 Load-bearing

The argument, and where a pitch drops it

  1. Flat means generous, which means exposed

    The cut

    The reason a stable swap is cheap is that the pool does not defend a price of one with slippage. Defence has been turned down on purpose. Anyone citing the tight spread should cite the depeg loss in the same sentence.

    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 later client, parameter or reward formula is a different object from this paragraph.

  2. A is a governance surface

    The cut

    Raising A makes trading nicer and makes a depeg more expensive for providers. Who may change A, and how fast, is part of the risk. The paper introduces the parameter. Deployments decide who turns the dial.

    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 paper is not a claim about any stablecoin's reserves.

  3. The pool is not an oracle of the peg

    The cut

    A flat internal price says the pool is balanced, or that A is high, not that each token can be redeemed for a dollar in a bank. External redemption is outside the invariant.

    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 later client, parameter or reward formula is a different object from this paragraph.

05 Register

What has to be true

  • Model · Not re-measured

    The assets are meant to track the same value most of the time. The curve is a bad fit for uncorrelated coins.

  • Model · Not re-measured

    Arbitrage against a redemption market exists. Without it the internal price is only a ratio of inventory.

  • Model · Not re-measured

    A is set by someone whose incentives a provider understands.

  • Network · Not re-measured

    Tokens do not rebase or charge hidden transfer fees that desynchronise the balances.

06 Divergence

What happened after the paper

Curve deployed StableSwap for dollar stablecoins and later generalised it. Several depegs showed the warehouse risk in public, including events where the pool became a large holder of the impaired asset. The paper's math did what it said. The losses came from the peg assumption failing, which the design does not prevent.

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

  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

The problem it names

A constant-product pool of two stablecoins quotes a meaningful spread even when both claim to be worth the same unit. That spread is a tax on the common case. A constant-sum pool quotes no spread and then goes bankrupt in inventory the moment the peg slips.

What the design proposes

  • An amplification parameter blends a constant-sum region with a constant-product tail.
  • The pool is for assets that share a unit of account, not for unrelated volatile pairs.
  • The invariant is explicit. Changing the amplification changes the risk, and the paper treats it as a parameter with consequences.

How the mechanism is specified

  • Near parity, a trader moves along a nearly flat price. Liquidity is concentrated where those traders are.
  • Far from parity, the curve steepens so the pool does not sell the last of the stronger asset at the peg price.
  • Later Curve gauges, voting and factory pools are not this note.

What this page does not treat as proven

  • The math assumes the assets ought to be near parity. If that assumption is false, the flat region is a source of loss, not efficiency.
  • Amplification is a risk setting. Higher is not 'better'.
  • The paper is not a claim about any stablecoin's reserves.

Why the desk still reads it

This is the first document we ask for when a venture designs a pool of assets 'that should be worth the same'. If they cannot say what happens when the assets stop being worth the same, they have not finished the design.

09 Lexicon

Terms, opened into the record

Amplification
The parameter A. Higher means a flatter curve near equal balances.
Stable invariant
A blend of constant-sum and constant-product so pegged assets trade tightly until they diverge.
Depeg
One asset leaving the shared price. The pool then accumulates it, because that is where the flat curve is generous.
Warehouse risk
The provider's exposure to ending up holding more of the asset that failed.

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.

This is Blockchain Lab's reading of a public design paper. It is not the paper, not a copy of it, and not an offer of tokens, equity, custody or a partnership. Later network behaviour can diverge from the text. Nothing here is investment, legal or technical advice.

Research status: Design paper. Last reviewed: 1 October 2026. This is a reading of a public paper, not investment, legal or security advice.