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mode 100644 index 0000000..b6f970c --- /dev/null +++ b/docs/concepts/core-concepts/bpt-oracles-example.md @@ -0,0 +1,108 @@ +--- +order: 4 +title: BPT Oracle Numerical Example +--- +# Numerical example + +Consider a Stable Pool containing USDC and USDT, where USDT has slightly de-pegged (say, to 0.98). + +p₁ = $1.00 (USDC), p₂ = $0.98 (USDT) +A = 100, D = 1000 (invariant) + +Step 1: Calculate the parameters (amplification coefficient, and "helper" constants derived from the Amplification parameter) + +a = A × n^(2n) = 100 × 2^4 = 1600 +b = a - n^n = 1600 - 2^2 = 1596 +c = b/a = 1596/1600 = 0.9975 + +Step 2: Calculate the r values (scaled prices) + +r₁ = p₁/a = 1.00/1600 = 0.000625 +r₂ = p₂/a = 0.98/1600 = 0.0006125 + +Step 3: Find the root, using Newton's method: + +Choose the starting point: k₀ = (1 + 1/(1+b)) × ρ + +k₀ = (1 + 1/(1+1596)) × 1633 = (1 + 1/1597) × 1633 ≈ 1634.02 + +Newton's method: +k_{n+1} = k_n - G(k_n)/G'(k_n); where + +G(k) = T(k)³ × P(k) - α +G'(k) = T²(k) × P(k) × [(3T'(k) × P(k) + T(k) × P'(k))/P(k)] + +And: +T'(k) = -r₁/(kr₁-1)² - r₂/(kr₂-1)² +P'(k) = P(k) × [r₁/(kr₁-1) + r₂/(kr₂-1)] + +First iteration (k₀ = 1634.02) +Calculate T(1634.02): + +T = 1/(1634.02×0.000625-1) + 1/(1634.02×0.0006125-1) - 1 +T = 1/(1.0213-1) + 1/(1.0008-1) - 1 +T = 1/0.0213 + 1/0.0008 - 1 = 46.95 + 1250 - 1 ≈ 1295.95 + +Calculate P(1634.02): + +P = (1634.02×0.000625-1) × (1634.02×0.0006125-1) +P = 0.0213 × 0.0008 ≈ 0.000017 + +Calculate G(1634.02): the "error" + +G = (1295.95)³ × 0.000017 - 1588.03 +G = 2.17×10⁹ × 0.000017 - 1588.03 ≈ 36,890 - 1588 ≈ 35,302 + +Calculate derivatives and find k₁: + +T' = -0.000625/(0.0213)² - 0.0006125/(0.0008)² ≈ -1380 - 956 ≈ -2336 +G' ≈ ... (complex calculation) ≈ 50.8 + +k₁ = 1634.02 - 35,302/50.8 ≈ 1634.02 - 694.9 ≈ 939.1 + +Continue iterations: +| Step | k̃_n | G(k̃_n) | k̃_{n+1} | +| ---- | ------- | ------ | ------- | +| 0 | 1634.02 | 35,302 | 939.1 | +| 1 | 939.1. | -285.4 | 1425.7 | +| 2 | 1425.7 | 892.1 | 1580.3 | +| 3 | 1580.3 | 124.7 | 1635.8 | +| 4 | 1635.8 | 8.2 | 1640.1 | +| 5 | 1640.1 | 0.1 | 1641.0 | +| 6 | 1641.0 | ~0 | 1641.0 | + +![Find the root](/images/BPTOracleIllustration.png) + +Step 4: Calculate T (using our found k̃ = 1641) + +Recall that T = 1/(k̃r₁ - 1) + 1/(k̃r₂ - 1) - 1 + +T = 1/(1641 × 0.000625 - 1) + 1/(1641 × 0.0006125 - 1) - 1 +T = 1/(1.025625 - 1) + 1/(1.0051125 - 1) - 1 +T = 1/0.025625 + 1/0.0051125 - 1 +T = 39.02 + 195.60 - 1 = 233.62 + +Step 5: Calculate effective balances + +Recall that x₁ = (cD)/(k̃r₁ - 1) × T⁻¹ + +x₁ = (0.9975 × 1000)/(1641 × 0.000625 - 1) × (1/233.62) +x₁ = 997.5/0.025625 × (1/233.62) = 166.69 + +x₂ = (cD)/(k̃r₂ - 1) × T⁻¹ +x₂ = (0.9975 × 1000)/(1641 × 0.0006125 - 1) × (1/233.62) +x₂ = 997.5/0.0051125 × (1/233.62) = 833.31 + +Step 6: Calculate total pool value + +Recall that Pool Value = p₁ × x₁ + p₂ × x₂ + +Pool Value = $1.00 × 166.69 + $0.98 × 833.31 +Pool Value = $166.69 + $816.64 = $983.33 + +Step 7: Calculate BPT price + +Recall that BPT Price = Pool Value / Total BPT Supply + +(If total BPT supply = 1000 tokens, since D = 1000, and starting prices were nominal at $1) +BPT Price = $983.33 / 1000 = $0.983 per BPT diff --git a/docs/concepts/core-concepts/bpt-oracles.md b/docs/concepts/core-concepts/bpt-oracles.md new file mode 100644 index 0000000..68f1c46 --- /dev/null +++ b/docs/concepts/core-concepts/bpt-oracles.md @@ -0,0 +1,106 @@ +--- +order: 4 +title: BPT as Collateral +--- +# Price Oracles for BPT as Collateral + +## Introduction + +Liquidity provider (LP) tokens represent proportional ownership in a pool of assets. In the Balancer ecosystem, these are known as BPT (Balancer Pool Tokens). When users add liquidity to a Balancer pool by depositing tokens, they receive corresponding Balancer Pool Tokens in return. These tokens represent their proportional share of the liquidity pool. + +With the rising popularity of lending protocol partners like [AAVE](https://aave.com/), there's growing interest in using these tokens as collateral, allowing users to borrow against their staked liquidity. However, LP tokens pose unique challenges for oracle design and risk management. Their value depends on both the underlying assets and the pool composition and parameters, making them potentially vulnerable to manipulation. Balancer's radical flexibility is a major benefit for builders - yet presents unique challenges for oracle building. Balancer supports not only arbitrary pool types, but also yield-bearing tokens with rate providers, and offers hooks that can alter swap fees, adjust swap results, or otherwise affect pool balances during operations. + +Flash loans - either explicit using Balancer V2 or other platforms, or implicit in Balancer's batch operations - are especially dangerous, and could be used to temporarily distort pool balances and pricing, inflating the apparent BPT value. The risk is not theoretical! Naive oracle implementations have been exploited many times in recent years: [Alpha Homora](https://blog.alphaventuredao.io/alpha-homora-v2-post-mortem/) lost over $38 million when an attacker manipulated LP token pricing to over-collateralize a loan, while [Harvest Finance](https://medium.com/harvest-finance/harvest-flashloan-economic-attack-post-mortem-3cf900d65217) saw $24 million drained through a similar manipulation of stablecoin Curve pools. These examples highlight the critical need for manipulation-resistant oracles when integrating LP tokens into lending systems. + +One first-line defense against implicit flash loans is the [WrappedBalancerPoolToken](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/vault/contracts/WrappedBalancerPoolToken.sol), and associated factory. This factory deploys wrapped versions of arbitrary BPT, which are freely interchangeable with "raw" BPT - but only when the Vault is locked (i.e., when there is no ongoing operation). This ensures that the BPT balance of the caller is "real," and not flash loaned: at least not from Balancer V3. It could still be an externally flash loaned from another source. It's one layer of "Swiss cheese" security, but not necessarily sufficient by itself. + +While "balance verification" is important for some operations (e.g., nested pools), what we really want is a reliable way to derive a reliable, non-manipulable price for a Balancer Pool Token: on-chain, and available during Vault operations. This enables many advanced use cases, including our target of BPT as collateral. + +To do this, we require externally derived, true market prices, as anything internal and calculated purely on chain could be front-run and manipulated. The current interface uses Chainlink oracles for this, but is easily adaptable to other protocols. There is unlikely to be a Chainlink oracle for the BPT itself (or we could just use that), so our pricing algorithm must operate using price feeds for the constituent tokens. It must incorporate the total pool value and supply - yet _not_ the actual token balances, which are manipulable. + +## Overview + +Instead of using the actual balances to derive the overall price, Balancer BPT oracles compute _theoretical_ balances which satisfy two constraints: + +* The "pool constraint": the theoretical balance invariant must equal the real balance invariant, so the value of the pool is equivalent and can legitimately be compared to the supply. +* The "price constraint": the token prices derived from the theoretical balances must be proportional to the oracle prices, so that the internal token prices correctly reflect the current market. + +We begin with a system of n+1 equations: n "gradient" equations (relating the internal to the oracle prices), and the invariant equation. So, that's n+1 equations with n unknowns: the theoretical token balances we are trying to find. We can linearize the gradient equations by introducing k̃, a sort of scaling factor that converts internal to external prices. Since by definition the prices are proportional, we can define k̃ as the constant of proportionality. + +We can then solve this system of linear gradient equations, and express the theoretical balances xⱼ in terms of k̃. + +Then the real magic happens - we can substitute those xⱼ expressions into the invariant equation, and reduce the system to a single equation in k̃. On chain, this equation can be solved for k̃ using Newton's method. Once we have k̃, we can compute the theoretical balances, sum the product of each token balance and oracle price to get the total pool value, then divide by the total supply to derive the final BPT price. + +## Derivation + +With x̃ representing the vector of theoretical token balances, the pool constraint can be expressed mathematically as: F(x̃, D) = 0 +This means that the theoretical balances must reproduce the real invariant. + +The price constraint can be expressed mathematically as: ∇f(x̃) = k̃·ρ + +This means the internal prices must match (i.e., be proportional to) the oracle prices. ρ (rho) is a "critical boundary" constraint on k̃. We can derive a minimum valid value of k̃ from the oracle prices and degree of price curvature; at this value, the T function goes to infinity. + +To calculate ρ: + +1. Calculate the amplification coefficient: a = A × n^(2n); A is the amplification parameter of the Stable Pool +2. Calculate the scaled prices: rᵢ = pᵢ / a for each token +3. Since k̃ must be greater than 1/rₙ for each token, the final lower bound is given by: ρ = 1 / min(r₁, r₂, ..., rₙ) + +Given these constraints, the key is to find k̃. To understand how, we start with the invariant equation for the pool: f(x₁, x₂, ..., xₙ) = D. This is some function which, operating on the real balances, produces a single invariant value D, representing the total value of the pool. The details vary, but the Balancer Vault requires this to be defined for every pool type. So far, we have implemented oracles for both Weighted and Stable Balancer pools. (ReCLAMM pools should also work, as they are fundamentally Weighted pools, just incorporating virtual balances.) + +The partial derivative ∂f/∂xⱼ represents how much the invariant changes per unit of token j, and the ratio of these partial derivatives represents the internal spot price of one token in terms of another. For instance, ∂f/∂x₂ / ∂f/∂x₁ would be the spot price of token 2 in terms of token 1. + +The n gradient equations look like: + +∂F/∂x₁ = k̃ · p₁ +∂F/∂x₂ = k̃ · p₂ +... +∂F/∂xₙ = k̃ · p₂ + +Since k̃ is constant, these equations are linear in xⱼ, so can be solved for each token: + +x₁ = [function of k̃] +x₂ = [function of k̃] +... + +We now apply the second constraint, substituting the x expressions into the pool constraint F(x̃, D) = 0. Since all the x expressions are functions of k̃, we now have a single equation in terms of k̃: one equation, one unknown. + +After a lot of algebra, the single equation can be written as: + +T(k̃)^(n+1) · P(k̃) = α; where + +T(k̃) = Σ(1/(k̃rᵢ - 1)) - 1; from the gradient equations, where the r values are the scaled prices described above; + +P(k̃) = ∏(k̃rᵢ - 1); also from the gradient equations; and + +α = a·c^(n+1); a constant derived from the pool parameters, where + +a = A·n^(2n); +b = a - n^n; and +c = b/a + +Unfortunately this "T equation" is non-linear in k̃, so it must be solved numerically. On-chain, we use Newton's method to find the root (= the value of k̃ that satisfies both constraints). In the mathematical paper referenced below, we prove that when n is even (e.g.; in the most common case of 2-token pools), there is a single root. If n is odd, there are two roots, where the correct one is the smaller. + +In summary: + +* Oracle prices tell us what the "fair" relative prices should be +* The gradient condition ensures that internal AMM prices correspond to these fair prices +* The invariant condition ensures that the theoretical balances are valid for the pool, and correctly represent the value +* k̃ is the common parameter: the "knob" we turn to make both conditions true simultaneously +* Once we find the right k̃, we can calculate the fair balances x̃ⱼ, and price the LP token + +See [this page](./bpt-oracles-example.md) for a numerical example. + +## References + +For a more detailed mathematical description of how this is applied to Stable Pools, see the [Pricing Stable Pool BPTs](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/docs/StableOracle.md) document in the V3 monorepo. + +True nerds can review the [Pricing StableSwap pools](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/docs/pricing_stableSwap_pools.pdf) paper by Sergio A. Yuhjtman, our resident mathematician. + +This paper goes much deeper into the mathematics, providing a rigorous theoretical backing for the computation method described in the docs. + +It reviews the mathematical properties of the StableSwap function, especially the upper/lower price bounds. + +It analyzes Newton's method, proving that the function G(k) is convex (which ensures convergence), and justifies the choice of starting point k₀. Newton's method is iterative, converging on the final value of k̃ by refining subsequent guesses, so it is important for performance to start in the right place. The paper proves the existence, uniqueness, and guaranteed monotonic convergence on k̃ from k₀. + +Finally, it analyzes edge cases, and proves that the boundary condition kr_i - 1 > 0 always holds under all supported conditions (i.e., balances, invariant, and amplification parameter are all > 0, and there are at least two tokens). \ No newline at end of file From 788c367fb49f7da5db13d13e1094cb8b0903c5c0 Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Tue, 5 Aug 2025 17:15:25 -0400 Subject: [PATCH 02/15] refactor: adjust order of other pages --- docs/concepts/core-concepts/concentrated-liquidity.md | 2 +- docs/concepts/core-concepts/pool-creator-fee.md | 2 +- docs/concepts/core-concepts/pool-role-accounts.md | 2 +- docs/concepts/core-concepts/rate-providers.md | 2 +- 4 files changed, 4 insertions(+), 4 deletions(-) diff --git a/docs/concepts/core-concepts/concentrated-liquidity.md b/docs/concepts/core-concepts/concentrated-liquidity.md index cf9536b..86b9fc5 100644 --- a/docs/concepts/core-concepts/concentrated-liquidity.md +++ b/docs/concepts/core-concepts/concentrated-liquidity.md @@ -1,5 +1,5 @@ --- -order: 7 +order: 8 title: Concentrated Liquidity --- # Concentrated Liquidity diff --git a/docs/concepts/core-concepts/pool-creator-fee.md b/docs/concepts/core-concepts/pool-creator-fee.md index 9d3e39c..e21756e 100644 --- a/docs/concepts/core-concepts/pool-creator-fee.md +++ b/docs/concepts/core-concepts/pool-creator-fee.md @@ -1,5 +1,5 @@ --- -order: 4 +order: 5 title: Pool Creator Fee --- ## Pool Creator Fee diff --git a/docs/concepts/core-concepts/pool-role-accounts.md b/docs/concepts/core-concepts/pool-role-accounts.md index 0c659d2..3004e65 100644 --- a/docs/concepts/core-concepts/pool-role-accounts.md +++ b/docs/concepts/core-concepts/pool-role-accounts.md @@ -1,5 +1,5 @@ --- -order: 5 +order: 6 title: Pool Role Accounts --- diff --git a/docs/concepts/core-concepts/rate-providers.md b/docs/concepts/core-concepts/rate-providers.md index 429975a..b6ca7e7 100644 --- a/docs/concepts/core-concepts/rate-providers.md +++ b/docs/concepts/core-concepts/rate-providers.md @@ -1,5 +1,5 @@ --- -order: 6 +order: 7 title: Rate Providers --- From 5365b2a8317d392b6e5281b3bed0a42586a89ec6 Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Tue, 5 Aug 2025 18:48:40 -0400 Subject: [PATCH 03/15] refactor: add Weighted Pool description --- docs/concepts/core-concepts/bpt-oracles.md | 22 ++++++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/docs/concepts/core-concepts/bpt-oracles.md b/docs/concepts/core-concepts/bpt-oracles.md index 68f1c46..fa9823c 100644 --- a/docs/concepts/core-concepts/bpt-oracles.md +++ b/docs/concepts/core-concepts/bpt-oracles.md @@ -31,8 +31,12 @@ We can then solve this system of linear gradient equations, and express the theo Then the real magic happens - we can substitute those xⱼ expressions into the invariant equation, and reduce the system to a single equation in k̃. On chain, this equation can be solved for k̃ using Newton's method. Once we have k̃, we can compute the theoretical balances, sum the product of each token balance and oracle price to get the total pool value, then divide by the total supply to derive the final BPT price. +See [this page](./bpt-oracles-contracts.md) for references to the BPT Oracle contracts. + ## Derivation +The following applies to Stable Pools, using the StableSwap invariant equation. (See below for a discussion of weighted pools.) + With x̃ representing the vector of theoretical token balances, the pool constraint can be expressed mathematically as: F(x̃, D) = 0 This means that the theoretical balances must reproduce the real invariant. @@ -91,6 +95,24 @@ In summary: See [this page](./bpt-oracles-example.md) for a numerical example. +## Weighted Pools + +Weighted and Stable Pools use the same general algorithm. While the complex StableSwap invariant necessitates Newton's method to find the scaling parameter k̃, then calculate effective balances and total value, the power-law invariant of the Weighted Pool allows us to solve the gradient and invariant conditions simultaneously, giving us TVL = k × Π((Pᵢ/Wᵢ)^Wᵢ) in one step. + +In particular, "mapping" the weighted pool solution onto the equivalent terms used above: + +* The theoretical balances x̃ᵢ = (TVL × Wᵢ)/Pᵢ, where TVL is the total pool value (referred to as Bᵢ in the WeightedLPOracle code docs). +* The Weighted invariant D = Π(Bᵢ^Wᵢ), computed directly using theoretical balances and weights (referred to as k in the WeightedLPOracle code docs). +* The scaling parameter k̃ is in the Weighted case simply equal to the TVL (C in the code docs). + +So, positing a normalization constant C such that C = (Pᵢ × Bᵢ / Wᵢ) for every token, the gradient "price constraint" is: Bᵢ = (C × Wᵢ)/Pᵢ + +We can then substitute this directly into the invariant (no complex polynomials here): D = Π((C × Wᵢ/Pᵢ)^Wᵢ) = C × Π((Wᵢ/Pᵢ)^Wᵢ) + +And then solve for C directly: C = k × Π((Pᵢ/Wᵢ)^Wᵢ) = TVL = Total pool value + +The price is then simply TVL / totalSupply. + ## References For a more detailed mathematical description of how this is applied to Stable Pools, see the [Pricing Stable Pool BPTs](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/docs/StableOracle.md) document in the V3 monorepo. 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zEwjDO&Gg@I@?p!jUF?FA+a@{a>1-28J6&t$yYa~!ucbS9aQFeKOZNb{kWdZ5F9>Rs za{M86z2iWD6SC)T;?_Aff8(P zZzriiqp%HFV7>Xbst;>{gD1T10^1nnx21$h4w@WbT-^8@DoZ%Yzybvl_`5^}GTv`9 zRdYiX#uXxP;~Q@P<6`6Q)mAu~1vsO&L|fs)z1(b{9#Vs5BQP$KzlWFN2|cV*FMvJq zy|=H;kbt|LNJbKHDC79M^{)tq1)6ym)&e7c`&vUoQiEnRBjO6`p_CCD|1(57n_uu+ SF+Z6B2s~Z=T-G@yGywoQLu%^) literal 0 HcmV?d00001 diff --git a/docs/concepts/core-concepts/bpt-oracles-contracts.md b/docs/concepts/core-concepts/bpt-oracles-contracts.md new file mode 100644 index 0000000..c2355cf --- /dev/null +++ b/docs/concepts/core-concepts/bpt-oracles-contracts.md @@ -0,0 +1,40 @@ +--- +order: 4 +title: BPT Oracle contracts +--- +# Overview + +We have implemented oracles for both Weighted and Stable Balancer pools. (ReCLAMM pools should also work, as they are fundamentally Weighted pools, just incorporating virtual balances.) These are in the standalone-utils package: `WeightedLPOracle` and `StableLPOracle`, and associated factories. + +![Inheritance Diagram](/images/BPTOracles.png) + +## Oracle Factories + +Oracles are created from the corresponding pool factories using the create function: + +`function create(IBasePool pool, AggregatorV3Interface[] memory feeds) external returns (ILPOracleBase oracle);` + +`AggregatorV3Interface` is a Chainlink price feed. + +This first computes an "OracleID" as the hash of the pool and price feed addresses. Since the tokens must be ordered, we know the price feed addresses will also be in the same order, so a given combination of the pool and price feeds is guaranteed unique, then calls an internal `_create` (implemented by derived contracts) to deploy the oracle with the given configuration, and registers it with the factory. + +The base factory contract [interface](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/interfaces/contracts/standalone-utils/ILPOracleFactoryBase.sol) defines functions to find an oracle given pool and feed addresses, and check whether a given oracle was deployed by the official factory: + +``` +function getOracle( + IBasePool pool, + AggregatorV3Interface[] memory feeds +) external view returns (ILPOracleBase oracle); + +function isOracleFromFactory(ILPOracleBase oracle) external view returns (bool success); +``` + +## Oracle contracts + +The common factory contract [interface](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/interfaces/contracts/standalone-utils/ILPOracleBase.sol) defines: + +`function calculateTVL(int256[] memory prices) external view returns (uint256 tvl);` + +This function computes the total value of the pool, solving the pool and price constraints simultaneously as described in the [main article](./bpt-oracles.md#derivation). + +Just as the price feeds implement the Chainlink interface `AggregatorV3Interface` to fetch individual token prices, the common factory [contract](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/contracts/LPOracleBase.sol) also implements this interface, and calling `latestRoundData` invokes the virtual `calculateTVL` function to get the total value, then divides by the total supply to get the BPT price. From a2e2133e96b22453639512d5a9f159af6de7fda1 Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Tue, 5 Aug 2025 19:01:38 -0400 Subject: [PATCH 05/15] refactor: add a note about oracle support to the BPT page --- docs/concepts/core-concepts/balancer-pool-tokens.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/docs/concepts/core-concepts/balancer-pool-tokens.md b/docs/concepts/core-concepts/balancer-pool-tokens.md index b3d66e5..dcdfac8 100644 --- a/docs/concepts/core-concepts/balancer-pool-tokens.md +++ b/docs/concepts/core-concepts/balancer-pool-tokens.md @@ -36,3 +36,11 @@ By doing this, the BalancerPoolToken contract ensures that Balancer Pool Tokens ## Composability As BPTs adhere to the ERC20 standard, they can seamlessly integrate as pool tokens in other pools. For instance, the BPT of an ERC4626 pool comprising wrapped versions of DAI, USDC, and USDT can be paired with tokens from new projects. This composability ensures the maintenance of deep and capital-efficient stable liquidity, while simultaneously creating efficient swap paths for the project token. + +## Oracles + +If Chainlink price feeds are available for all tokens, Weighted and Stable Pool BPTs can be priced in USD terms using the corresponding LP Oracle contracts: [WeightedLPOracle](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/contracts/WeightedLPOracle.sol) and [StableLPOracle](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/contracts/StableLPOracle.sol), which implement [this interface](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/interfaces/contracts/standalone-utils/ILPOracleBase.sol) as well as the `AggregatorV3Interface` Chainlink price feed interface. This allows users to call `latestRoundData` on the oracle contract to get an accurate, non-manipulable BPT price, just as if it were a Chainlink oracle itself. + +Note that it would be possible to generalize these contracts to support other kinds of price feeds; the only function of the price oracle is to fetch the current market prices. The pricing algorithm and all logic is contained in the LP oracle code (and mostly all in the base contracts). + +The most common use for these contracts is enabling Balancer BPT to be used as collateral on lending platforms. See the [BPT as Collateral](./bpt-oracles.md) docs for more details. \ No newline at end of file From 8069cea54d5e10b9770d1217f5c6bebe435cbc4d Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Tue, 5 Aug 2025 19:16:03 -0400 Subject: [PATCH 06/15] refactor: move into folder --- docs/concepts/core-concepts/balancer-pool-tokens.md | 2 +- .../core-concepts/{ => bpt-oracles}/bpt-oracles-contracts.md | 0 .../core-concepts/{ => bpt-oracles}/bpt-oracles-example.md | 0 docs/concepts/core-concepts/{ => bpt-oracles}/bpt-oracles.md | 2 ++ 4 files changed, 3 insertions(+), 1 deletion(-) rename docs/concepts/core-concepts/{ => bpt-oracles}/bpt-oracles-contracts.md (100%) rename docs/concepts/core-concepts/{ => bpt-oracles}/bpt-oracles-example.md (100%) rename docs/concepts/core-concepts/{ => bpt-oracles}/bpt-oracles.md (99%) diff --git a/docs/concepts/core-concepts/balancer-pool-tokens.md b/docs/concepts/core-concepts/balancer-pool-tokens.md index dcdfac8..3508b62 100644 --- a/docs/concepts/core-concepts/balancer-pool-tokens.md +++ b/docs/concepts/core-concepts/balancer-pool-tokens.md @@ -43,4 +43,4 @@ If Chainlink price feeds are available for all tokens, Weighted and Stable Pool Note that it would be possible to generalize these contracts to support other kinds of price feeds; the only function of the price oracle is to fetch the current market prices. The pricing algorithm and all logic is contained in the LP oracle code (and mostly all in the base contracts). -The most common use for these contracts is enabling Balancer BPT to be used as collateral on lending platforms. See the [BPT as Collateral](./bpt-oracles.md) docs for more details. \ No newline at end of file +The most common use for these contracts is enabling Balancer BPT to be used as collateral on lending platforms. See the [BPT as Collateral](./bpt-oracles/bpt-oracles.md) docs for more details. \ No newline at end of file diff --git a/docs/concepts/core-concepts/bpt-oracles-contracts.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md similarity index 100% rename from docs/concepts/core-concepts/bpt-oracles-contracts.md rename to docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md diff --git a/docs/concepts/core-concepts/bpt-oracles-example.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md similarity index 100% rename from docs/concepts/core-concepts/bpt-oracles-example.md rename to docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md diff --git a/docs/concepts/core-concepts/bpt-oracles.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md similarity index 99% rename from docs/concepts/core-concepts/bpt-oracles.md rename to docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md index fa9823c..48415f2 100644 --- a/docs/concepts/core-concepts/bpt-oracles.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md @@ -115,6 +115,8 @@ The price is then simply TVL / totalSupply. ## References +See the [contracts](./bpt-oracles-contracts.md) page for practical examples of using the oracles. + For a more detailed mathematical description of how this is applied to Stable Pools, see the [Pricing Stable Pool BPTs](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/docs/StableOracle.md) document in the V3 monorepo. True nerds can review the [Pricing StableSwap pools](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/docs/pricing_stableSwap_pools.pdf) paper by Sergio A. Yuhjtman, our resident mathematician. From 6cf7eee691d4a7d6e35594a8254d9a8bbcb030e2 Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Tue, 5 Aug 2025 23:33:49 -0400 Subject: [PATCH 07/15] review of first page --- .../core-concepts/bpt-oracles/bpt-oracles.md | 132 +++++++++++++----- 1 file changed, 97 insertions(+), 35 deletions(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md index 48415f2..9d2db94 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md @@ -8,80 +8,134 @@ title: BPT as Collateral Liquidity provider (LP) tokens represent proportional ownership in a pool of assets. In the Balancer ecosystem, these are known as BPT (Balancer Pool Tokens). When users add liquidity to a Balancer pool by depositing tokens, they receive corresponding Balancer Pool Tokens in return. These tokens represent their proportional share of the liquidity pool. -With the rising popularity of lending protocol partners like [AAVE](https://aave.com/), there's growing interest in using these tokens as collateral, allowing users to borrow against their staked liquidity. However, LP tokens pose unique challenges for oracle design and risk management. Their value depends on both the underlying assets and the pool composition and parameters, making them potentially vulnerable to manipulation. Balancer's radical flexibility is a major benefit for builders - yet presents unique challenges for oracle building. Balancer supports not only arbitrary pool types, but also yield-bearing tokens with rate providers, and offers hooks that can alter swap fees, adjust swap results, or otherwise affect pool balances during operations. +With the rising popularity of lending protocol partners like [AAVE](https://aave.com/), there's growing interest in using these tokens as collateral, allowing users to borrow against their staked liquidity. However, LP tokens pose unique challenges for oracle design and risk management. Their value depends on both the underlying assets and the pool composition and parameters, making them potentially vulnerable to manipulation. + +Balancer's radical flexibility is a major benefit for builders - yet presents unique challenges for oracle building. Balancer supports not only arbitrary pool types, but also yield-bearing tokens with rate providers, and offers hooks that can alter swap fees, adjust swap results, or otherwise affect pool balances during operations. Flash loans - either explicit using Balancer V2 or other platforms, or implicit in Balancer's batch operations - are especially dangerous, and could be used to temporarily distort pool balances and pricing, inflating the apparent BPT value. The risk is not theoretical! Naive oracle implementations have been exploited many times in recent years: [Alpha Homora](https://blog.alphaventuredao.io/alpha-homora-v2-post-mortem/) lost over $38 million when an attacker manipulated LP token pricing to over-collateralize a loan, while [Harvest Finance](https://medium.com/harvest-finance/harvest-flashloan-economic-attack-post-mortem-3cf900d65217) saw $24 million drained through a similar manipulation of stablecoin Curve pools. These examples highlight the critical need for manipulation-resistant oracles when integrating LP tokens into lending systems. -One first-line defense against implicit flash loans is the [WrappedBalancerPoolToken](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/vault/contracts/WrappedBalancerPoolToken.sol), and associated factory. This factory deploys wrapped versions of arbitrary BPT, which are freely interchangeable with "raw" BPT - but only when the Vault is locked (i.e., when there is no ongoing operation). This ensures that the BPT balance of the caller is "real," and not flash loaned: at least not from Balancer V3. It could still be an externally flash loaned from another source. It's one layer of "Swiss cheese" security, but not necessarily sufficient by itself. +One first-line defense against implicit flash loans is the [WrappedBalancerPoolToken](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/vault/contracts/WrappedBalancerPoolToken.sol), and its associated factory. This factory deploys wrapped versions of arbitrary BPT, which are freely interchangeable with "raw" BPT - but only when the Vault is locked (i.e., when there is no ongoing operation). This ensures that the BPT balance of the caller is "real," and not flash loaned: at least not from Balancer V3. (It could still be an externally flash loaned from another source.) It's one layer of "Swiss cheese" security, but not necessarily sufficient by itself. While "balance verification" is important for some operations (e.g., nested pools), what we really want is a reliable way to derive a reliable, non-manipulable price for a Balancer Pool Token: on-chain, and available during Vault operations. This enables many advanced use cases, including our target of BPT as collateral. -To do this, we require externally derived, true market prices, as anything internal and calculated purely on chain could be front-run and manipulated. The current interface uses Chainlink oracles for this, but is easily adaptable to other protocols. There is unlikely to be a Chainlink oracle for the BPT itself (or we could just use that), so our pricing algorithm must operate using price feeds for the constituent tokens. It must incorporate the total pool value and supply - yet _not_ the actual token balances, which are manipulable. +To do this, we require externally derived, true market prices, as anything internal and calculated purely on-chain could be front-run and manipulated. The current interface uses Chainlink oracles for this, but is easily adaptable to other protocols. There is unlikely to be a Chainlink oracle for the BPT itself (or we could just use that), so our pricing algorithm must operate using price feeds for the constituent tokens. It must incorporate the total pool value and supply - yet _not_ the actual token balances, which are manipulable. ## Overview Instead of using the actual balances to derive the overall price, Balancer BPT oracles compute _theoretical_ balances which satisfy two constraints: -* The "pool constraint": the theoretical balance invariant must equal the real balance invariant, so the value of the pool is equivalent and can legitimately be compared to the supply. -* The "price constraint": the token prices derived from the theoretical balances must be proportional to the oracle prices, so that the internal token prices correctly reflect the current market. +* The "pool constraint": the theoretical balance invariant must equal the real balance invariant, so that the value of the pool is equivalent and can legitimately be scaled by the supply. +* The "price constraint": the token prices derived from the theoretical balances must be proportional to the oracle prices, so that the internal token prices correctly reflect the current state of the market. -We begin with a system of n+1 equations: n "gradient" equations (relating the internal to the oracle prices), and the invariant equation. So, that's n+1 equations with n unknowns: the theoretical token balances we are trying to find. We can linearize the gradient equations by introducing k̃, a sort of scaling factor that converts internal to external prices. Since by definition the prices are proportional, we can define k̃ as the constant of proportionality. +We begin with a system of n+1 equations: n "gradient" equations (relating the internal prices to the oracle prices), plus the invariant equation. So, that's n+1 equations with n unknowns: the theoretical token balances we are trying to find. We can linearize the gradient equations by introducing k̃, a sort of scaling factor that converts internal to external prices. Since by definition the prices are proportional, we can define k̃ as this constant of proportionality. We can then solve this system of linear gradient equations, and express the theoretical balances xⱼ in terms of k̃. -Then the real magic happens - we can substitute those xⱼ expressions into the invariant equation, and reduce the system to a single equation in k̃. On chain, this equation can be solved for k̃ using Newton's method. Once we have k̃, we can compute the theoretical balances, sum the product of each token balance and oracle price to get the total pool value, then divide by the total supply to derive the final BPT price. +Then the real magic happens - we can substitute those xⱼ expressions into the invariant equation, and reduce the system to a single equation in k̃. On chain, this equation can be solved using Newton's method. Once we have k̃, we can compute the theoretical balances, sum the product of each token balance and oracle price to get the total pool value, then divide by the total supply to derive the final BPT price. See [this page](./bpt-oracles-contracts.md) for references to the BPT Oracle contracts. ## Derivation -The following applies to Stable Pools, using the StableSwap invariant equation. (See below for a discussion of weighted pools.) +The following applies to Stable Pools, using the StableSwap invariant equation. (See below for a discussion of the simpler weighted pools.) + +With x̃ representing the vector of theoretical token balances, the pool constraint can be expressed mathematically as: + +F(x̃) = D; or F(x̃, D) = 0 -With x̃ representing the vector of theoretical token balances, the pool constraint can be expressed mathematically as: F(x̃, D) = 0 This means that the theoretical balances must reproduce the real invariant. -The price constraint can be expressed mathematically as: ∇f(x̃) = k̃·ρ +The price constraint can be expressed mathematically as: -This means the internal prices must match (i.e., be proportional to) the oracle prices. ρ (rho) is a "critical boundary" constraint on k̃. We can derive a minimum valid value of k̃ from the oracle prices and degree of price curvature; at this value, the T function goes to infinity. +$$ +\\nabla f(\\tilde{x}) = \\tilde{k} \\cdot \\rho +$$ + +This means that the internal prices must match (i.e., be proportional to) the oracle prices. ρ (rho) is a "critical boundary" constraint on k̃. We can derive a minimum valid value of k̃ from the oracle prices and degree of price curvature: at this value or below, the "T curve" (described below) goes to infinity and the equation is no longer soluble. To calculate ρ: -1. Calculate the amplification coefficient: a = A × n^(2n); A is the amplification parameter of the Stable Pool -2. Calculate the scaled prices: rᵢ = pᵢ / a for each token +1. Compute the amplification coefficient: a = A × n^(2n); A is the amplification parameter of the Stable Pool +2. Compute the scaled prices: rᵢ = pᵢ / a for each token; these are the market prices "normalized" by the pool state 3. Since k̃ must be greater than 1/rₙ for each token, the final lower bound is given by: ρ = 1 / min(r₁, r₂, ..., rₙ) -Given these constraints, the key is to find k̃. To understand how, we start with the invariant equation for the pool: f(x₁, x₂, ..., xₙ) = D. This is some function which, operating on the real balances, produces a single invariant value D, representing the total value of the pool. The details vary, but the Balancer Vault requires this to be defined for every pool type. So far, we have implemented oracles for both Weighted and Stable Balancer pools. (ReCLAMM pools should also work, as they are fundamentally Weighted pools, just incorporating virtual balances.) +Given these constraints, the key is to find k̃. To understand how, we start with the invariant equation for the pool: + +$$ +f(x_1, x_2, \\dots, x_n) = D +$$ + +This is some function which, operating on the real balances, produces a single invariant value D, representing the total value of the pool. The details vary, but the Balancer Vault requires this to be defined for every pool type. So far, we have implemented oracles for both Weighted and Stable Balancer pools. (ReCLAMM pools should also work, as they are fundamentally Weighted pools, just incorporating virtual balances.) The partial derivative ∂f/∂xⱼ represents how much the invariant changes per unit of token j, and the ratio of these partial derivatives represents the internal spot price of one token in terms of another. For instance, ∂f/∂x₂ / ∂f/∂x₁ would be the spot price of token 2 in terms of token 1. The n gradient equations look like: -∂F/∂x₁ = k̃ · p₁ -∂F/∂x₂ = k̃ · p₂ +$$ +\\frac{\\partial F}{\\partial x_1} = \\tilde{k} \\cdot p_1 +$$ + +$$ +\\frac{\\partial F}{\\partial x_2} = \\tilde{k} \\cdot p_2 +$$ + ... -∂F/∂xₙ = k̃ · p₂ + +$$ +\\frac{\\partial F}{\\partial x_n} = \\tilde{k} \\cdot p_n +$$ Since k̃ is constant, these equations are linear in xⱼ, so can be solved for each token: -x₁ = [function of k̃] -x₂ = [function of k̃] +$$ +x_1 = \\text{[function of } \\tilde{k} \\text{]} +$$ + +$$ +x_2 = \\text{[function of } \\tilde{k} \\text{]} +$$ + ... We now apply the second constraint, substituting the x expressions into the pool constraint F(x̃, D) = 0. Since all the x expressions are functions of k̃, we now have a single equation in terms of k̃: one equation, one unknown. After a lot of algebra, the single equation can be written as: -T(k̃)^(n+1) · P(k̃) = α; where +$$ +T(\\tilde{k})^{n+1} \\cdot P(\\tilde{k}) = \\alpha +$$ -T(k̃) = Σ(1/(k̃rᵢ - 1)) - 1; from the gradient equations, where the r values are the scaled prices described above; +where: -P(k̃) = ∏(k̃rᵢ - 1); also from the gradient equations; and +$$ +T(\\tilde{k}) = \\sum \\left( \\frac{1}{\\tilde{k} r_i - 1} \\right) - 1 +$$ -α = a·c^(n+1); a constant derived from the pool parameters, where +from the gradient equations, where the \\( r_i \\) are the scaled prices described above; -a = A·n^(2n); -b = a - n^n; and -c = b/a +$$ +P(\\tilde{k}) = \\prod (\\tilde{k} r_i - 1) +$$ + +also from the gradient equations; and + +$$ +\\alpha = a \\cdot c^{n+1} +$$ + +a constant derived from the pool parameters, where + +$$ +a = A \\cdot n^{2n} +$$ + +$$ +b = a - n^n +$$ + +$$ +c = \\frac{b}{a} +$$ Unfortunately this "T equation" is non-linear in k̃, so it must be solved numerically. On-chain, we use Newton's method to find the root (= the value of k̃ that satisfies both constraints). In the mathematical paper referenced below, we prove that when n is even (e.g.; in the most common case of 2-token pools), there is a single root. If n is odd, there are two roots, where the correct one is the smaller. @@ -90,14 +144,16 @@ In summary: * Oracle prices tell us what the "fair" relative prices should be * The gradient condition ensures that internal AMM prices correspond to these fair prices * The invariant condition ensures that the theoretical balances are valid for the pool, and correctly represent the value -* k̃ is the common parameter: the "knob" we turn to make both conditions true simultaneously +* k̃ is the common scaling parameter: the "knob" we adjust to make both conditions true simultaneously * Once we find the right k̃, we can calculate the fair balances x̃ⱼ, and price the LP token See [this page](./bpt-oracles-example.md) for a numerical example. ## Weighted Pools -Weighted and Stable Pools use the same general algorithm. While the complex StableSwap invariant necessitates Newton's method to find the scaling parameter k̃, then calculate effective balances and total value, the power-law invariant of the Weighted Pool allows us to solve the gradient and invariant conditions simultaneously, giving us TVL = k × Π((Pᵢ/Wᵢ)^Wᵢ) in one step. +Weighted and Stable Pools use the same general algorithm. While the complex StableSwap invariant requires Newton's method to find the scaling parameter k̃, then calculate effective balances and total value, the power-law invariant of the Weighted Pool allows us to solve the gradient and invariant conditions simultaneously, giving us: + +TVL = k × Π((Pᵢ/Wᵢ)^Wᵢ) in one step. In particular, "mapping" the weighted pool solution onto the equivalent terms used above: @@ -105,11 +161,17 @@ In particular, "mapping" the weighted pool solution onto the equivalent terms us * The Weighted invariant D = Π(Bᵢ^Wᵢ), computed directly using theoretical balances and weights (referred to as k in the WeightedLPOracle code docs). * The scaling parameter k̃ is in the Weighted case simply equal to the TVL (C in the code docs). -So, positing a normalization constant C such that C = (Pᵢ × Bᵢ / Wᵢ) for every token, the gradient "price constraint" is: Bᵢ = (C × Wᵢ)/Pᵢ +So, positing a normalization constant C such that C = (Pᵢ × Bᵢ / Wᵢ) for every token, the gradient "price constraint" is: + +Bᵢ = (C × Wᵢ)/Pᵢ + +We can then substitute this directly into the invariant (no complex polynomials here): + +D = Π((C × Wᵢ/Pᵢ)^Wᵢ) = C × Π((Wᵢ/Pᵢ)^Wᵢ) -We can then substitute this directly into the invariant (no complex polynomials here): D = Π((C × Wᵢ/Pᵢ)^Wᵢ) = C × Π((Wᵢ/Pᵢ)^Wᵢ) +And then solve for C directly: -And then solve for C directly: C = k × Π((Pᵢ/Wᵢ)^Wᵢ) = TVL = Total pool value +C = k × Π((Pᵢ/Wᵢ)^Wᵢ) = TVL = Total pool value The price is then simply TVL / totalSupply. @@ -119,12 +181,12 @@ See the [contracts](./bpt-oracles-contracts.md) page for practical examples of u For a more detailed mathematical description of how this is applied to Stable Pools, see the [Pricing Stable Pool BPTs](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/docs/StableOracle.md) document in the V3 monorepo. -True nerds can review the [Pricing StableSwap pools](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/docs/pricing_stableSwap_pools.pdf) paper by Sergio A. Yuhjtman, our resident mathematician. +True math nerds can review the [Pricing StableSwap pools](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/standalone-utils/docs/pricing_stableSwap_pools.pdf) paper by Sergio A. Yuhjtman, our resident mathematician. -This paper goes much deeper into the mathematics, providing a rigorous theoretical backing for the computation method described in the docs. +This paper goes much deeper into the mathematics, providing a rigorous theoretical backing for the computation methods described in the docs. It reviews the mathematical properties of the StableSwap function, especially the upper/lower price bounds. -It analyzes Newton's method, proving that the function G(k) is convex (which ensures convergence), and justifies the choice of starting point k₀. Newton's method is iterative, converging on the final value of k̃ by refining subsequent guesses, so it is important for performance to start in the right place. The paper proves the existence, uniqueness, and guaranteed monotonic convergence on k̃ from k₀. +It analyzes Newton's method, proving that the function G(k) is convex (which ensures convergence), and justifies the choice of starting point k₀. Newton's method is iterative, converging on the final value of k̃ by refining subsequent guesses, so it is important for performance to start in the right place. The paper proves the existence, uniqueness, and guaranteed monotonic convergence on k̃ from k₀. -Finally, it analyzes edge cases, and proves that the boundary condition kr_i - 1 > 0 always holds under all supported conditions (i.e., balances, invariant, and amplification parameter are all > 0, and there are at least two tokens). \ No newline at end of file +Finally, it analyzes edge cases, and proves that the boundary condition k̃rᵢ - 1 > 0 always holds under all supported conditions (i.e., balances, invariant, and amplification parameter are all > 0, and there are at least two tokens). \ No newline at end of file From b84a55afc0b678b24ecbbee2983f1f50a42b9bc6 Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Tue, 5 Aug 2025 23:45:41 -0400 Subject: [PATCH 08/15] flail: try to render them properly --- .../core-concepts/bpt-oracles/bpt-oracles.md | 68 ++++--------------- 1 file changed, 12 insertions(+), 56 deletions(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md index 9d2db94..433560a 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md @@ -47,9 +47,7 @@ This means that the theoretical balances must reproduce the real invariant. The price constraint can be expressed mathematically as: -$$ -\\nabla f(\\tilde{x}) = \\tilde{k} \\cdot \\rho -$$ +∇f(x̃) = k̃ · ρ This means that the internal prices must match (i.e., be proportional to) the oracle prices. ρ (rho) is a "critical boundary" constraint on k̃. We can derive a minimum valid value of k̃ from the oracle prices and degree of price curvature: at this value or below, the "T curve" (described below) goes to infinity and the equation is no longer soluble. @@ -61,9 +59,7 @@ To calculate ρ: Given these constraints, the key is to find k̃. To understand how, we start with the invariant equation for the pool: -$$ -f(x_1, x_2, \\dots, x_n) = D -$$ +f(x₁, x₂, ..., xₙ) = D This is some function which, operating on the real balances, produces a single invariant value D, representing the total value of the pool. The details vary, but the Balancer Vault requires this to be defined for every pool type. So far, we have implemented oracles for both Weighted and Stable Balancer pools. (ReCLAMM pools should also work, as they are fundamentally Weighted pools, just incorporating virtual balances.) @@ -71,71 +67,31 @@ The partial derivative ∂f/∂xⱼ represents how much the invariant changes pe The n gradient equations look like: -$$ -\\frac{\\partial F}{\\partial x_1} = \\tilde{k} \\cdot p_1 -$$ +∂F/∂x₁ = k̃ · p₁ -$$ -\\frac{\\partial F}{\\partial x_2} = \\tilde{k} \\cdot p_2 -$$ +∂F/∂x₂ = k̃ · p₂ ... -$$ -\\frac{\\partial F}{\\partial x_n} = \\tilde{k} \\cdot p_n -$$ - -Since k̃ is constant, these equations are linear in xⱼ, so can be solved for each token: - -$$ -x_1 = \\text{[function of } \\tilde{k} \\text{]} -$$ - -$$ -x_2 = \\text{[function of } \\tilde{k} \\text{]} -$$ - -... +∂F/∂xₙ = k̃ · p₂ We now apply the second constraint, substituting the x expressions into the pool constraint F(x̃, D) = 0. Since all the x expressions are functions of k̃, we now have a single equation in terms of k̃: one equation, one unknown. After a lot of algebra, the single equation can be written as: -$$ -T(\\tilde{k})^{n+1} \\cdot P(\\tilde{k}) = \\alpha -$$ - -where: - -$$ -T(\\tilde{k}) = \\sum \\left( \\frac{1}{\\tilde{k} r_i - 1} \\right) - 1 -$$ - -from the gradient equations, where the \\( r_i \\) are the scaled prices described above; - -$$ -P(\\tilde{k}) = \\prod (\\tilde{k} r_i - 1) -$$ +T(k̃)^(n+1) · P(k̃) = α; where -also from the gradient equations; and +T(k̃) = Σ(1/(k̃rᵢ - 1)) - 1; from the gradient equations, where the r values are the scaled prices described above; -$$ -\\alpha = a \\cdot c^{n+1} -$$ +P(k̃) = ∏(k̃rᵢ - 1); also from the gradient equations; and -a constant derived from the pool parameters, where +α = a·c^(n+1); a constant derived from the pool parameters, where -$$ -a = A \\cdot n^{2n} -$$ +a = A·n^(2n); -$$ -b = a - n^n -$$ +b = a - n^n; and -$$ -c = \\frac{b}{a} -$$ +c = b/a Unfortunately this "T equation" is non-linear in k̃, so it must be solved numerically. On-chain, we use Newton's method to find the root (= the value of k̃ that satisfies both constraints). In the mathematical paper referenced below, we prove that when n is even (e.g.; in the most common case of 2-token pools), there is a single root. If n is odd, there are two roots, where the correct one is the smaller. From 98c5ba38144fdb93f3b321a0511b51b9684cb702 Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Tue, 5 Aug 2025 23:50:30 -0400 Subject: [PATCH 09/15] flail: keep trying --- .../core-concepts/bpt-oracles/bpt-oracles.md | 17 ++++++----------- 1 file changed, 6 insertions(+), 11 deletions(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md index 433560a..2dafa2f 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md @@ -67,12 +67,9 @@ The partial derivative ∂f/∂xⱼ represents how much the invariant changes pe The n gradient equations look like: -∂F/∂x₁ = k̃ · p₁ - -∂F/∂x₂ = k̃ · p₂ - -... - +∂F/∂x₁ = k̃ · p₁
+∂F/∂x₂ = k̃ · p₂
+...
∂F/∂xₙ = k̃ · p₂ We now apply the second constraint, substituting the x expressions into the pool constraint F(x̃, D) = 0. Since all the x expressions are functions of k̃, we now have a single equation in terms of k̃: one equation, one unknown. @@ -85,12 +82,10 @@ T(k̃) = Σ(1/(k̃rᵢ - 1)) - 1; from the gradient equations, where the r value P(k̃) = ∏(k̃rᵢ - 1); also from the gradient equations; and -α = a·c^(n+1); a constant derived from the pool parameters, where - -a = A·n^(2n); - -b = a - n^n; and +α = a·c^(n+1); a constant derived from the pool parameters, where: +a = A·n^(2n);
+b = a - n^n; and
c = b/a Unfortunately this "T equation" is non-linear in k̃, so it must be solved numerically. On-chain, we use Newton's method to find the root (= the value of k̃ that satisfies both constraints). In the mathematical paper referenced below, we prove that when n is even (e.g.; in the most common case of 2-token pools), there is a single root. If n is odd, there are two roots, where the correct one is the smaller. From cf1131b3e22700dfc95d839fd66b5e4ba1fb63f0 Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Wed, 6 Aug 2025 00:08:30 -0400 Subject: [PATCH 10/15] formatting --- .../bpt-oracles/bpt-oracles-contracts.md | 2 +- .../bpt-oracles/bpt-oracles-example.md | 43 ++++++++++--------- 2 files changed, 24 insertions(+), 21 deletions(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md index c2355cf..4298da8 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md @@ -16,7 +16,7 @@ Oracles are created from the corresponding pool factories using the create funct `AggregatorV3Interface` is a Chainlink price feed. -This first computes an "OracleID" as the hash of the pool and price feed addresses. Since the tokens must be ordered, we know the price feed addresses will also be in the same order, so a given combination of the pool and price feeds is guaranteed unique, then calls an internal `_create` (implemented by derived contracts) to deploy the oracle with the given configuration, and registers it with the factory. +This first computes an "OracleID" as the hash of the pool and price feed addresses. Since the tokens must be ordered, we know the price feed addresses will also be in the same order, so a given combination of the pool and price feeds is guaranteed unique. It then calls an internal `_create` (implemented by derived contracts) to deploy the oracle with the given configuration, and registers it with the factory. The base factory contract [interface](https://github.com/balancer/balancer-v3-monorepo/blob/main/pkg/interfaces/contracts/standalone-utils/ILPOracleFactoryBase.sol) defines functions to find an oracle given pool and feed addresses, and check whether a given oracle was deployed by the official factory: diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md index b6f970c..0075dc2 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md @@ -6,18 +6,18 @@ title: BPT Oracle Numerical Example Consider a Stable Pool containing USDC and USDT, where USDT has slightly de-pegged (say, to 0.98). -p₁ = $1.00 (USDC), p₂ = $0.98 (USDT) +p₁ = $1.00 (USDC), p₂ = $0.98 (USDT)
A = 100, D = 1000 (invariant) Step 1: Calculate the parameters (amplification coefficient, and "helper" constants derived from the Amplification parameter) -a = A × n^(2n) = 100 × 2^4 = 1600 -b = a - n^n = 1600 - 2^2 = 1596 +a = A × n^(2n) = 100 × 2^4 = 1600
+b = a - n^n = 1600 - 2^2 = 1596
c = b/a = 1596/1600 = 0.9975 Step 2: Calculate the r values (scaled prices) -r₁ = p₁/a = 1.00/1600 = 0.000625 +r₁ = p₁/a = 1.00/1600 = 0.000625
r₂ = p₂/a = 0.98/1600 = 0.0006125 Step 3: Find the root, using Newton's method: @@ -29,39 +29,39 @@ k₀ = (1 + 1/(1+1596)) × 1633 = (1 + 1/1597) × 1633 ≈ 1634.02 Newton's method: k_{n+1} = k_n - G(k_n)/G'(k_n); where -G(k) = T(k)³ × P(k) - α +G(k) = T(k)³ × P(k) - α
G'(k) = T²(k) × P(k) × [(3T'(k) × P(k) + T(k) × P'(k))/P(k)] And: -T'(k) = -r₁/(kr₁-1)² - r₂/(kr₂-1)² +T'(k) = -r₁/(kr₁-1)² - r₂/(kr₂-1)²
P'(k) = P(k) × [r₁/(kr₁-1) + r₂/(kr₂-1)] First iteration (k₀ = 1634.02) Calculate T(1634.02): -T = 1/(1634.02×0.000625-1) + 1/(1634.02×0.0006125-1) - 1 -T = 1/(1.0213-1) + 1/(1.0008-1) - 1 +T = 1/(1634.02×0.000625-1) + 1/(1634.02×0.0006125-1) - 1
+T = 1/(1.0213-1) + 1/(1.0008-1) - 1
T = 1/0.0213 + 1/0.0008 - 1 = 46.95 + 1250 - 1 ≈ 1295.95 Calculate P(1634.02): -P = (1634.02×0.000625-1) × (1634.02×0.0006125-1) +P = (1634.02×0.000625-1) × (1634.02×0.0006125-1)
P = 0.0213 × 0.0008 ≈ 0.000017 Calculate G(1634.02): the "error" -G = (1295.95)³ × 0.000017 - 1588.03 +G = (1295.95)³ × 0.000017 - 1588.03
G = 2.17×10⁹ × 0.000017 - 1588.03 ≈ 36,890 - 1588 ≈ 35,302 Calculate derivatives and find k₁: -T' = -0.000625/(0.0213)² - 0.0006125/(0.0008)² ≈ -1380 - 956 ≈ -2336 +T' = -0.000625/(0.0213)² - 0.0006125/(0.0008)² ≈ -1380 - 956 ≈ -2336
G' ≈ ... (complex calculation) ≈ 50.8 k₁ = 1634.02 - 35,302/50.8 ≈ 1634.02 - 694.9 ≈ 939.1 Continue iterations: -| Step | k̃_n | G(k̃_n) | k̃_{n+1} | +| Step | k̃ₙ | G(k̃ₙ) | k̃ₙ₊₁ | | ---- | ------- | ------ | ------- | | 0 | 1634.02 | 35,302 | 939.1 | | 1 | 939.1. | -285.4 | 1425.7 | @@ -69,7 +69,9 @@ Continue iterations: | 3 | 1580.3 | 124.7 | 1635.8 | | 4 | 1635.8 | 8.2 | 1640.1 | | 5 | 1640.1 | 0.1 | 1641.0 | -| 6 | 1641.0 | ~0 | 1641.0 | +| 6 | 1641.0 | ~0 | 1641.0 | + +Graphical representation of the T curve: ![Find the root](/images/BPTOracleIllustration.png) @@ -77,27 +79,27 @@ Step 4: Calculate T (using our found k̃ = 1641) Recall that T = 1/(k̃r₁ - 1) + 1/(k̃r₂ - 1) - 1 -T = 1/(1641 × 0.000625 - 1) + 1/(1641 × 0.0006125 - 1) - 1 -T = 1/(1.025625 - 1) + 1/(1.0051125 - 1) - 1 -T = 1/0.025625 + 1/0.0051125 - 1 +T = 1/(1641 × 0.000625 - 1) + 1/(1641 × 0.0006125 - 1) - 1
+T = 1/(1.025625 - 1) + 1/(1.0051125 - 1) - 1
+T = 1/0.025625 + 1/0.0051125 - 1
T = 39.02 + 195.60 - 1 = 233.62 Step 5: Calculate effective balances Recall that x₁ = (cD)/(k̃r₁ - 1) × T⁻¹ -x₁ = (0.9975 × 1000)/(1641 × 0.000625 - 1) × (1/233.62) +x₁ = (0.9975 × 1000)/(1641 × 0.000625 - 1) × (1/233.62)
x₁ = 997.5/0.025625 × (1/233.62) = 166.69 -x₂ = (cD)/(k̃r₂ - 1) × T⁻¹ -x₂ = (0.9975 × 1000)/(1641 × 0.0006125 - 1) × (1/233.62) +x₂ = (cD)/(k̃r₂ - 1) × T⁻¹
+x₂ = (0.9975 × 1000)/(1641 × 0.0006125 - 1) × (1/233.62)
x₂ = 997.5/0.0051125 × (1/233.62) = 833.31 Step 6: Calculate total pool value Recall that Pool Value = p₁ × x₁ + p₂ × x₂ -Pool Value = $1.00 × 166.69 + $0.98 × 833.31 +Pool Value = $1.00 × 166.69 + $0.98 × 833.31
Pool Value = $166.69 + $816.64 = $983.33 Step 7: Calculate BPT price @@ -105,4 +107,5 @@ Step 7: Calculate BPT price Recall that BPT Price = Pool Value / Total BPT Supply (If total BPT supply = 1000 tokens, since D = 1000, and starting prices were nominal at $1) + BPT Price = $983.33 / 1000 = $0.983 per BPT From 9f735806013f041c4fc459f6403c1d0a27c3096c Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Wed, 6 Aug 2025 00:14:51 -0400 Subject: [PATCH 11/15] more formatting --- .../core-concepts/bpt-oracles/bpt-oracles-example.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md index 0075dc2..a7f08c1 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-example.md @@ -26,8 +26,8 @@ Choose the starting point: k₀ = (1 + 1/(1+b)) × ρ k₀ = (1 + 1/(1+1596)) × 1633 = (1 + 1/1597) × 1633 ≈ 1634.02 -Newton's method: -k_{n+1} = k_n - G(k_n)/G'(k_n); where +Newton's method:
+kₙ₊₁ = kₙ − G(kₙ) / G′(kₙ); where G(k) = T(k)³ × P(k) - α
G'(k) = T²(k) × P(k) × [(3T'(k) × P(k) + T(k) × P'(k))/P(k)] @@ -37,6 +37,7 @@ T'(k) = -r₁/(kr₁-1)² - r₂/(kr₂-1)²
P'(k) = P(k) × [r₁/(kr₁-1) + r₂/(kr₂-1)] First iteration (k₀ = 1634.02) + Calculate T(1634.02): T = 1/(1634.02×0.000625-1) + 1/(1634.02×0.0006125-1) - 1
From 96d6747b4d5e0d4f9cd565862d84d8cbe3ac689d Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Thu, 7 Aug 2025 09:55:59 -0400 Subject: [PATCH 12/15] fix: discussion of roots and convergence --- docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md index 2dafa2f..b5ebb18 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md @@ -88,7 +88,7 @@ a = A·n^(2n);
b = a - n^n; and
c = b/a -Unfortunately this "T equation" is non-linear in k̃, so it must be solved numerically. On-chain, we use Newton's method to find the root (= the value of k̃ that satisfies both constraints). In the mathematical paper referenced below, we prove that when n is even (e.g.; in the most common case of 2-token pools), there is a single root. If n is odd, there are two roots, where the correct one is the smaller. +Unfortunately this "T equation" is non-linear in k̃, so it must be solved numerically. On-chain, we use Newton's method to find the root (= the value of k̃ that satisfies both constraints). In the mathematical paper referenced below, we prove that given the specified starting point, it will converge to the correct solution. There may be many roots, especially with higher numbers of tokens. The correct one is the smallest non-negative root, closest to the origin. In summary: From 29cf664329e67f9480f5084c00fe76b3814a153f Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Sat, 9 Aug 2025 20:46:13 -0400 Subject: [PATCH 13/15] docs: move stable-specific comments; add notes on usage with rate providers --- .../core-concepts/bpt-oracles/bpt-oracles.md | 26 ++++++++++++++----- 1 file changed, 19 insertions(+), 7 deletions(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md index b5ebb18..111e73f 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles.md @@ -27,17 +27,29 @@ Instead of using the actual balances to derive the overall price, Balancer BPT o * The "pool constraint": the theoretical balance invariant must equal the real balance invariant, so that the value of the pool is equivalent and can legitimately be scaled by the supply. * The "price constraint": the token prices derived from the theoretical balances must be proportional to the oracle prices, so that the internal token prices correctly reflect the current state of the market. -We begin with a system of n+1 equations: n "gradient" equations (relating the internal prices to the oracle prices), plus the invariant equation. So, that's n+1 equations with n unknowns: the theoretical token balances we are trying to find. We can linearize the gradient equations by introducing k̃, a sort of scaling factor that converts internal to external prices. Since by definition the prices are proportional, we can define k̃ as this constant of proportionality. +See [this page](./bpt-oracles-contracts.md) for references to the BPT Oracle contracts. -We can then solve this system of linear gradient equations, and express the theoretical balances xⱼ in terms of k̃. +## Usage with Rate Providers -Then the real magic happens - we can substitute those xⱼ expressions into the invariant equation, and reduce the system to a single equation in k̃. On chain, this equation can be solved using Newton's method. Once we have k̃, we can compute the theoretical balances, sum the product of each token balance and oracle price to get the total pool value, then divide by the total supply to derive the final BPT price. +In practical usage with different kinds of pools, there are some subtleties. For boosted pools, or other pools where tokens have rate providers, it's very important to choose a compatible price feed. There are several cases: -See [this page](./bpt-oracles-contracts.md) for references to the BPT Oracle contracts. +1) Regular tokens, no rate providers. This is the simplest case (e.g., BAL/WETH or WETH/USDC). We just need price feeds corresponding to the USD prices of ETH, BAL, and USDC. Of course, the price feeds could also have some other reference (e.g., EUR), as long as they are all consistent. + +2) Boosted pools with yield-bearing tokens (e.g., wstETH/USDC, or waWETH/waUSDC). Here we would typically have rate providers that converted the wrapped tokens to the underlying value tokens: wstETH -> ETH, waWETH -> ETH, waUSDC -> USDC. Since calculations use "live balances," which incorporate the rates, balances are always expressed in underlying tokens. Therefore, the price feeds should also correspond to the underlying tokens: ETH and USDC, in this case, same as in the "regular token" case above. + +3) Pools with double-wrapped tokens, such as waWstETH. What to use here depends on the details of the rate provider. Essentially, the price feed needs to match the target of the rate provider. If the rate provider itself converts waWstETH -> WETH, then the price feed should just be the regular underlying WETH/ETH price (since WETH is pegged 1-to-1 to ETH by definition). However, if the rate provider converts waWstETH -> wstETH, you would need a price feed for wstETH: not ETH. -## Derivation +4) Pools with RWA / commodity tokens, like XAUt. Here the rate provider is already effectively a price feed, converting XAUt -> USD directly. If you combined this rate provider with an XAUt price feed, it would do the conversion twice. So in this case, you would need a "constant price" price feed, that always returned 1. -The following applies to Stable Pools, using the StableSwap invariant equation. (See below for a discussion of the simpler weighted pools.) +## Mathematical Derivation + +### Stable Pools + +We begin with a system of n+1 equations: n "gradient" equations (relating the internal prices to the oracle prices), plus the invariant equation. So, that's n+1 equations with n unknowns: the theoretical token balances we are trying to find. We can linearize the gradient equations by introducing k̃, a sort of scaling factor that converts internal to external prices. Since by definition the prices are proportional, we can define k̃ as this constant of proportionality. + +We can then solve this system of linear gradient equations, and express the theoretical balances xⱼ in terms of k̃. + +Then the real magic happens - we can substitute those xⱼ expressions into the invariant equation, and reduce the system to a single equation in k̃. On chain, this equation can be solved using Newton's method. Once we have k̃, we can compute the theoretical balances, sum the product of each token balance and oracle price to get the total pool value, then divide by the total supply to derive the final BPT price. With x̃ representing the vector of theoretical token balances, the pool constraint can be expressed mathematically as: @@ -100,7 +112,7 @@ In summary: See [this page](./bpt-oracles-example.md) for a numerical example. -## Weighted Pools +### Weighted Pools Weighted and Stable Pools use the same general algorithm. While the complex StableSwap invariant requires Newton's method to find the scaling parameter k̃, then calculate effective balances and total value, the power-law invariant of the Weighted Pool allows us to solve the gradient and invariant conditions simultaneously, giving us: From 954dc369b629a1d436910e5a35c3027aa189c80e Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Thu, 21 Aug 2025 16:42:10 -0400 Subject: [PATCH 14/15] Add note explaining that the given feeds must match the pool tokens. See audit issue L-05. --- .../concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md index 4298da8..69a5fbf 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md @@ -14,7 +14,7 @@ Oracles are created from the corresponding pool factories using the create funct `function create(IBasePool pool, AggregatorV3Interface[] memory feeds) external returns (ILPOracleBase oracle);` -`AggregatorV3Interface` is a Chainlink price feed. +`AggregatorV3Interface` is a Chainlink price feed. Note that this assumes the feed array is parallel to the pool tokens; i.e., the feed at each position is the correct one for the corresponding pool token. There is no way for the code to check this, so responsibility falls on the caller to ensure that this is the case. See the [Usage with Rate Providers](./bpt-oracles.md#usage-with-rate-providers) section for further considerations. This first computes an "OracleID" as the hash of the pool and price feed addresses. Since the tokens must be ordered, we know the price feed addresses will also be in the same order, so a given combination of the pool and price feeds is guaranteed unique. It then calls an internal `_create` (implemented by derived contracts) to deploy the oracle with the given configuration, and registers it with the factory. From 1f20d8a51bcfffc3ce0a217e0c2d03bb4e5a6a33 Mon Sep 17 00:00:00 2001 From: Jeff Bennett Date: Fri, 22 Aug 2025 10:52:27 -0400 Subject: [PATCH 15/15] Add comment about correcting oracle creation mistakes --- .../concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md index 69a5fbf..5a879c7 100644 --- a/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md +++ b/docs/concepts/core-concepts/bpt-oracles/bpt-oracles-contracts.md @@ -14,7 +14,7 @@ Oracles are created from the corresponding pool factories using the create funct `function create(IBasePool pool, AggregatorV3Interface[] memory feeds) external returns (ILPOracleBase oracle);` -`AggregatorV3Interface` is a Chainlink price feed. Note that this assumes the feed array is parallel to the pool tokens; i.e., the feed at each position is the correct one for the corresponding pool token. There is no way for the code to check this, so responsibility falls on the caller to ensure that this is the case. See the [Usage with Rate Providers](./bpt-oracles.md#usage-with-rate-providers) section for further considerations. +`AggregatorV3Interface` is a Chainlink price feed. Note that this assumes the feed array is parallel to the pool tokens; i.e., the feed at each position is the correct one for the corresponding pool token. There is no way for the code to check this, so responsibility falls on the caller to ensure that this is the case. See the [Usage with Rate Providers](./bpt-oracles.md#usage-with-rate-providers) section for further considerations. Note that there are no restrictions in the factories that limit oracle creation, so any mistakes can be remedied by simply calling create again with correct values. This first computes an "OracleID" as the hash of the pool and price feed addresses. Since the tokens must be ordered, we know the price feed addresses will also be in the same order, so a given combination of the pool and price feeds is guaranteed unique. It then calls an internal `_create` (implemented by derived contracts) to deploy the oracle with the given configuration, and registers it with the factory.