LibraryMarkets2020Design paperCorpus record
Uniswap v2 Core
Uniswap. Hayden Adams, Noah Zinsmeister, Dan Robinson.
The 2020 core paper for Uniswap v2: a constant-product automated market maker, with arbitrary ERC-20 pairs, price accumulators, and a flash-swap callback. It is the clearest short specification of the pool that much of later DeFi either forked or assumed.
Uniswap v2 prices a pair with a constant product: the pool multiplies its two reserves and refuses any trade that would shrink that product, before the fee.
- Evidence
- Primary paper
- Re-measured
- No
- Assumptions
- 4
- Records linked
- 6
Code
Source, repository, and what is actually hosted
- Uniswap v2 core paperhttps://uniswap.org/whitepaper.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.
Claim 01 · Paper model
Anyone can pool two tokens
There is no order book and no listing committee. Liquidity providers deposit both assets and receive a claim on the pool.
Claim 02 · Paper model
The price is the ratio of reserves
A trader sends one asset in and receives the other out, leaving the product of the reserves no smaller than before, plus a fee that stays in the pool.
Claim 03 · Paper model
The fee is how liquidity is paid
The paper's 0.30 percent is not a toll to a company. It accrues to the reserves, so the liquidity token becomes a claim on a slightly larger pool.
Claim 04 · Paper model
Flash swaps appear here
A caller may withdraw and repay inside one transaction, or fail the whole transaction. The paper makes the pool a primitive other contracts can compose, which is also how it can be attacked.
Claim 05 · Paper model
Price oracles are a side effect
The paper adds a time-weighted price accumulator so other contracts can read a manipulated-resistant average. A spot price at the end of one block is not that oracle.
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.
01 Anyone can pool two tokens
Observation
What the study says
There is no order book and no listing committee. Liquidity providers deposit both assets and receive a claim on the pool.
Model
What has to hold
Both tokens are standard and do not take a fee on transfer or rebase balances. Weird tokens break the reserve accounting.
Falsifier
What would retire it
What happens if one of the tokens charges a transfer fee?
02 The price is the ratio of reserves
Observation
What the study says
A trader sends one asset in and receives the other out, leaving the product of the reserves no smaller than before, plus a fee that stays in the pool.
Model
What has to hold
Arbitrageurs can trade when the pool price drifts from other markets. Without them the invariant does not track a fair price.
03 The fee is how liquidity is paid
Observation
What the study says
The paper's 0.30 percent is not a toll to a company. It accrues to the reserves, so the liquidity token becomes a claim on a slightly larger pool.
Model
What has to hold
The time-weighted oracle is used by anyone who needs a price. The spot reserves are not a price feed.
Falsifier
What would retire it
Who receives the fee, and is it the paper's 0.30 percent or a later setting?
04 Flash swaps appear here
Observation
What the study says
A caller may withdraw and repay inside one transaction, or fail the whole transaction. The paper makes the pool a primitive other contracts can compose, which is also how it can be attacked.
Model
What has to hold
Arbitrageurs can trade when the pool price drifts from other markets. Without them the invariant does not track a fair price.
05 Price oracles are a side effect
Observation
What the study says
The paper adds a time-weighted price accumulator so other contracts can read a manipulated-resistant average. A spot price at the end of one block is not that oracle.
Model
What has to hold
The time-weighted oracle is used by anyone who needs a price. The spot reserves are not a price feed.
03 Sequence
One action, as an operating tape
- 01A liquidity provider deposits both tokens in the current ratio and receives pool tokens.
- 02A trader sends token A. The contract computes how much token B leaves so that the product of reserves does not fall, ignoring the fee that is kept.
- 03Reserves update. The implicit price, A per B, moves.
- 04If the trader is using a flash swap, they must pay the pool back before the transaction ends, or the call reverts.
- 05When the provider withdraws, they burn pool tokens and receive their share of both reserves, fees included, and losses included.
04 Load-bearing
The argument, and where a pitch drops it
The invariant is the whole market maker
The cut
Constant product means large trades move the price a lot, and the pool never runs out of either asset in theory: the price goes to an extreme instead. That is a design for long-tail pairs, not a design that mimics a deep order book at one price.
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 is not a promise of a good price. It is a function of reserves.
Liquidity providers are short volatility
The cut
If the outside price moves and arbitrageurs rebalance the pool, the provider ends with more of the falling asset. The fee is the compensation the paper offers. It does not promise the fee will be enough. Impermanent loss is this arithmetic, not a moral failure of the provider.
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 is not a promise of a good price. It is a function of reserves.
Composability includes the attacker
The cut
A flash swap that must repay inside the transaction is safe for the pool's accounting and unsafe for any other contract that trusts a spot price the swap just moved. The paper's oracle section exists because the spot price is a toy.
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 is not a promise of a good price. It is a function of reserves.
05 Register
What has to be true
Model · Not re-measured
Both tokens are standard and do not take a fee on transfer or rebase balances. Weird tokens break the reserve accounting.
Model · Not re-measured
Arbitrageurs can trade when the pool price drifts from other markets. Without them the invariant does not track a fair price.
Model · Not re-measured
Users set a minimum output. The contract will happily trade at a ruined price if the caller does not constrain it.
Model · Not re-measured
The time-weighted oracle is used by anyone who needs a price. The spot reserves are not a price feed.
06 Divergence
What happened after the paper
Uniswap v2 became the reference pool on Ethereum and was followed by v3's concentrated liquidity, which changes the invariant from 'the whole price range' to 'a chosen interval'. Read v2 for the constant product and the oracle accumulator. Do not describe a v3 position as if it were this paper.
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
- 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
Order books need makers who stay online. Uniswap's design lets a pool of two tokens quote a price from its own reserves, so a trader can swap against the contract without a counterparty sitting in the book.
What the design proposes
- The invariant is the product of the two reserves, up to the fee. A trade moves the reserves along that curve.
- Anyone may add liquidity in proportion to the reserves and receive a claim on the pool.
- A cumulative price is stored so other contracts can read a time-weighted average without trusting the spot price.
How the mechanism is specified
- The fee stays in the pool. Liquidity providers earn it only by being in the pool while volume happens, and they eat divergence loss when the price moves.
- Flash swaps let a user receive tokens and pay inside the same transaction, or revert.
- The core contracts are not the router, the interface, or the later v3 concentrated-liquidity paper.
What this page does not treat as proven
- The invariant is not a promise of a good price. It is a function of reserves.
- Divergence loss is not a bug in the paper. It is the cost of the curve.
- This page does not describe governance, the UNI token, or v3. Those are separate.
09 Lexicon
Terms, opened into the record
- Constant product
- The rule that the two reserves, multiplied, do not fall when someone trades.
- Pool token
- A claim on a share of both reserves, including fees and including any inventory loss.
- Flash swap
- A withdrawal that must be repaid before the transaction ends, or the transaction reverts.
- Time-weighted price
- An average of the pool's price over time, harder to push inside a single block than the spot ratio.
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.