From 60ab139a6ae6b6262159971d08f8d447f1423eb3 Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Fri, 8 Sep 2023 15:04:53 -0500
Subject: [PATCH 01/11] Make rewardToken mutable to prepare for governance

---
 core/.gas-snapshot                         | 30 +++++++++++-----------
 core/src/Factory.sol                       | 12 ++++-----
 core/src/Ledger.sol                        |  2 +-
 core/src/libraries/constants/Constants.sol |  2 +-
 4 files changed, 23 insertions(+), 23 deletions(-)

diff --git a/core/.gas-snapshot b/core/.gas-snapshot
index 060b0c47..13f24b28 100644
--- a/core/.gas-snapshot
+++ b/core/.gas-snapshot
@@ -1,26 +1,26 @@
 BorrowerGasTest:test_addMargin() (gas: 16203)
-BorrowerGasTest:test_borrow() (gas: 110492)
+BorrowerGasTest:test_borrow() (gas: 110489)
 BorrowerGasTest:test_getUniswapPositions() (gas: 5219)
-BorrowerGasTest:test_modify() (gas: 82111)
-BorrowerGasTest:test_modifyWithAnte() (gas: 88566)
-BorrowerGasTest:test_repay() (gas: 111851)
-BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257726)
+BorrowerGasTest:test_modify() (gas: 82108)
+BorrowerGasTest:test_modifyWithAnte() (gas: 88563)
+BorrowerGasTest:test_repay() (gas: 111848)
+BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257723)
 BorrowerGasTest:test_uniswapDepositStandard() (gas: 167558)
-BorrowerGasTest:test_uniswapWithdraw() (gas: 147623)
-BorrowerGasTest:test_withdraw() (gas: 105631)
-FactoryGasTest:test_createBorrower() (gas: 156437)
-FactoryGasTest:test_createMarket() (gas: 3900597)
+BorrowerGasTest:test_uniswapWithdraw() (gas: 147620)
+BorrowerGasTest:test_withdraw() (gas: 105628)
+FactoryGasTest:test_createBorrower() (gas: 156431)
+FactoryGasTest:test_createMarket() (gas: 3900591)
 LenderGasTest:test_accrueInterest() (gas: 46287)
 LenderGasTest:test_borrow() (gas: 40812)
 LenderGasTest:test_deposit() (gas: 53639)
 LenderGasTest:test_depositWithCourier() (gas: 53785)
 LenderGasTest:test_redeem() (gas: 53334)
-LenderGasTest:test_redeemWithCourier() (gas: 83730)
+LenderGasTest:test_redeemWithCourier() (gas: 83726)
 LenderGasTest:test_repay() (gas: 44752)
-LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51020)
-LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59179)
-LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95598)
-LiquidatorGasTest:test_warn() (gas: 35026)
-LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130185)
+LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51017)
+LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59176)
+LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95596)
+LiquidatorGasTest:test_warn() (gas: 35023)
+LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130182)
 VolatilityGasTest:test_consult() (gas: 43075)
 VolatilityGasTest:test_updateNoBinarySearch() (gas: 145880)
\ No newline at end of file
diff --git a/core/src/Factory.sol b/core/src/Factory.sol
index ac00a399..14669fe8 100644
--- a/core/src/Factory.sol
+++ b/core/src/Factory.sol
@@ -47,10 +47,10 @@ contract Factory {
 
     IRateModel public immutable RATE_MODEL;
 
-    ERC20 public immutable REWARDS_TOKEN;
-
     address public immutable LENDER_IMPLEMENTATION;
 
+    ERC20 public rewardsToken;
+
     /*//////////////////////////////////////////////////////////////
                              WORLD STORAGE
     //////////////////////////////////////////////////////////////*/
@@ -80,12 +80,12 @@ contract Factory {
                               CONSTRUCTOR
     //////////////////////////////////////////////////////////////*/
 
-    constructor(VolatilityOracle oracle, IRateModel rateModel, ERC20 rewardsToken) {
+    constructor(VolatilityOracle oracle, IRateModel rateModel, ERC20 rewardsToken_) {
         ORACLE = oracle;
         RATE_MODEL = rateModel;
-        REWARDS_TOKEN = rewardsToken;
-
         LENDER_IMPLEMENTATION = address(new Lender(address(this)));
+
+        rewardsToken = rewardsToken_;
     }
 
     function pause(IUniswapV3Pool pool) external {
@@ -178,6 +178,6 @@ contract Factory {
             }
         }
 
-        REWARDS_TOKEN.safeTransfer(beneficiary, earned);
+        rewardsToken.safeTransfer(beneficiary, earned);
     }
 }
diff --git a/core/src/Ledger.sol b/core/src/Ledger.sol
index da702a31..be6cd333 100644
--- a/core/src/Ledger.sol
+++ b/core/src/Ledger.sol
@@ -300,7 +300,7 @@ contract Ledger {
      * @return The maximum amount of `asset()` that can be withdrawn
      */
     function maxWithdraw(address owner) external view returns (uint256) {
-        return convertToAssets(this.maxRedeem(owner));
+        return convertToAssets(maxRedeem(owner));
     }
 
     /*//////////////////////////////////////////////////////////////
diff --git a/core/src/libraries/constants/Constants.sol b/core/src/libraries/constants/Constants.sol
index 3d2938eb..80e45f5a 100644
--- a/core/src/libraries/constants/Constants.sol
+++ b/core/src/libraries/constants/Constants.sol
@@ -29,7 +29,7 @@ uint256 constant MAX_RATE = 706354;
 
 /// @dev The default amount of Ether required to take on debt in a `Borrower`. The `Factory` can override this value
 /// on a per-market basis.
-uint216 constant DEFAULT_ANTE = 0.1 ether;
+uint216 constant DEFAULT_ANTE = 0.01 ether;
 
 /// @dev The default number of standard deviations of price movement used to determine probe prices for `Borrower`
 /// solvency. The `Factory` can override this value on a per-market basis.

From e87383b2a9e08dbcafb65f578a6127e13ba6a949 Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Fri, 8 Sep 2023 16:21:33 -0500
Subject: [PATCH 02/11] layout

---
 core/.storage-layout.md | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/core/.storage-layout.md b/core/.storage-layout.md
index 0ebcc522..e4bcd4b0 100644
--- a/core/.storage-layout.md
+++ b/core/.storage-layout.md
@@ -24,10 +24,11 @@ forge inspect --pretty src/Borrower.sol:Borrower storage-layout
 forge inspect --pretty src/Factory.sol:Factory storage-layout
 | Name          | Type                                                          | Slot | Offset | Bytes | Contract                |
 |---------------|---------------------------------------------------------------|------|--------|-------|-------------------------|
-| getMarket     | mapping(contract IUniswapV3Pool => struct Factory.Market)     | 0    | 0      | 32    | src/Factory.sol:Factory |
-| getParameters | mapping(contract IUniswapV3Pool => struct Factory.Parameters) | 1    | 0      | 32    | src/Factory.sol:Factory |
-| isLender      | mapping(address => bool)                                      | 2    | 0      | 32    | src/Factory.sol:Factory |
-| isBorrower    | mapping(address => bool)                                      | 3    | 0      | 32    | src/Factory.sol:Factory |
-| couriers      | mapping(uint32 => struct Factory.Courier)                     | 4    | 0      | 32    | src/Factory.sol:Factory |
-| isCourier     | mapping(address => bool)                                      | 5    | 0      | 32    | src/Factory.sol:Factory |
+| rewardsToken  | contract ERC20                                                | 0    | 0      | 20    | src/Factory.sol:Factory |
+| getMarket     | mapping(contract IUniswapV3Pool => struct Factory.Market)     | 1    | 0      | 32    | src/Factory.sol:Factory |
+| getParameters | mapping(contract IUniswapV3Pool => struct Factory.Parameters) | 2    | 0      | 32    | src/Factory.sol:Factory |
+| isLender      | mapping(address => bool)                                      | 3    | 0      | 32    | src/Factory.sol:Factory |
+| isBorrower    | mapping(address => bool)                                      | 4    | 0      | 32    | src/Factory.sol:Factory |
+| couriers      | mapping(uint32 => struct Factory.Courier)                     | 5    | 0      | 32    | src/Factory.sol:Factory |
+| isCourier     | mapping(address => bool)                                      | 6    | 0      | 32    | src/Factory.sol:Factory |
 

From c568b4e2ead3d104a7a499e3cb79c6c430cc18df Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Fri, 8 Sep 2023 21:11:18 -0500
Subject: [PATCH 03/11] Add governance methods in Factory

---
 core/.gas-snapshot                           | 42 ++++-----
 core/script/Deploy.s.sol                     | 18 +++-
 core/src/Factory.sol                         | 98 +++++++++++++++++---
 core/src/Ledger.sol                          |  5 +
 core/src/Lender.sol                          | 23 +++--
 core/src/libraries/Rewards.sol               |  2 +-
 core/src/libraries/constants/Constants.sol   | 22 ++++-
 core/test/Borrower.t.sol                     |  5 +-
 core/test/Liquidator.t.sol                   |  5 +-
 core/test/Utils.sol                          |  9 +-
 core/test/gas/BorrowerGas.t.sol              |  5 +-
 core/test/gas/FactoryGas.t.sol               |  7 +-
 core/test/gas/LiquidatorGas.t.sol            |  5 +-
 core/test/invariants/ERC4626Invariants.t.sol |  3 +-
 14 files changed, 184 insertions(+), 65 deletions(-)

diff --git a/core/.gas-snapshot b/core/.gas-snapshot
index 13f24b28..68f8f045 100644
--- a/core/.gas-snapshot
+++ b/core/.gas-snapshot
@@ -1,26 +1,26 @@
 BorrowerGasTest:test_addMargin() (gas: 16203)
-BorrowerGasTest:test_borrow() (gas: 110489)
+BorrowerGasTest:test_borrow() (gas: 110555)
 BorrowerGasTest:test_getUniswapPositions() (gas: 5219)
-BorrowerGasTest:test_modify() (gas: 82108)
-BorrowerGasTest:test_modifyWithAnte() (gas: 88563)
-BorrowerGasTest:test_repay() (gas: 111848)
-BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257723)
+BorrowerGasTest:test_modify() (gas: 82152)
+BorrowerGasTest:test_modifyWithAnte() (gas: 88607)
+BorrowerGasTest:test_repay() (gas: 111914)
+BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257767)
 BorrowerGasTest:test_uniswapDepositStandard() (gas: 167558)
-BorrowerGasTest:test_uniswapWithdraw() (gas: 147620)
-BorrowerGasTest:test_withdraw() (gas: 105628)
-FactoryGasTest:test_createBorrower() (gas: 156431)
-FactoryGasTest:test_createMarket() (gas: 3900591)
-LenderGasTest:test_accrueInterest() (gas: 46287)
-LenderGasTest:test_borrow() (gas: 40812)
-LenderGasTest:test_deposit() (gas: 53639)
-LenderGasTest:test_depositWithCourier() (gas: 53785)
-LenderGasTest:test_redeem() (gas: 53334)
-LenderGasTest:test_redeemWithCourier() (gas: 83726)
-LenderGasTest:test_repay() (gas: 44752)
-LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51017)
-LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59176)
-LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95596)
-LiquidatorGasTest:test_warn() (gas: 35023)
-LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130182)
+BorrowerGasTest:test_uniswapWithdraw() (gas: 147656)
+BorrowerGasTest:test_withdraw() (gas: 105672)
+FactoryGasTest:test_createBorrower() (gas: 156519)
+FactoryGasTest:test_createMarket() (gas: 3905006)
+LenderGasTest:test_accrueInterest() (gas: 46070)
+LenderGasTest:test_borrow() (gas: 40834)
+LenderGasTest:test_deposit() (gas: 53422)
+LenderGasTest:test_depositWithCourier() (gas: 53568)
+LenderGasTest:test_redeem() (gas: 53114)
+LenderGasTest:test_redeemWithCourier() (gas: 83506)
+LenderGasTest:test_repay() (gas: 44774)
+LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51083)
+LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59264)
+LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95666)
+LiquidatorGasTest:test_warn() (gas: 35067)
+LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130248)
 VolatilityGasTest:test_consult() (gas: 43075)
 VolatilityGasTest:test_updateNoBinarySearch() (gas: 145880)
\ No newline at end of file
diff --git a/core/script/Deploy.s.sol b/core/script/Deploy.s.sol
index 44354a62..6f4afe22 100644
--- a/core/script/Deploy.s.sol
+++ b/core/script/Deploy.s.sol
@@ -3,19 +3,27 @@ pragma solidity 0.8.17;
 
 import "forge-std/Script.sol";
 
-import {Factory, ERC20} from "../src/Factory.sol";
-import {RateModel} from "../src/RateModel.sol";
-import {VolatilityOracle} from "../src/VolatilityOracle.sol";
+import {Factory, ERC20} from "src/Factory.sol";
+import {Lender} from "src/Lender.sol";
+import {RateModel} from "src/RateModel.sol";
+import {VolatilityOracle} from "src/VolatilityOracle.sol";
 
 bytes32 constant TAG = bytes32(uint256(0xA10EBE1A));
+address constant GOVERNOR = address(0);
+address constant RESERVE = address(0);
 
 contract DeployScript is Script {
     function run() external {
         vm.startBroadcast(vm.envUint("PRIVATE_KEY"));
 
         VolatilityOracle oracle = new VolatilityOracle{salt: TAG}();
-        RateModel rateModel = new RateModel{salt: TAG}();  
-        /*Factory factory =*/ new Factory{salt: TAG}(oracle, rateModel, ERC20(address(0)));
+        RateModel rateModel = new RateModel{salt: TAG}();
+        /*Factory factory =*/ new Factory{salt: TAG}({
+            governor: GOVERNOR,
+            reserve: RESERVE,
+            oracle: oracle,
+            defaultRateModel: rateModel
+        });
 
         vm.stopBroadcast();
     }
diff --git a/core/src/Factory.sol b/core/src/Factory.sol
index 14669fe8..f06de0dc 100644
--- a/core/src/Factory.sol
+++ b/core/src/Factory.sol
@@ -10,6 +10,12 @@ import {
     DEFAULT_ANTE,
     DEFAULT_N_SIGMA,
     DEFAULT_RESERVE_FACTOR,
+    CONSTRAINT_N_SIGMA_MIN,
+    CONSTRAINT_N_SIGMA_MAX,
+    CONSTRAINT_RESERVE_FACTOR_MIN,
+    CONSTRAINT_RESERVE_FACTOR_MAX,
+    CONSTRAINT_ANTE_MAX,
+    CONSTRAINT_PAUSE_INTERVAL_MAX,
     UNISWAP_AVG_WINDOW
 } from "./libraries/constants/Constants.sol";
 
@@ -43,12 +49,22 @@ contract Factory {
         uint32 pausedUntilTime;
     }
 
-    VolatilityOracle public immutable ORACLE;
+    struct MarketConfig {
+        Parameters parameters;
+        IRateModel rateModel0;
+        IRateModel rateModel1;
+        uint8 reserveFactor0;
+        uint8 reserveFactor1;
+    }
 
-    IRateModel public immutable RATE_MODEL;
+    address public immutable GOVERNOR;
+
+    VolatilityOracle public immutable ORACLE;
 
     address public immutable LENDER_IMPLEMENTATION;
 
+    IRateModel public immutable DEFAULT_RATE_MODEL;
+
     ERC20 public rewardsToken;
 
     /*//////////////////////////////////////////////////////////////
@@ -80,12 +96,11 @@ contract Factory {
                               CONSTRUCTOR
     //////////////////////////////////////////////////////////////*/
 
-    constructor(VolatilityOracle oracle, IRateModel rateModel, ERC20 rewardsToken_) {
+    constructor(address governor, address reserve, VolatilityOracle oracle, IRateModel defaultRateModel) {
+        GOVERNOR = governor;
         ORACLE = oracle;
-        RATE_MODEL = rateModel;
-        LENDER_IMPLEMENTATION = address(new Lender(address(this)));
-
-        rewardsToken = rewardsToken_;
+        LENDER_IMPLEMENTATION = address(new Lender(reserve));
+        DEFAULT_RATE_MODEL = defaultRateModel;
     }
 
     function pause(IUniswapV3Pool pool) external {
@@ -96,7 +111,7 @@ contract Factory {
     }
 
     /*//////////////////////////////////////////////////////////////
-                             WORLD CREATION
+                            WORLD MANAGEMENT
     //////////////////////////////////////////////////////////////*/
 
     function createMarket(IUniswapV3Pool pool) external {
@@ -105,19 +120,31 @@ contract Factory {
         address asset0 = pool.token0();
         address asset1 = pool.token1();
 
+        // Deploy market-specific components
         bytes32 salt = keccak256(abi.encodePacked(pool));
         Lender lender0 = Lender(LENDER_IMPLEMENTATION.cloneDeterministic({salt: salt, data: abi.encodePacked(asset0)}));
         Lender lender1 = Lender(LENDER_IMPLEMENTATION.cloneDeterministic({salt: salt, data: abi.encodePacked(asset1)}));
+        Borrower borrowerImplementation = new Borrower(ORACLE, pool, lender0, lender1);
 
-        lender0.initialize(RATE_MODEL, DEFAULT_RESERVE_FACTOR);
-        lender1.initialize(RATE_MODEL, DEFAULT_RESERVE_FACTOR);
+        // Store deployment addresses
+        getMarket[pool] = Market(lender0, lender1, borrowerImplementation);
         isLender[address(lender0)] = true;
         isLender[address(lender1)] = true;
 
-        Borrower borrowerImplementation = new Borrower(ORACLE, pool, lender0, lender1);
+        // Initialize lenders and set default market config
+        lender0.initialize();
+        lender1.initialize();
+        _setMarketConfig(
+            pool,
+            MarketConfig(
+                Parameters(DEFAULT_ANTE, DEFAULT_N_SIGMA, 0),
+                DEFAULT_RATE_MODEL,
+                DEFAULT_RATE_MODEL,
+                DEFAULT_RESERVE_FACTOR,
+                DEFAULT_RESERVE_FACTOR
+            )
+        );
 
-        getMarket[pool] = Market(lender0, lender1, borrowerImplementation);
-        getParameters[pool] = Parameters(DEFAULT_ANTE, DEFAULT_N_SIGMA, 0);
         emit CreateMarket(pool, lender0, lender1);
     }
 
@@ -180,4 +207,49 @@ contract Factory {
 
         rewardsToken.safeTransfer(beneficiary, earned);
     }
+
+    /*//////////////////////////////////////////////////////////////
+                               GOVERNANCE
+    //////////////////////////////////////////////////////////////*/
+
+    function governRewardsToken(ERC20 rewardsToken_) external {
+        require(msg.sender == GOVERNOR && address(rewardsToken) == address(0));
+        rewardsToken = rewardsToken_;
+    }
+
+    function governRewardsRate(Lender lender, uint56 rate) external {
+        require(msg.sender == GOVERNOR);
+        lender.setRewardsRate(rate);
+    }
+
+    function governMarketConfig(IUniswapV3Pool pool, MarketConfig memory marketConfig) external {
+        require(msg.sender == GOVERNOR);
+
+        require(
+            // nSigma: min, max
+            (CONSTRAINT_N_SIGMA_MIN <= marketConfig.parameters.nSigma &&
+                marketConfig.parameters.nSigma <= CONSTRAINT_N_SIGMA_MAX) &&
+                // ante: max
+                (marketConfig.parameters.ante <= CONSTRAINT_ANTE_MAX) &&
+                // pauseUntilTime: max
+                (marketConfig.parameters.pausedUntilTime <= block.timestamp + CONSTRAINT_PAUSE_INTERVAL_MAX) &&
+                // reserveFactor0: min, max
+                (CONSTRAINT_RESERVE_FACTOR_MIN <= marketConfig.reserveFactor0 &&
+                    marketConfig.reserveFactor0 <= CONSTRAINT_RESERVE_FACTOR_MAX) &&
+                // reserveFactor1: min, max
+                (CONSTRAINT_RESERVE_FACTOR_MIN <= marketConfig.reserveFactor1 &&
+                    marketConfig.reserveFactor1 <= CONSTRAINT_RESERVE_FACTOR_MAX),
+            "Aloe: constraints"
+        );
+
+        _setMarketConfig(pool, marketConfig);
+    }
+
+    function _setMarketConfig(IUniswapV3Pool pool, MarketConfig memory marketConfig) private {
+        getParameters[pool] = marketConfig.parameters;
+
+        Market memory market = getMarket[pool];
+        market.lender0.setRateModelAndReserveFactor(marketConfig.rateModel0, marketConfig.reserveFactor0);
+        market.lender1.setRateModelAndReserveFactor(marketConfig.rateModel1, marketConfig.reserveFactor1);
+    }
 }
diff --git a/core/src/Ledger.sol b/core/src/Ledger.sol
index be6cd333..3b6d7a6c 100644
--- a/core/src/Ledger.sol
+++ b/core/src/Ledger.sol
@@ -76,8 +76,13 @@ contract Ledger {
                          GOVERNABLE PARAMETERS
     //////////////////////////////////////////////////////////////*/
 
+    /**
+     * @dev `rateModel.getYieldPerSecond` is given 100000 gas, and the output is clamped to `MAX_RATE`. If
+     * the call reverts, it's treated the same as if it returned 0.
+     */
     IRateModel public rateModel;
 
+    /// @dev The portion of interest that accrues to the `RESERVE`. Expressed as a reciprocal, e.g. 16 → 6.25%
     uint8 public reserveFactor;
 
     /*//////////////////////////////////////////////////////////////
diff --git a/core/src/Lender.sol b/core/src/Lender.sol
index 5501ba33..effdaf47 100644
--- a/core/src/Lender.sol
+++ b/core/src/Lender.sol
@@ -5,7 +5,7 @@ import {FixedPointMathLib} from "solmate/utils/FixedPointMathLib.sol";
 import {ERC20, SafeTransferLib} from "solmate/utils/SafeTransferLib.sol";
 import {SafeCastLib} from "solmate/utils/SafeCastLib.sol";
 
-import {BORROWS_SCALER, ONE, MIN_RESERVE_FACTOR, MAX_RESERVE_FACTOR} from "./libraries/constants/Constants.sol";
+import {BORROWS_SCALER, ONE} from "./libraries/constants/Constants.sol";
 import {Q112} from "./libraries/constants/Q.sol";
 import {Rewards} from "./libraries/Rewards.sol";
 
@@ -50,23 +50,32 @@ contract Lender is Ledger {
 
     constructor(address reserve) Ledger(reserve) {}
 
-    function initialize(IRateModel rateModel_, uint8 reserveFactor_) external {
+    function initialize() external {
         require(borrowIndex == 0);
         borrowIndex = uint72(ONE);
         lastAccrualTime = uint32(block.timestamp);
 
         initialDomainSeparator = _computeDomainSeparator();
         initialChainId = block.chainid;
+    }
 
+    /// @notice Sets the `rateModel` and `reserveFactor`. Only the `FACTORY` can call this.
+    function setRateModelAndReserveFactor(IRateModel rateModel_, uint8 reserveFactor_) external {
+        require(msg.sender == address(FACTORY));
         rateModel = rateModel_;
-        require(MIN_RESERVE_FACTOR <= reserveFactor_ && reserveFactor_ <= MAX_RESERVE_FACTOR);
         reserveFactor = reserveFactor_;
     }
 
-    // TODO: governance-only functions for:
-    // - depositing/withdrawing the rewards token
-    // - setting the rewards rate
-    // - setting reserve factor and rate model
+    /**
+     * @notice Sets the rewards rate. May be 0. Only the `FACTORY` can call this.
+     * @param rate The rewards rate, specified in [token units per second]. If non-zero, keep between 10^19 and
+     * 10^24 token units per year for smooth operation. Assuming `FACTORY.rewardsToken()` has 18 decimals, this is
+     * between 10 and 1 million tokens per year.
+     */
+    function setRewardsRate(uint56 rate) external {
+        require(msg.sender == address(FACTORY));
+        Rewards.setRate(rate);
+    }
 
     function whitelist(address borrower) external {
         // Requirements:
diff --git a/core/src/libraries/Rewards.sol b/core/src/libraries/Rewards.sol
index c12da8fb..d33dfcb0 100644
--- a/core/src/libraries/Rewards.sol
+++ b/core/src/libraries/Rewards.sol
@@ -38,7 +38,7 @@ library Rewards {
     }
 
     /**
-     * @notice Sets the pool's reward rate. May be 0.
+     * @notice Sets the pool's rewards rate. May be 0.
      * @param rate The rewards rate, specified as [token units per second]. Keep between 10^19 and 10^24
      * token units per year for smooth operation -- between 10 and 1 million tokens, assuming 18 decimals.
      */
diff --git a/core/src/libraries/constants/Constants.sol b/core/src/libraries/constants/Constants.sol
index 80e45f5a..193c7977 100644
--- a/core/src/libraries/constants/Constants.sol
+++ b/core/src/libraries/constants/Constants.sol
@@ -36,18 +36,30 @@ uint216 constant DEFAULT_ANTE = 0.01 ether;
 uint8 constant DEFAULT_N_SIGMA = 5;
 
 /// @dev The default portion of interest that will accrue to a `Lender`'s `RESERVE` address.
-/// Expressed as a reciprocal, e.g. 8 → 12.5%
-uint8 constant DEFAULT_RESERVE_FACTOR = 8;
+/// Expressed as a reciprocal, e.g. 16 → 6.25%
+uint8 constant DEFAULT_RESERVE_FACTOR = 16;
 
 /*//////////////////////////////////////////////////////////////
-                        GOVERNANCE BOUNDS
+                        GOVERNANCE CONSTRAINTS
 //////////////////////////////////////////////////////////////*/
 
+/// @dev The lowest number of standard deviations of price movement allowed for determining `Borrower` probe prices
+uint8 constant CONSTRAINT_N_SIGMA_MIN = 4;
+
+/// @dev The highest number of standard deviations of price movement allowed for determining `Borrower` probe prices
+uint8 constant CONSTRAINT_N_SIGMA_MAX = 5;
+
 /// @dev The lower bound on what any `Lender`'s reserve factor can be. Expressed as reciprocal, e.g. 4 → 25%
-uint256 constant MIN_RESERVE_FACTOR = 4;
+uint8 constant CONSTRAINT_RESERVE_FACTOR_MIN = 4;
 
 /// @dev The upper bound on what any `Lender`'s reserve factor can be. Expressed as reciprocal, e.g. 20 → 5%
-uint256 constant MAX_RESERVE_FACTOR = 20;
+uint8 constant CONSTRAINT_RESERVE_FACTOR_MAX = 20;
+
+/// @dev The maximum amount of Ether that `Borrower`s can be required to post before taking on debt
+uint216 constant CONSTRAINT_ANTE_MAX = 0.1 ether;
+
+/// @dev The maximum uninterrupted amount of time for which borrowing can be paused by governance
+uint32 constant CONSTRAINT_PAUSE_INTERVAL_MAX = 2 days;
 
 /*//////////////////////////////////////////////////////////////
                             LIQUIDATION
diff --git a/core/test/Borrower.t.sol b/core/test/Borrower.t.sol
index 2a9ad6c2..baa5d856 100644
--- a/core/test/Borrower.t.sol
+++ b/core/test/Borrower.t.sol
@@ -50,9 +50,10 @@ contract BorrowerTest is Test, IManager {
         vm.rollFork(15_348_451);
 
         Factory factory = new Factory(
+            address(0),
+            address(0),
             VolatilityOracle(address(new VolatilityOracleMock())),
-            new RateModel(),
-            ERC20(address(0))
+            new RateModel()
         );
 
         factory.createMarket(pool);
diff --git a/core/test/Liquidator.t.sol b/core/test/Liquidator.t.sol
index d8186026..3847454f 100644
--- a/core/test/Liquidator.t.sol
+++ b/core/test/Liquidator.t.sol
@@ -28,9 +28,10 @@ contract LiquidatorTest is Test, IManager, ILiquidator {
         vm.rollFork(15_348_451);
 
         Factory factory = new Factory(
+            address(0),
+            address(0),
             VolatilityOracle(address(new VolatilityOracleMock())),
-            new RateModel(),
-            ERC20(address(0))
+            new RateModel()
         );
 
         factory.createMarket(pool);
diff --git a/core/test/Utils.sol b/core/test/Utils.sol
index a7a66cbf..9caf5669 100644
--- a/core/test/Utils.sol
+++ b/core/test/Utils.sol
@@ -22,13 +22,16 @@ function deploySingleBorrower(IUniswapV3Pool pool, Lender lender0, Lender lender
 contract FactoryForLenderTests is Factory {
     constructor(
         RateModel rateModel,
-        ERC20 rewardsToken
-    ) Factory(VolatilityOracle(address(0)), rateModel, rewardsToken) {}
+        ERC20 rewardsToken_
+    ) Factory(address(0), address(this), VolatilityOracle(address(0)), rateModel) {
+        rewardsToken = rewardsToken_;
+    }
 
     function deploySingleLender(ERC20 asset) external returns (Lender) {
         address proxy = ClonesWithImmutableArgs.clone(LENDER_IMPLEMENTATION, abi.encodePacked(address(asset)));
 
-        Lender(proxy).initialize(RATE_MODEL, 8);
+        Lender(proxy).initialize();
+        Lender(proxy).setRateModelAndReserveFactor(DEFAULT_RATE_MODEL, 8);
         return Lender(proxy);
     }
 }
diff --git a/core/test/gas/BorrowerGas.t.sol b/core/test/gas/BorrowerGas.t.sol
index 88b2a8f0..c2f7c26d 100644
--- a/core/test/gas/BorrowerGas.t.sol
+++ b/core/test/gas/BorrowerGas.t.sol
@@ -28,9 +28,10 @@ contract BorrowerGasTest is Test, IManager {
         vm.rollFork(15_348_451);
 
         Factory factory = new Factory(
+            address(0),
+            address(0),
             VolatilityOracle(address(new VolatilityOracleMock())),
-            new RateModel(),
-            ERC20(address(0))
+            new RateModel()
         );
 
         factory.createMarket(pool);
diff --git a/core/test/gas/FactoryGas.t.sol b/core/test/gas/FactoryGas.t.sol
index fa58e7db..62298634 100644
--- a/core/test/gas/FactoryGas.t.sol
+++ b/core/test/gas/FactoryGas.t.sol
@@ -17,7 +17,12 @@ contract FactoryGasTest is Test {
         vm.createSelectFork(vm.rpcUrl("mainnet"));
         vm.rollFork(15_348_451);
 
-        factory = new Factory(new VolatilityOracle(), new RateModel(), ERC20(address(0)));
+        factory = new Factory(
+            address(0),
+            address(0),
+            new VolatilityOracle(),
+            new RateModel()
+        );
     }
 
     function setUp() public {
diff --git a/core/test/gas/LiquidatorGas.t.sol b/core/test/gas/LiquidatorGas.t.sol
index 2cb95b25..b9abf5e3 100644
--- a/core/test/gas/LiquidatorGas.t.sol
+++ b/core/test/gas/LiquidatorGas.t.sol
@@ -28,9 +28,10 @@ contract LiquidatorGasTest is Test, IManager, ILiquidator {
         vm.rollFork(15_348_451);
 
         Factory factory = new Factory(
+            address(0),
+            address(0),
             VolatilityOracle(address(new VolatilityOracleMock())),
-            new RateModel(),
-            ERC20(address(0))
+            new RateModel()
         );
 
         factory.createMarket(pool);
diff --git a/core/test/invariants/ERC4626Invariants.t.sol b/core/test/invariants/ERC4626Invariants.t.sol
index d705247b..fee0e66d 100644
--- a/core/test/invariants/ERC4626Invariants.t.sol
+++ b/core/test/invariants/ERC4626Invariants.t.sol
@@ -39,7 +39,8 @@ contract ERC4626InvariantsTest is Test {
                 abi.encodePacked(address(asset))
             ));
             RateModel rateModel = new RateModel();
-            lender.initialize(rateModel, 8); // TODO: replace 8 with an env var
+            lender.initialize();
+            lender.setRateModelAndReserveFactor(rateModel, 8); // TODO: replace 8 with an env var
 
             vault = ERC4626(address(lender));
             vaultHarness = new ERC4626Harness(lender);

From e7cacbf38d961b524add6e38b367aa06512b472e Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Fri, 8 Sep 2023 21:13:49 -0500
Subject: [PATCH 04/11] Tweak

---
 core/src/Factory.sol | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/core/src/Factory.sol b/core/src/Factory.sol
index f06de0dc..a74c266a 100644
--- a/core/src/Factory.sol
+++ b/core/src/Factory.sol
@@ -111,7 +111,7 @@ contract Factory {
     }
 
     /*//////////////////////////////////////////////////////////////
-                            WORLD MANAGEMENT
+                             WORLD CREATION
     //////////////////////////////////////////////////////////////*/
 
     function createMarket(IUniswapV3Pool pool) external {

From deb6700dd7bff1cee23201a23a286339581e7b68 Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Sat, 9 Sep 2023 23:08:25 -0500
Subject: [PATCH 05/11] gs

---
 core/.gas-snapshot | 44 ++++++++++++++++++++++----------------------
 1 file changed, 22 insertions(+), 22 deletions(-)

diff --git a/core/.gas-snapshot b/core/.gas-snapshot
index 68f8f045..04bb3a5d 100644
--- a/core/.gas-snapshot
+++ b/core/.gas-snapshot
@@ -1,26 +1,26 @@
 BorrowerGasTest:test_addMargin() (gas: 16203)
-BorrowerGasTest:test_borrow() (gas: 110555)
+BorrowerGasTest:test_borrow() (gas: 110489)
 BorrowerGasTest:test_getUniswapPositions() (gas: 5219)
-BorrowerGasTest:test_modify() (gas: 82152)
-BorrowerGasTest:test_modifyWithAnte() (gas: 88607)
-BorrowerGasTest:test_repay() (gas: 111914)
-BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257767)
+BorrowerGasTest:test_modify() (gas: 82108)
+BorrowerGasTest:test_modifyWithAnte() (gas: 88563)
+BorrowerGasTest:test_repay() (gas: 111848)
+BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257723)
 BorrowerGasTest:test_uniswapDepositStandard() (gas: 167558)
-BorrowerGasTest:test_uniswapWithdraw() (gas: 147656)
-BorrowerGasTest:test_withdraw() (gas: 105672)
-FactoryGasTest:test_createBorrower() (gas: 156519)
-FactoryGasTest:test_createMarket() (gas: 3905006)
-LenderGasTest:test_accrueInterest() (gas: 46070)
-LenderGasTest:test_borrow() (gas: 40834)
-LenderGasTest:test_deposit() (gas: 53422)
-LenderGasTest:test_depositWithCourier() (gas: 53568)
-LenderGasTest:test_redeem() (gas: 53114)
-LenderGasTest:test_redeemWithCourier() (gas: 83506)
-LenderGasTest:test_repay() (gas: 44774)
-LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51083)
-LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59264)
-LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95666)
-LiquidatorGasTest:test_warn() (gas: 35067)
-LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130248)
+BorrowerGasTest:test_uniswapWithdraw() (gas: 147620)
+BorrowerGasTest:test_withdraw() (gas: 105628)
+FactoryGasTest:test_createBorrower() (gas: 156431)
+FactoryGasTest:test_createMarket() (gas: 3900591)
+LenderGasTest:test_accrueInterest() (gas: 46287)
+LenderGasTest:test_borrow() (gas: 40812)
+LenderGasTest:test_deposit() (gas: 53639)
+LenderGasTest:test_depositWithCourier() (gas: 53785)
+LenderGasTest:test_redeem() (gas: 53334)
+LenderGasTest:test_redeemWithCourier() (gas: 83726)
+LenderGasTest:test_repay() (gas: 44752)
+LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51017)
+LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59176)
+LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95596)
+LiquidatorGasTest:test_warn() (gas: 35023)
+LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130182)
 VolatilityGasTest:test_consult() (gas: 43075)
-VolatilityGasTest:test_updateNoBinarySearch() (gas: 145880)
\ No newline at end of file
+VolatilityGasTest:test_updateNoBinarySearch() (gas: 145910)
\ No newline at end of file

From 661e986dd69f02d34b18963f8747d51a7fcf811b Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Sun, 10 Sep 2023 00:45:39 -0500
Subject: [PATCH 06/11] gs

---
 core/.gas-snapshot | 42 +++++++++++++++++++++---------------------
 1 file changed, 21 insertions(+), 21 deletions(-)

diff --git a/core/.gas-snapshot b/core/.gas-snapshot
index 04bb3a5d..23aab4bf 100644
--- a/core/.gas-snapshot
+++ b/core/.gas-snapshot
@@ -1,26 +1,26 @@
 BorrowerGasTest:test_addMargin() (gas: 16203)
-BorrowerGasTest:test_borrow() (gas: 110489)
+BorrowerGasTest:test_borrow() (gas: 110555)
 BorrowerGasTest:test_getUniswapPositions() (gas: 5219)
-BorrowerGasTest:test_modify() (gas: 82108)
-BorrowerGasTest:test_modifyWithAnte() (gas: 88563)
-BorrowerGasTest:test_repay() (gas: 111848)
-BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257723)
+BorrowerGasTest:test_modify() (gas: 82152)
+BorrowerGasTest:test_modifyWithAnte() (gas: 88607)
+BorrowerGasTest:test_repay() (gas: 111914)
+BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257767)
 BorrowerGasTest:test_uniswapDepositStandard() (gas: 167558)
-BorrowerGasTest:test_uniswapWithdraw() (gas: 147620)
-BorrowerGasTest:test_withdraw() (gas: 105628)
-FactoryGasTest:test_createBorrower() (gas: 156431)
-FactoryGasTest:test_createMarket() (gas: 3900591)
-LenderGasTest:test_accrueInterest() (gas: 46287)
-LenderGasTest:test_borrow() (gas: 40812)
-LenderGasTest:test_deposit() (gas: 53639)
-LenderGasTest:test_depositWithCourier() (gas: 53785)
-LenderGasTest:test_redeem() (gas: 53334)
-LenderGasTest:test_redeemWithCourier() (gas: 83726)
-LenderGasTest:test_repay() (gas: 44752)
-LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51017)
-LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59176)
-LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95596)
-LiquidatorGasTest:test_warn() (gas: 35023)
-LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130182)
+BorrowerGasTest:test_uniswapWithdraw() (gas: 147656)
+BorrowerGasTest:test_withdraw() (gas: 105672)
+FactoryGasTest:test_createBorrower() (gas: 156519)
+FactoryGasTest:test_createMarket() (gas: 3905006)
+LenderGasTest:test_accrueInterest() (gas: 46070)
+LenderGasTest:test_borrow() (gas: 40834)
+LenderGasTest:test_deposit() (gas: 53422)
+LenderGasTest:test_depositWithCourier() (gas: 53568)
+LenderGasTest:test_redeem() (gas: 53114)
+LenderGasTest:test_redeemWithCourier() (gas: 83506)
+LenderGasTest:test_repay() (gas: 44774)
+LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51083)
+LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59264)
+LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95666)
+LiquidatorGasTest:test_warn() (gas: 35067)
+LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130248)
 VolatilityGasTest:test_consult() (gas: 43075)
 VolatilityGasTest:test_updateNoBinarySearch() (gas: 145910)
\ No newline at end of file

From 9f6b61bcd3bef0b788707a9e8266fa159e342680 Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Sun, 10 Sep 2023 20:54:26 -0500
Subject: [PATCH 07/11] Remove extra sig digs from IV and improve constants

---
 core/.gas-snapshot                         |  28 ++---
 core/src/VolatilityOracle.sol              |   4 +-
 core/src/libraries/BalanceSheet.sol        |  31 +++--
 core/src/libraries/Volatility.sol          |   9 +-
 core/src/libraries/constants/Constants.sol |  32 ++---
 core/test/Utils.sol                        |   2 +-
 core/test/VolatilityOracle.t.sol           |  14 +--
 core/test/libraries/BalanceSheet.t.sol     | 139 ++++++++++++++-------
 core/test/libraries/Volatility.t.sol       |  10 +-
 9 files changed, 163 insertions(+), 106 deletions(-)

diff --git a/core/.gas-snapshot b/core/.gas-snapshot
index 23aab4bf..d77ccd12 100644
--- a/core/.gas-snapshot
+++ b/core/.gas-snapshot
@@ -1,15 +1,15 @@
 BorrowerGasTest:test_addMargin() (gas: 16203)
-BorrowerGasTest:test_borrow() (gas: 110555)
+BorrowerGasTest:test_borrow() (gas: 110565)
 BorrowerGasTest:test_getUniswapPositions() (gas: 5219)
-BorrowerGasTest:test_modify() (gas: 82152)
-BorrowerGasTest:test_modifyWithAnte() (gas: 88607)
-BorrowerGasTest:test_repay() (gas: 111914)
-BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257767)
+BorrowerGasTest:test_modify() (gas: 82162)
+BorrowerGasTest:test_modifyWithAnte() (gas: 88617)
+BorrowerGasTest:test_repay() (gas: 111924)
+BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257777)
 BorrowerGasTest:test_uniswapDepositStandard() (gas: 167558)
-BorrowerGasTest:test_uniswapWithdraw() (gas: 147656)
-BorrowerGasTest:test_withdraw() (gas: 105672)
+BorrowerGasTest:test_uniswapWithdraw() (gas: 147664)
+BorrowerGasTest:test_withdraw() (gas: 105682)
 FactoryGasTest:test_createBorrower() (gas: 156519)
-FactoryGasTest:test_createMarket() (gas: 3905006)
+FactoryGasTest:test_createMarket() (gas: 3903606)
 LenderGasTest:test_accrueInterest() (gas: 46070)
 LenderGasTest:test_borrow() (gas: 40834)
 LenderGasTest:test_deposit() (gas: 53422)
@@ -17,10 +17,10 @@ LenderGasTest:test_depositWithCourier() (gas: 53568)
 LenderGasTest:test_redeem() (gas: 53114)
 LenderGasTest:test_redeemWithCourier() (gas: 83506)
 LenderGasTest:test_repay() (gas: 44774)
-LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51083)
-LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59264)
-LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95666)
-LiquidatorGasTest:test_warn() (gas: 35067)
-LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130248)
+LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51093)
+LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59274)
+LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95674)
+LiquidatorGasTest:test_warn() (gas: 35077)
+LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130258)
 VolatilityGasTest:test_consult() (gas: 43075)
-VolatilityGasTest:test_updateNoBinarySearch() (gas: 145910)
\ No newline at end of file
+VolatilityGasTest:test_updateNoBinarySearch() (gas: 145902)
\ No newline at end of file
diff --git a/core/src/VolatilityOracle.sol b/core/src/VolatilityOracle.sol
index 1dcb2890..96356eb5 100644
--- a/core/src/VolatilityOracle.sol
+++ b/core/src/VolatilityOracle.sol
@@ -4,8 +4,8 @@ pragma solidity 0.8.17;
 import {IUniswapV3Pool} from "v3-core/contracts/interfaces/IUniswapV3Pool.sol";
 
 import {
-    IV_MAX,
     IV_SCALE,
+    IV_COLD_START,
     IV_CHANGE_PER_SECOND,
     UNISWAP_AVG_WINDOW,
     FEE_GROWTH_AVG_WINDOW,
@@ -38,7 +38,7 @@ contract VolatilityOracle {
 
         if (lastWrites[pool].time == 0) {
             feeGrowthGlobals[pool][0] = _getFeeGrowthGlobalsNow(pool);
-            lastWrites[pool] = LastWrite({index: 0, time: uint32(block.timestamp), iv: uint216(IV_MAX)});
+            lastWrites[pool] = LastWrite({index: 0, time: uint32(block.timestamp), iv: IV_COLD_START});
         }
     }
 
diff --git a/core/src/libraries/BalanceSheet.sol b/core/src/libraries/BalanceSheet.sol
index f710d7f1..1ed79acb 100644
--- a/core/src/libraries/BalanceSheet.sol
+++ b/core/src/libraries/BalanceSheet.sol
@@ -4,8 +4,8 @@ pragma solidity 0.8.17;
 import {FixedPointMathLib as SoladyMath} from "solady/utils/FixedPointMathLib.sol";
 
 import {
-    IV_MIN,
-    IV_MAX,
+    LTV_MIN,
+    LTV_MAX,
     MAX_LEVERAGE,
     LIQUIDATION_INCENTIVE,
     MANIPULATION_THRESHOLD_DIVISOR
@@ -32,6 +32,18 @@ struct Prices {
 /// @notice Provides functions for computing a `Borrower`'s health
 /// @author Aloe Labs, Inc.
 library BalanceSheet {
+    /// @dev The minimum percentage that can be added/subtracted to the TWAP to get probe prices
+    uint256 internal constant PROBE_PERCENT_MIN =
+        1e12 -
+            (LTV_MAX * (LIQUIDATION_INCENTIVE * MAX_LEVERAGE + LIQUIDATION_INCENTIVE + MAX_LEVERAGE)) /
+            (LIQUIDATION_INCENTIVE * MAX_LEVERAGE);
+
+    /// @dev The maximum percentage that can be added/subtracted to the TWAP to get probe prices
+    uint256 internal constant PROBE_PERCENT_MAX =
+        1e12 -
+            (LTV_MIN * (LIQUIDATION_INCENTIVE * MAX_LEVERAGE + LIQUIDATION_INCENTIVE + MAX_LEVERAGE)) /
+            (LIQUIDATION_INCENTIVE * MAX_LEVERAGE);
+
     function isHealthy(
         Prices memory prices,
         Assets memory mem,
@@ -87,11 +99,11 @@ library BalanceSheet {
         uint56 metric
     ) internal pure returns (uint160 a, uint160 b, bool isSus) {
         unchecked {
-            iv = nSigma * SoladyMath.clamp(iv, IV_MIN, IV_MAX);
+            iv = SoladyMath.clamp(nSigma * iv, PROBE_PERCENT_MIN, PROBE_PERCENT_MAX);
             isSus = metric > _manipulationThreshold(_effectiveCollateralFactor(iv));
 
-            a = uint160((sqrtMeanPriceX96 * SoladyMath.sqrt(1e18 - iv)) / 1e9);
-            b = uint160(SoladyMath.min((sqrtMeanPriceX96 * SoladyMath.sqrt(1e18 + iv)) / 1e9, type(uint160).max));
+            a = uint160((sqrtMeanPriceX96 * SoladyMath.sqrt(1e12 - iv)) / 1e6);
+            b = uint160(SoladyMath.min((sqrtMeanPriceX96 * SoladyMath.sqrt(1e12 + iv)) / 1e6, type(uint160).max));
         }
     }
 
@@ -123,18 +135,17 @@ library BalanceSheet {
         }
     }
 
-    /// @dev Equivalent to \\( \frac{log_{1.0001} \left( \frac{10^{18}}{cf} \right)}{12} \\)
-    /// assuming `MANIPULATION_THRESHOLD_DIVISOR` is 24
+    /// @dev Equivalent to \\( \frac{log_{1.0001} \left( \frac{10^{12}}{cf} \right)}{\text{MANIPULATION_THRESHOLD_DIVISOR}} \\)
     function _manipulationThreshold(uint256 cf) private pure returns (uint24) {
-        return uint24(-TickMath.getTickAtSqrtRatio(uint160(cf)) - 501937) / MANIPULATION_THRESHOLD_DIVISOR;
+        return uint24(-TickMath.getTickAtSqrtRatio(uint160(cf)) - 778261) / (2 * MANIPULATION_THRESHOLD_DIVISOR);
     }
 
     /// @dev Equivalent to \\( \frac{1 - σ}{1 + \frac{1}{liquidationIncentive} + \frac{1}{maxLeverage}} \\) where
-    /// \\( σ = \frac{clampedAndScaledIV}{10^{18}} \\) in floating point
+    /// \\( σ = \frac{clampedAndScaledIV}{10^{12}} \\) in floating point
     function _effectiveCollateralFactor(uint256 clampedAndScaledIV) private pure returns (uint256 cf) {
         unchecked {
             cf =
-                ((1e18 - clampedAndScaledIV) * (LIQUIDATION_INCENTIVE * MAX_LEVERAGE)) /
+                ((1e12 - clampedAndScaledIV) * (LIQUIDATION_INCENTIVE * MAX_LEVERAGE)) /
                 (LIQUIDATION_INCENTIVE * MAX_LEVERAGE + LIQUIDATION_INCENTIVE + MAX_LEVERAGE);
         }
     }
diff --git a/core/src/libraries/Volatility.sol b/core/src/libraries/Volatility.sol
index 6b133e34..19dad4a2 100644
--- a/core/src/libraries/Volatility.sol
+++ b/core/src/libraries/Volatility.sol
@@ -37,14 +37,14 @@ library Volatility {
      * @param a The pool's cumulative feeGrowthGlobals some time in the past
      * @param b The pool's cumulative feeGrowthGlobals as of the current block
      * @param scale The timescale (in seconds) in which IV should be reported, e.g. hourly, daily, annualized
-     * @return An estimate of the implied volatility scaled by 1e18
+     * @return An estimate of the implied volatility scaled by 1e12
      */
     function estimate(
         PoolMetadata memory metadata,
         Oracle.PoolData memory data,
         FeeGrowthGlobals memory a,
         FeeGrowthGlobals memory b,
-        uint256 scale
+        uint32 scale
     ) internal pure returns (uint256) {
         uint256 tickTvl = computeTickTvl(metadata.tickSpacing, data.currentTick, data.sqrtPriceX96, data.tickLiquidity);
 
@@ -73,9 +73,8 @@ library Volatility {
         if (volumeGamma0Gamma1 > (1 << 128)) volumeGamma0Gamma1 = (1 << 128);
 
         unchecked {
-            // Scale volume to the target time frame
-            volumeGamma0Gamma1 = (volumeGamma0Gamma1 * scale) / (b.timestamp - a.timestamp);
-            return SoladyMath.sqrt((4e36 * volumeGamma0Gamma1) / tickTvl);
+            // Scale volume to the target time frame, divide by `tickTvl`, and sqrt for final result
+            return SoladyMath.sqrt((4e24 * volumeGamma0Gamma1 * scale) / (b.timestamp - a.timestamp) / tickTvl);
         }
     }
 
diff --git a/core/src/libraries/constants/Constants.sol b/core/src/libraries/constants/Constants.sol
index 7f6fd23c..5b7a5cda 100644
--- a/core/src/libraries/constants/Constants.sol
+++ b/core/src/libraries/constants/Constants.sol
@@ -65,6 +65,14 @@ uint32 constant CONSTRAINT_PAUSE_INTERVAL_MAX = 2 days;
                             LIQUIDATION
 //////////////////////////////////////////////////////////////*/
 
+/// @dev The minimum loan-to-value ratio. Actual ratio is based on implied volatility; this is just a lower bound.
+/// Expressed as a 1e12 percentage, e.g. 0.10e12 → 10%
+uint256 constant LTV_MIN = 0.10e12;
+
+/// @dev The maximum loan-to-value ratio. Actual ratio is based on implied volatility; this is just a upper bound.
+/// Expressed as a 1e12 percentage, e.g. 0.90e12 → 90%
+uint256 constant LTV_MAX = 0.90e12;
+
 /// @dev \\( 1 + \frac{1}{\text{MAX_LEVERAGE}} \\) should be greater than the maximum feasible single-block
 /// `accrualFactor` so that liquidators have time to respond to interest updates
 uint256 constant MAX_LEVERAGE = 200;
@@ -77,26 +85,22 @@ uint256 constant LIQUIDATION_GRACE_PERIOD = 2 minutes;
                             IV AND TWAP
 //////////////////////////////////////////////////////////////*/
 
-/// @dev The minimum implied volatility. Clamped to this **before** multiplying by `nSigma`.
-/// Expressed as a wad percentage at `IV_SCALE`, e.g. {0.01e18, 24 hours} → 1% daily → 19% annual
-uint256 constant IV_MIN = 0.01e18;
-
-/// @dev The maximum implied volatility. Clamped to this **before** multiplying by `nSigma`.
-/// Expressed as a wad percentage at `IV_SCALE`, e.g. {0.18e18, 24 hours} → 18% daily → 344% annual
-/// To avoid underflow in `BalanceSheet.computeProbePrices`, ensure that `IV_MAX * nSigma <= 1e18`
-uint256 constant IV_MAX = 0.18e18;
-
 /// @dev The timescale of implied volatility, applied to measurements and calculations. When `BalanceSheet` detects
 /// that an `nSigma` event would cause insolvency in this time period, it enables liquidations. So if you squint your
 /// eyes and wave your hands enough, this is (in expectation) the time liquidators have to act before the protocol
 /// accrues bad debt.
-uint256 constant IV_SCALE = 24 hours;
+uint32 constant IV_SCALE = 24 hours;
+
+/// @dev The initial value of implied volatility, used when `VolatilityOracle.prepare` is called for a new pool.
+/// Expressed as a 1e12 percentage at `IV_SCALE`, e.g. {0.20e12, 24 hours} → 20% daily → 382% annual. Error on the
+/// side of making this too large (resulting in low LTV).
+uint128 constant IV_COLD_START = 0.20e12;
 
 /// @dev The maximum rate at which (reported) implied volatility can change. Raw samples in `VolatilityOracle.update`
 /// are clamped (before being stored) so as not to exceed this rate.
-/// Expressed in wad percentage points at `IV_SCALE` **per second**, e.g. {462962962962, 24 hours} means daily IV can
+/// Expressed in 1e12 percentage points at `IV_SCALE` **per second**, e.g. {462962, 24 hours} means daily IV can
 /// change by 0.0000463 percentage points per second → 4 percentage points per day.
-uint256 constant IV_CHANGE_PER_SECOND = 462962962962;
+uint256 constant IV_CHANGE_PER_SECOND = 462962;
 
 /// @dev To estimate volume, we need 2 samples. One is always at the current block, the other is from
 /// `FEE_GROWTH_AVG_WINDOW` seconds ago, +/- `FEE_GROWTH_SAMPLE_PERIOD / 2`. Larger values make the resulting volume
@@ -124,5 +128,5 @@ uint32 constant UNISWAP_AVG_WINDOW = 30 minutes;
 /// threshold is calculated as follows:
 ///
 /// \\( \text{manipulationThreshold} =
-/// 2 \cdot \frac{log_{1.0001}\left( \frac{1}{\text{collateralFactor}} \right)}{\text{MANIPULATION_THRESHOLD_DIVISOR}} \\)
-uint24 constant MANIPULATION_THRESHOLD_DIVISOR = 24;
+/// \frac{log_{1.0001}\left( \frac{1}{\text{collateralFactor}} \right)}{\text{MANIPULATION_THRESHOLD_DIVISOR}} \\)
+uint24 constant MANIPULATION_THRESHOLD_DIVISOR = 12;
diff --git a/core/test/Utils.sol b/core/test/Utils.sol
index 9caf5669..7342f6dc 100644
--- a/core/test/Utils.sol
+++ b/core/test/Utils.sol
@@ -48,7 +48,7 @@ contract VolatilityOracleMock {
 
     function consult(IUniswapV3Pool pool, uint40 seed) external view returns (uint56, uint160, uint256) {
         (Oracle.PoolData memory data, uint56 metric) = Oracle.consult(pool, seed);
-        return (metric, data.sqrtMeanPriceX96, 0.025e18);
+        return (metric, data.sqrtMeanPriceX96, 0.025e12);
     }
 }
 
diff --git a/core/test/VolatilityOracle.t.sol b/core/test/VolatilityOracle.t.sol
index d22f4308..c98f1be1 100644
--- a/core/test/VolatilityOracle.t.sol
+++ b/core/test/VolatilityOracle.t.sol
@@ -40,7 +40,7 @@ contract VolatilityOracleTest is Test {
 
             assertGt(metric, 0);
             assertGt(price, 0);
-            assertEqDecimal(iv, 0, 18);
+            assertEqDecimal(iv, 0, 12);
         }
     }
 
@@ -72,7 +72,7 @@ contract VolatilityOracleTest is Test {
             assertEq(fggTime, block.timestamp);
             assertEq(index, 0);
             assertEq(time, block.timestamp);
-            assertEqDecimal(iv, IV_MAX, 18);
+            assertEqDecimal(iv, IV_COLD_START, 12);
         }
 
         vm.expectRevert(bytes("Aloe: cardinality"));
@@ -96,12 +96,12 @@ contract VolatilityOracleTest is Test {
             (, , uint256 ivOld) = oracle.consult(pool, (1 << 32));
             (, , uint256 ivNew) = oracle.update(pool, (1 << 32));
 
-            assertEqDecimal(ivOld, ivOldExpected, 18);
-            assertEqDecimal(ivNew, ivOld, 18);
+            assertEqDecimal(ivOld, ivOldExpected, 12);
+            assertEqDecimal(ivNew, ivOld, 12);
 
             (index, time, ivNew) = oracle.lastWrites(pool);
 
-            assertEqDecimal(ivNew, ivOld, 18);
+            assertEqDecimal(ivNew, ivOld, 12);
             assertEq(index, 1);
             assertEq(time, block.timestamp);
         }
@@ -125,7 +125,7 @@ contract VolatilityOracleTest is Test {
             (, , uint256 ivNew) = oracle.update(pool, (1 << 32));
             (bytes32[] memory reads, bytes32[] memory writes) = vm.accesses(address(oracle));
 
-            assertEqDecimal(ivNew, ivOld, 18);
+            assertEqDecimal(ivNew, ivOld, 12);
             assertEq(reads.length, 1);
             assertEq(writes.length, 0);
         }
@@ -180,7 +180,7 @@ contract VolatilityOracleTest is Test {
             (, , uint256 ivWritten) = oracle.update(pool, (1 << 32));
             (uint256 newIndex, uint256 newTime, uint256 ivStored) = oracle.lastWrites(pool);
 
-            assertEqDecimal(ivStored, ivWritten, 18);
+            assertEqDecimal(ivStored, ivWritten, 12);
             assertEq(newIndex, (currentIndex + 1) % FEE_GROWTH_ARRAY_LENGTH);
 
             uint256 maxChange = (newTime - currentTime) * IV_CHANGE_PER_SECOND;
diff --git a/core/test/libraries/BalanceSheet.t.sol b/core/test/libraries/BalanceSheet.t.sol
index 12c539ef..60c0ae22 100644
--- a/core/test/libraries/BalanceSheet.t.sol
+++ b/core/test/libraries/BalanceSheet.t.sol
@@ -3,6 +3,7 @@ pragma solidity 0.8.17;
 
 import "forge-std/Test.sol";
 
+import {CONSTRAINT_N_SIGMA_MIN, CONSTRAINT_N_SIGMA_MAX, LTV_MIN, IV_COLD_START} from "src/libraries/constants/Constants.sol";
 import {BalanceSheet, TickMath, square} from "src/libraries/BalanceSheet.sol";
 
 import {FixedPointMathLib as SoladyMath} from "solady/utils/FixedPointMathLib.sol";
@@ -14,124 +15,166 @@ contract BalanceSheetTest is Test {
     function test_spec_computeProbePrices() public {
         bool isSus;
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.00e18, 5, 87);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.00e12, 5, 87);
         assertFalse(isSus, "0.00 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.00e18, 5, 88);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.00e12, 5, 88);
         assertTrue(isSus, "0.00 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.01e18, 5, 87);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.01e12, 5, 87);
         assertFalse(isSus, "0.01 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.01e18, 5, 88);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.01e12, 5, 88);
         assertTrue(isSus, "0.01 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.02e18, 5, 132);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.02e12, 5, 132);
         assertFalse(isSus, "0.02 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.02e18, 5, 133);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.02e12, 5, 133);
         assertTrue(isSus, "0.02 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.03e18, 5, 180);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.03e12, 5, 180);
         assertFalse(isSus, "0.03 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.03e18, 5, 181);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.03e12, 5, 181);
         assertTrue(isSus, "0.03 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.04e18, 5, 230);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.04e12, 5, 230);
         assertFalse(isSus, "0.04 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.04e18, 5, 231);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.04e12, 5, 231);
         assertTrue(isSus, "0.04 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.05e18, 5, 284);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.05e12, 5, 284);
         assertFalse(isSus, "0.05 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.05e18, 5, 285);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.05e12, 5, 285);
         assertTrue(isSus, "0.05 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.06e18, 5, 341);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.06e12, 5, 341);
         assertFalse(isSus, "0.06 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.06e18, 5, 342);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.06e12, 5, 342);
         assertTrue(isSus, "0.06 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.07e18, 5, 403);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.07e12, 5, 403);
         assertFalse(isSus, "0.07 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.07e18, 5, 404);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.07e12, 5, 404);
         assertTrue(isSus, "0.07 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.08e18, 5, 470);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.08e12, 5, 470);
         assertFalse(isSus, "0.08 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.08e18, 5, 471);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.08e12, 5, 471);
         assertTrue(isSus, "0.08 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.09e18, 5, 542);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.09e12, 5, 542);
         assertFalse(isSus, "0.09 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.09e18, 5, 543);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.09e12, 5, 543);
         assertTrue(isSus, "0.09 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.10e18, 5, 622);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.10e12, 5, 622);
         assertFalse(isSus, "0.10 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.10e18, 5, 623);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.10e12, 5, 623);
         assertTrue(isSus, "0.10 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.11e18, 5, 710);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.11e12, 5, 710);
         assertFalse(isSus, "0.11 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.11e18, 5, 711);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.11e12, 5, 711);
         assertTrue(isSus, "0.11 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.12e18, 5, 808);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.12e12, 5, 808);
         assertFalse(isSus, "0.12 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.12e18, 5, 809);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.12e12, 5, 809);
         assertTrue(isSus, "0.12 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.13e18, 5, 919);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.13e12, 5, 919);
         assertFalse(isSus, "0.13 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.13e18, 5, 920);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.13e12, 5, 920);
         assertTrue(isSus, "0.13 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.14e18, 5, 1048);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.14e12, 5, 1048);
         assertFalse(isSus, "0.14 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.14e18, 5, 1049);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.14e12, 5, 1049);
         assertTrue(isSus, "0.14 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.15e18, 5, 1199);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.15e12, 5, 1199);
         assertFalse(isSus, "0.15 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.15e18, 5, 1200);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.15e12, 5, 1200);
         assertTrue(isSus, "0.15 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.16e18, 5, 1385);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.16e12, 5, 1385);
         assertFalse(isSus, "0.16 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.16e18, 5, 1386);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.16e12, 5, 1386);
         assertTrue(isSus, "0.16 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.17e18, 5, 1625);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.17e12, 5, 1625);
         assertFalse(isSus, "0.17 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.17e18, 5, 1626);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.17e12, 5, 1626);
         assertTrue(isSus, "0.17 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.18e18, 5, 1963);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.18e12, 5, 1918);
         assertFalse(isSus, "0.18 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.18e18, 5, 1964);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.18e12, 5, 1919);
         assertTrue(isSus, "0.18 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.19e18, 5, 1963);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.19e12, 5, 1918);
         assertFalse(isSus, "0.19 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.19e18, 5, 1964);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.19e12, 5, 1919);
         assertTrue(isSus, "0.19 true");
+
+        (, , isSus) = BalanceSheet.computeProbePrices(0, IV_COLD_START, 5, 1918);
+        assertFalse(isSus, "cold start false");
+        (, , isSus) = BalanceSheet.computeProbePrices(0, IV_COLD_START, 5, 1919);
+        assertTrue(isSus, "cold start true");
     }
 
-    function test_computeProbePrices(uint160 sqrtMeanPriceX96, uint256 sigma) public {
+    function test_computeProbePrices(uint160 sqrtMeanPriceX96, uint256 iv, uint256 nSigma) public {
         // The lower bound is related to how precise our assertion is. For prices to be correct within 0.01%,
         // the sqrtPrice must be >= 2^40 (approximately). Calculations for that are here:
         // https://www.desmos.com/calculator/gfbkcnt0vs
         // The upper bound is due to the fact that the result (specifically `b`) must fit in uint160. The maximum
-        // volatility factor is 1 + 5*0.18, so we divide `TickMath.MAX_SQRT_RATIO` by sqrt(1e18 + 5*0.18e18)
-        sqrtMeanPriceX96 = uint160(bound(sqrtMeanPriceX96, (1 << 40), TickMath.MAX_SQRT_RATIO / 1.0863e9));
-        (uint256 a, uint256 b, ) = BalanceSheet.computeProbePrices(sqrtMeanPriceX96, sigma, 5, 0);
+        // volatility factor is 1 + IV_AWARE_PROBE_PERCENT_MAX, so we divide `TickMath.MAX_SQRT_RATIO` by
+        // sqrt(1e12 + IV_AWARE_PROBE_PERCENT_MAX)
+        sqrtMeanPriceX96 = uint160(bound(sqrtMeanPriceX96, (1 << 40), uint256(TickMath.MAX_SQRT_RATIO) * 1e6 / 1376408));
+        nSigma = uint160(bound(nSigma, CONSTRAINT_N_SIGMA_MIN, CONSTRAINT_N_SIGMA_MAX));
+
+        (uint256 a, uint256 b, ) = BalanceSheet.computeProbePrices(sqrtMeanPriceX96, iv, nSigma, 0);
 
         uint256 price = square(sqrtMeanPriceX96);
         a = square(uint160(a));
         b = square(uint160(b));
 
-        if (sigma < 0.01e18) sigma = 0.01e18;
-        else if (sigma > 0.18e18) sigma = 0.18e18;
+        if (iv < BalanceSheet.PROBE_PERCENT_MIN / nSigma) iv = BalanceSheet.PROBE_PERCENT_MIN / nSigma;
+        else if (iv > BalanceSheet.PROBE_PERCENT_MAX / nSigma) iv = BalanceSheet.PROBE_PERCENT_MAX / nSigma;
+
+        assertApproxEqRel(a, SoladyMath.fullMulDiv(price, 1e12 - nSigma * iv, 1e12), 0.0001e18);
+        assertApproxEqRel(b, SoladyMath.fullMulDiv(price, 1e12 + nSigma * iv, 1e12), 0.0001e18);
+    }
+
+    function test_constants() public {
+        assertEq(BalanceSheet.PROBE_PERCENT_MIN, 50500000000);
+        assertEq(BalanceSheet.PROBE_PERCENT_MAX, 894500000000);
+
+        // Necessary for collateral factor computation to work
+        assertGt(LTV_MIN, TickMath.MIN_SQRT_RATIO);
+    }
+
+    /// @dev We have to override this because we need 512 bit multiplication in the assertion
+    function assertApproxEqRel(
+        uint256 a,
+        uint256 b,
+        uint256 maxPercentDelta // An 18 decimal fixed point number, where 1e18 == 100%
+    ) internal override {
+        if (b == 0) return assertEq(a, b); // If the expected is 0, actual must be too.
+
+        uint256 percentDelta = _percentDelta(a, b);
+
+        if (percentDelta > maxPercentDelta) {
+            emit log("Error: a ~= b not satisfied [uint]");
+            emit log_named_uint("    Expected", b);
+            emit log_named_uint("      Actual", a);
+            emit log_named_decimal_uint(" Max % Delta", maxPercentDelta, 18);
+            emit log_named_decimal_uint("     % Delta", percentDelta, 18);
+            fail();
+        }
+    }
+
+    function _percentDelta(uint256 a, uint256 b) private pure returns (uint256) {
+        uint256 absDelta = stdMath.delta(a, b);
 
-        assertApproxEqRel(a, SoladyMath.fullMulDiv(price, 1e18 - 5 * sigma, 1e18), 0.0001e18);
-        assertApproxEqRel(b, SoladyMath.fullMulDiv(price, 1e18 + 5 * sigma, 1e18), 0.0001e18);
+        return SoladyMath.fullMulDivUp(absDelta, 1e18, b);
     }
 }
diff --git a/core/test/libraries/Volatility.t.sol b/core/test/libraries/Volatility.t.sol
index 0e9b6ca4..28731571 100644
--- a/core/test/libraries/Volatility.t.sol
+++ b/core/test/libraries/Volatility.t.sol
@@ -35,7 +35,7 @@ contract VolatilityTest is Test {
             ),
             1 days
         );
-        assertEq(dailyIV, 20405953715139097); // 2.041%
+        assertEq(dailyIV, 20405953715); // 2.041%
 
         dailyIV = Volatility.estimate(
             metadata,
@@ -52,7 +52,7 @@ contract VolatilityTest is Test {
             ),
             1 hours
         );
-        assertEq(dailyIV, 4165347859745125); // 0.417%
+        assertEq(dailyIV, 4165347859); // 0.417%
 
         dailyIV = Volatility.estimate(
             metadata,
@@ -65,7 +65,7 @@ contract VolatilityTest is Test {
             ),
             1 days
         );
-        assertEq(dailyIV, 6970260375825778); // 0.697%
+        assertEq(dailyIV, 6970260375); // 0.697%
 
         dailyIV = Volatility.estimate(
             metadata,
@@ -272,7 +272,7 @@ contract VolatilityTest is Test {
         uint32 oracleLookback,
         uint128 tickLiquidity,
         uint32 scale
-    ) public view {
+    ) public {
         scale = uint32(bound(scale, 1 minutes, 2 days));
         oracleLookback = uint32(bound(oracleLookback, 15 seconds, 1 days));
         secondsPerLiquidityX128 = uint160(bound(secondsPerLiquidityX128, feeGrowthSampleAge, type(uint160).max));
@@ -313,7 +313,7 @@ contract VolatilityTest is Test {
             b.timestamp = feeGrowthSampleAge;
         }
 
-        Volatility.estimate(metadata, data, a, b, scale);
+        assertLt(Volatility.estimate(metadata, data, a, b, scale), 1 << 128);
     }
 
     function boundTick(int24 tick, int24 tickSpacing) private pure returns (int24) {

From e5a1a41fb2d8acff631340e6873cc709d3b3945a Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Sun, 10 Sep 2023 21:53:14 -0500
Subject: [PATCH 08/11] Move constants back to constants file

---
 core/src/libraries/BalanceSheet.sol        | 16 ++-----------
 core/src/libraries/constants/Constants.sol | 27 ++++++++++++++++------
 core/test/libraries/BalanceSheet.t.sol     | 23 +++++++++++++-----
 3 files changed, 39 insertions(+), 27 deletions(-)

diff --git a/core/src/libraries/BalanceSheet.sol b/core/src/libraries/BalanceSheet.sol
index 1ed79acb..a11ed7d1 100644
--- a/core/src/libraries/BalanceSheet.sol
+++ b/core/src/libraries/BalanceSheet.sol
@@ -4,10 +4,10 @@ pragma solidity 0.8.17;
 import {FixedPointMathLib as SoladyMath} from "solady/utils/FixedPointMathLib.sol";
 
 import {
-    LTV_MIN,
-    LTV_MAX,
     MAX_LEVERAGE,
     LIQUIDATION_INCENTIVE,
+    PROBE_PERCENT_MIN,
+    PROBE_PERCENT_MAX,
     MANIPULATION_THRESHOLD_DIVISOR
 } from "./constants/Constants.sol";
 import {square, mulDiv128} from "./MulDiv.sol";
@@ -32,18 +32,6 @@ struct Prices {
 /// @notice Provides functions for computing a `Borrower`'s health
 /// @author Aloe Labs, Inc.
 library BalanceSheet {
-    /// @dev The minimum percentage that can be added/subtracted to the TWAP to get probe prices
-    uint256 internal constant PROBE_PERCENT_MIN =
-        1e12 -
-            (LTV_MAX * (LIQUIDATION_INCENTIVE * MAX_LEVERAGE + LIQUIDATION_INCENTIVE + MAX_LEVERAGE)) /
-            (LIQUIDATION_INCENTIVE * MAX_LEVERAGE);
-
-    /// @dev The maximum percentage that can be added/subtracted to the TWAP to get probe prices
-    uint256 internal constant PROBE_PERCENT_MAX =
-        1e12 -
-            (LTV_MIN * (LIQUIDATION_INCENTIVE * MAX_LEVERAGE + LIQUIDATION_INCENTIVE + MAX_LEVERAGE)) /
-            (LIQUIDATION_INCENTIVE * MAX_LEVERAGE);
-
     function isHealthy(
         Prices memory prices,
         Assets memory mem,
diff --git a/core/src/libraries/constants/Constants.sol b/core/src/libraries/constants/Constants.sol
index 5b7a5cda..29258c2f 100644
--- a/core/src/libraries/constants/Constants.sol
+++ b/core/src/libraries/constants/Constants.sol
@@ -65,6 +65,17 @@ uint32 constant CONSTRAINT_PAUSE_INTERVAL_MAX = 2 days;
                             LIQUIDATION
 //////////////////////////////////////////////////////////////*/
 
+/// @dev \\( 1 + \frac{1}{\text{MAX_LEVERAGE}} \\) should be greater than the maximum feasible single-block
+/// `accrualFactor` so that liquidators have time to respond to interest updates
+uint256 constant MAX_LEVERAGE = 200;
+
+/// @dev The discount that liquidators receive when swapping assets. Expressed as reciprocal, e.g. 20 → 5%
+uint256 constant LIQUIDATION_INCENTIVE = 20;
+
+/// @dev The minimum time that must pass between `Borrower.warn` and `Borrower.liquidate` for any liquidation that
+/// involves the swap callbacks (`swap1For0` and `swap0For1`). There is no grace period for in-kind liquidations.
+uint256 constant LIQUIDATION_GRACE_PERIOD = 2 minutes;
+
 /// @dev The minimum loan-to-value ratio. Actual ratio is based on implied volatility; this is just a lower bound.
 /// Expressed as a 1e12 percentage, e.g. 0.10e12 → 10%
 uint256 constant LTV_MIN = 0.10e12;
@@ -73,13 +84,15 @@ uint256 constant LTV_MIN = 0.10e12;
 /// Expressed as a 1e12 percentage, e.g. 0.90e12 → 90%
 uint256 constant LTV_MAX = 0.90e12;
 
-/// @dev \\( 1 + \frac{1}{\text{MAX_LEVERAGE}} \\) should be greater than the maximum feasible single-block
-/// `accrualFactor` so that liquidators have time to respond to interest updates
-uint256 constant MAX_LEVERAGE = 200;
-
-uint256 constant LIQUIDATION_INCENTIVE = 20; // Expressed as reciprocal, e.g. 20 → 5%
+/// @dev The minimum percentage that can be added/subtracted to the TWAP to get probe prices in `BalanceSheet`
+uint256 constant PROBE_PERCENT_MIN = 1e12 -
+    (LTV_MAX * (LIQUIDATION_INCENTIVE * MAX_LEVERAGE + LIQUIDATION_INCENTIVE + MAX_LEVERAGE)) /
+    (LIQUIDATION_INCENTIVE * MAX_LEVERAGE);
 
-uint256 constant LIQUIDATION_GRACE_PERIOD = 2 minutes;
+/// @dev The maximum percentage that can be added/subtracted to the TWAP to get probe prices in `BalanceSheet`
+uint256 constant PROBE_PERCENT_MAX = 1e12 -
+    (LTV_MIN * (LIQUIDATION_INCENTIVE * MAX_LEVERAGE + LIQUIDATION_INCENTIVE + MAX_LEVERAGE)) /
+    (LIQUIDATION_INCENTIVE * MAX_LEVERAGE);
 
 /*//////////////////////////////////////////////////////////////
                             IV AND TWAP
@@ -94,7 +107,7 @@ uint32 constant IV_SCALE = 24 hours;
 /// @dev The initial value of implied volatility, used when `VolatilityOracle.prepare` is called for a new pool.
 /// Expressed as a 1e12 percentage at `IV_SCALE`, e.g. {0.20e12, 24 hours} → 20% daily → 382% annual. Error on the
 /// side of making this too large (resulting in low LTV).
-uint128 constant IV_COLD_START = 0.20e12;
+uint128 constant IV_COLD_START = uint128(PROBE_PERCENT_MAX / DEFAULT_N_SIGMA);
 
 /// @dev The maximum rate at which (reported) implied volatility can change. Raw samples in `VolatilityOracle.update`
 /// are clamped (before being stored) so as not to exceed this rate.
diff --git a/core/test/libraries/BalanceSheet.t.sol b/core/test/libraries/BalanceSheet.t.sol
index 60c0ae22..2337ad38 100644
--- a/core/test/libraries/BalanceSheet.t.sol
+++ b/core/test/libraries/BalanceSheet.t.sol
@@ -3,7 +3,15 @@ pragma solidity 0.8.17;
 
 import "forge-std/Test.sol";
 
-import {CONSTRAINT_N_SIGMA_MIN, CONSTRAINT_N_SIGMA_MAX, LTV_MIN, IV_COLD_START} from "src/libraries/constants/Constants.sol";
+import {
+    DEFAULT_N_SIGMA,
+    CONSTRAINT_N_SIGMA_MIN,
+    CONSTRAINT_N_SIGMA_MAX,
+    LTV_MIN,
+    PROBE_PERCENT_MIN,
+    PROBE_PERCENT_MAX,
+    IV_COLD_START
+} from "src/libraries/constants/Constants.sol";
 import {BalanceSheet, TickMath, square} from "src/libraries/BalanceSheet.sol";
 
 import {FixedPointMathLib as SoladyMath} from "solady/utils/FixedPointMathLib.sol";
@@ -128,7 +136,9 @@ contract BalanceSheetTest is Test {
         // The upper bound is due to the fact that the result (specifically `b`) must fit in uint160. The maximum
         // volatility factor is 1 + IV_AWARE_PROBE_PERCENT_MAX, so we divide `TickMath.MAX_SQRT_RATIO` by
         // sqrt(1e12 + IV_AWARE_PROBE_PERCENT_MAX)
-        sqrtMeanPriceX96 = uint160(bound(sqrtMeanPriceX96, (1 << 40), uint256(TickMath.MAX_SQRT_RATIO) * 1e6 / 1376408));
+        sqrtMeanPriceX96 = uint160(
+            bound(sqrtMeanPriceX96, (1 << 40), (uint256(TickMath.MAX_SQRT_RATIO) * 1e6) / 1376408)
+        );
         nSigma = uint160(bound(nSigma, CONSTRAINT_N_SIGMA_MIN, CONSTRAINT_N_SIGMA_MAX));
 
         (uint256 a, uint256 b, ) = BalanceSheet.computeProbePrices(sqrtMeanPriceX96, iv, nSigma, 0);
@@ -137,16 +147,17 @@ contract BalanceSheetTest is Test {
         a = square(uint160(a));
         b = square(uint160(b));
 
-        if (iv < BalanceSheet.PROBE_PERCENT_MIN / nSigma) iv = BalanceSheet.PROBE_PERCENT_MIN / nSigma;
-        else if (iv > BalanceSheet.PROBE_PERCENT_MAX / nSigma) iv = BalanceSheet.PROBE_PERCENT_MAX / nSigma;
+        if (iv < PROBE_PERCENT_MIN / nSigma) iv = PROBE_PERCENT_MIN / nSigma;
+        else if (iv > PROBE_PERCENT_MAX / nSigma) iv = PROBE_PERCENT_MAX / nSigma;
 
         assertApproxEqRel(a, SoladyMath.fullMulDiv(price, 1e12 - nSigma * iv, 1e12), 0.0001e18);
         assertApproxEqRel(b, SoladyMath.fullMulDiv(price, 1e12 + nSigma * iv, 1e12), 0.0001e18);
     }
 
     function test_constants() public {
-        assertEq(BalanceSheet.PROBE_PERCENT_MIN, 50500000000);
-        assertEq(BalanceSheet.PROBE_PERCENT_MAX, 894500000000);
+        // Just checking that things are reasonable
+        assertEqDecimal(PROBE_PERCENT_MIN, 50500000000, 12);
+        assertEqDecimal(PROBE_PERCENT_MAX, 894500000000, 12);
 
         // Necessary for collateral factor computation to work
         assertGt(LTV_MIN, TickMath.MIN_SQRT_RATIO);

From 51671a58c936941645748347050a0e4b4dfc8516 Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Sun, 10 Sep 2023 21:56:51 -0500
Subject: [PATCH 09/11] Note on TickMath

---
 core/src/libraries/constants/Constants.sol | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/core/src/libraries/constants/Constants.sol b/core/src/libraries/constants/Constants.sol
index 29258c2f..4b0e2e7f 100644
--- a/core/src/libraries/constants/Constants.sol
+++ b/core/src/libraries/constants/Constants.sol
@@ -77,7 +77,8 @@ uint256 constant LIQUIDATION_INCENTIVE = 20;
 uint256 constant LIQUIDATION_GRACE_PERIOD = 2 minutes;
 
 /// @dev The minimum loan-to-value ratio. Actual ratio is based on implied volatility; this is just a lower bound.
-/// Expressed as a 1e12 percentage, e.g. 0.10e12 → 10%
+/// Expressed as a 1e12 percentage, e.g. 0.10e12 → 10%. Must be greater than `TickMath.MIN_SQRT_RATIO` because
+/// we reuse a base 1.0001 logarithm in `BalanceSheet`
 uint256 constant LTV_MIN = 0.10e12;
 
 /// @dev The maximum loan-to-value ratio. Actual ratio is based on implied volatility; this is just a upper bound.

From 441e9aada2917aebe75ded7f7a8b10ac6cb75f87 Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Sun, 10 Sep 2023 23:22:08 -0500
Subject: [PATCH 10/11] Add digit to nSigma so it's more governable

---
 core/.gas-snapshot                         | 30 ++++----
 core/src/libraries/BalanceSheet.sol        |  2 +-
 core/src/libraries/Volatility.sol          |  1 +
 core/src/libraries/constants/Constants.sol | 16 ++--
 core/test/libraries/BalanceSheet.t.sol     | 88 +++++++++++-----------
 5 files changed, 72 insertions(+), 65 deletions(-)

diff --git a/core/.gas-snapshot b/core/.gas-snapshot
index d77ccd12..0c9ebb2e 100644
--- a/core/.gas-snapshot
+++ b/core/.gas-snapshot
@@ -1,15 +1,15 @@
 BorrowerGasTest:test_addMargin() (gas: 16203)
-BorrowerGasTest:test_borrow() (gas: 110565)
+BorrowerGasTest:test_borrow() (gas: 110577)
 BorrowerGasTest:test_getUniswapPositions() (gas: 5219)
-BorrowerGasTest:test_modify() (gas: 82162)
-BorrowerGasTest:test_modifyWithAnte() (gas: 88617)
-BorrowerGasTest:test_repay() (gas: 111924)
-BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257777)
+BorrowerGasTest:test_modify() (gas: 82174)
+BorrowerGasTest:test_modifyWithAnte() (gas: 88629)
+BorrowerGasTest:test_repay() (gas: 111936)
+BorrowerGasTest:test_uniswapDepositInBorrower() (gas: 257789)
 BorrowerGasTest:test_uniswapDepositStandard() (gas: 167558)
-BorrowerGasTest:test_uniswapWithdraw() (gas: 147664)
-BorrowerGasTest:test_withdraw() (gas: 105682)
+BorrowerGasTest:test_uniswapWithdraw() (gas: 147673)
+BorrowerGasTest:test_withdraw() (gas: 105694)
 FactoryGasTest:test_createBorrower() (gas: 156519)
-FactoryGasTest:test_createMarket() (gas: 3903606)
+FactoryGasTest:test_createMarket() (gas: 3904606)
 LenderGasTest:test_accrueInterest() (gas: 46070)
 LenderGasTest:test_borrow() (gas: 40834)
 LenderGasTest:test_deposit() (gas: 53422)
@@ -17,10 +17,10 @@ LenderGasTest:test_depositWithCourier() (gas: 53568)
 LenderGasTest:test_redeem() (gas: 53114)
 LenderGasTest:test_redeemWithCourier() (gas: 83506)
 LenderGasTest:test_repay() (gas: 44774)
-LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51093)
-LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59274)
-LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95674)
-LiquidatorGasTest:test_warn() (gas: 35077)
-LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130258)
-VolatilityGasTest:test_consult() (gas: 43075)
-VolatilityGasTest:test_updateNoBinarySearch() (gas: 145902)
\ No newline at end of file
+LiquidatorGasTest:test_noCallbackOneAsset() (gas: 51105)
+LiquidatorGasTest:test_noCallbackTwoAssets() (gas: 59286)
+LiquidatorGasTest:test_noCallbackTwoAssetsAndUniswapPosition() (gas: 95684)
+LiquidatorGasTest:test_warn() (gas: 35089)
+LiquidatorGasTest:test_withCallbackAndSwap() (gas: 130270)
+VolatilityGasTest:test_consult() (gas: 43024)
+VolatilityGasTest:test_updateNoBinarySearch() (gas: 145908)
\ No newline at end of file
diff --git a/core/src/libraries/BalanceSheet.sol b/core/src/libraries/BalanceSheet.sol
index a11ed7d1..2005cd42 100644
--- a/core/src/libraries/BalanceSheet.sol
+++ b/core/src/libraries/BalanceSheet.sol
@@ -87,7 +87,7 @@ library BalanceSheet {
         uint56 metric
     ) internal pure returns (uint160 a, uint160 b, bool isSus) {
         unchecked {
-            iv = SoladyMath.clamp(nSigma * iv, PROBE_PERCENT_MIN, PROBE_PERCENT_MAX);
+            iv = SoladyMath.clamp((nSigma * iv) / 10, PROBE_PERCENT_MIN, PROBE_PERCENT_MAX);
             isSus = metric > _manipulationThreshold(_effectiveCollateralFactor(iv));
 
             a = uint160((sqrtMeanPriceX96 * SoladyMath.sqrt(1e12 - iv)) / 1e6);
diff --git a/core/src/libraries/Volatility.sol b/core/src/libraries/Volatility.sol
index 19dad4a2..200d7032 100644
--- a/core/src/libraries/Volatility.sol
+++ b/core/src/libraries/Volatility.sol
@@ -32,6 +32,7 @@ library Volatility {
 
     /**
      * @notice Estimates implied volatility using [this math](https://lambert-guillaume.medium.com/on-chain-volatility-and-uniswap-v3-d031b98143d1).
+     * @dev The return value can fit in uint128 if necessary
      * @param metadata The pool's metadata (may be cached)
      * @param data A summary of the pool's state from `pool.slot0` `pool.observe` and `pool.liquidity`
      * @param a The pool's cumulative feeGrowthGlobals some time in the past
diff --git a/core/src/libraries/constants/Constants.sol b/core/src/libraries/constants/Constants.sol
index 4b0e2e7f..6ed74f72 100644
--- a/core/src/libraries/constants/Constants.sol
+++ b/core/src/libraries/constants/Constants.sol
@@ -32,8 +32,8 @@ uint256 constant MAX_RATE = 706354;
 uint216 constant DEFAULT_ANTE = 0.01 ether;
 
 /// @dev The default number of standard deviations of price movement used to determine probe prices for `Borrower`
-/// solvency. The `Factory` can override this value on a per-market basis.
-uint8 constant DEFAULT_N_SIGMA = 5;
+/// solvency. The `Factory` can override this value on a per-market basis. Expressed x10, e.g. 50 → 5σ
+uint8 constant DEFAULT_N_SIGMA = 50;
 
 /// @dev The default portion of interest that will accrue to a `Lender`'s `RESERVE` address.
 /// Expressed as a reciprocal, e.g. 16 → 6.25%
@@ -43,11 +43,13 @@ uint8 constant DEFAULT_RESERVE_FACTOR = 16;
                         GOVERNANCE CONSTRAINTS
 //////////////////////////////////////////////////////////////*/
 
-/// @dev The lowest number of standard deviations of price movement allowed for determining `Borrower` probe prices
-uint8 constant CONSTRAINT_N_SIGMA_MIN = 4;
+/// @dev The lowest number of standard deviations of price movement allowed for determining `Borrower` probe prices.
+/// Expressed x10, e.g. 40 → 4σ
+uint8 constant CONSTRAINT_N_SIGMA_MIN = 40;
 
-/// @dev The highest number of standard deviations of price movement allowed for determining `Borrower` probe prices
-uint8 constant CONSTRAINT_N_SIGMA_MAX = 5;
+/// @dev The highest number of standard deviations of price movement allowed for determining `Borrower` probe prices.
+/// Expressed x10, e.g. 80 → 8σ
+uint8 constant CONSTRAINT_N_SIGMA_MAX = 80;
 
 /// @dev The lower bound on what any `Lender`'s reserve factor can be. Expressed as reciprocal, e.g. 4 → 25%
 uint8 constant CONSTRAINT_RESERVE_FACTOR_MIN = 4;
@@ -108,7 +110,7 @@ uint32 constant IV_SCALE = 24 hours;
 /// @dev The initial value of implied volatility, used when `VolatilityOracle.prepare` is called for a new pool.
 /// Expressed as a 1e12 percentage at `IV_SCALE`, e.g. {0.20e12, 24 hours} → 20% daily → 382% annual. Error on the
 /// side of making this too large (resulting in low LTV).
-uint128 constant IV_COLD_START = uint128(PROBE_PERCENT_MAX / DEFAULT_N_SIGMA);
+uint128 constant IV_COLD_START = uint128((PROBE_PERCENT_MAX * 10) / CONSTRAINT_N_SIGMA_MIN);
 
 /// @dev The maximum rate at which (reported) implied volatility can change. Raw samples in `VolatilityOracle.update`
 /// are clamped (before being stored) so as not to exceed this rate.
diff --git a/core/test/libraries/BalanceSheet.t.sol b/core/test/libraries/BalanceSheet.t.sol
index 2337ad38..bc462bca 100644
--- a/core/test/libraries/BalanceSheet.t.sol
+++ b/core/test/libraries/BalanceSheet.t.sol
@@ -23,109 +23,109 @@ contract BalanceSheetTest is Test {
     function test_spec_computeProbePrices() public {
         bool isSus;
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.00e12, 5, 87);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.00e12, 50, 87);
         assertFalse(isSus, "0.00 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.00e12, 5, 88);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.00e12, 50, 88);
         assertTrue(isSus, "0.00 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.01e12, 5, 87);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.01e12, 50, 87);
         assertFalse(isSus, "0.01 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.01e12, 5, 88);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.01e12, 50, 88);
         assertTrue(isSus, "0.01 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.02e12, 5, 132);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.02e12, 50, 132);
         assertFalse(isSus, "0.02 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.02e12, 5, 133);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.02e12, 50, 133);
         assertTrue(isSus, "0.02 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.03e12, 5, 180);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.03e12, 50, 180);
         assertFalse(isSus, "0.03 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.03e12, 5, 181);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.03e12, 50, 181);
         assertTrue(isSus, "0.03 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.04e12, 5, 230);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.04e12, 50, 230);
         assertFalse(isSus, "0.04 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.04e12, 5, 231);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.04e12, 50, 231);
         assertTrue(isSus, "0.04 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.05e12, 5, 284);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.05e12, 50, 284);
         assertFalse(isSus, "0.05 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.05e12, 5, 285);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.05e12, 50, 285);
         assertTrue(isSus, "0.05 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.06e12, 5, 341);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.06e12, 50, 341);
         assertFalse(isSus, "0.06 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.06e12, 5, 342);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.06e12, 50, 342);
         assertTrue(isSus, "0.06 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.07e12, 5, 403);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.07e12, 50, 403);
         assertFalse(isSus, "0.07 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.07e12, 5, 404);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.07e12, 50, 404);
         assertTrue(isSus, "0.07 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.08e12, 5, 470);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.08e12, 50, 470);
         assertFalse(isSus, "0.08 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.08e12, 5, 471);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.08e12, 50, 471);
         assertTrue(isSus, "0.08 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.09e12, 5, 542);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.09e12, 50, 542);
         assertFalse(isSus, "0.09 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.09e12, 5, 543);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.09e12, 50, 543);
         assertTrue(isSus, "0.09 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.10e12, 5, 622);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.10e12, 50, 622);
         assertFalse(isSus, "0.10 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.10e12, 5, 623);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.10e12, 50, 623);
         assertTrue(isSus, "0.10 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.11e12, 5, 710);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.11e12, 50, 710);
         assertFalse(isSus, "0.11 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.11e12, 5, 711);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.11e12, 50, 711);
         assertTrue(isSus, "0.11 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.12e12, 5, 808);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.12e12, 50, 808);
         assertFalse(isSus, "0.12 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.12e12, 5, 809);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.12e12, 50, 809);
         assertTrue(isSus, "0.12 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.13e12, 5, 919);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.13e12, 50, 919);
         assertFalse(isSus, "0.13 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.13e12, 5, 920);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.13e12, 50, 920);
         assertTrue(isSus, "0.13 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.14e12, 5, 1048);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.14e12, 50, 1048);
         assertFalse(isSus, "0.14 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.14e12, 5, 1049);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.14e12, 50, 1049);
         assertTrue(isSus, "0.14 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.15e12, 5, 1199);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.15e12, 50, 1199);
         assertFalse(isSus, "0.15 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.15e12, 5, 1200);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.15e12, 50, 1200);
         assertTrue(isSus, "0.15 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.16e12, 5, 1385);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.16e12, 50, 1385);
         assertFalse(isSus, "0.16 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.16e12, 5, 1386);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.16e12, 50, 1386);
         assertTrue(isSus, "0.16 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.17e12, 5, 1625);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.17e12, 50, 1625);
         assertFalse(isSus, "0.17 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.17e12, 5, 1626);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.17e12, 50, 1626);
         assertTrue(isSus, "0.17 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.18e12, 5, 1918);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.18e12, 50, 1918);
         assertFalse(isSus, "0.18 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.18e12, 5, 1919);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.18e12, 50, 1919);
         assertTrue(isSus, "0.18 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.19e12, 5, 1918);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.19e12, 50, 1918);
         assertFalse(isSus, "0.19 false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.19e12, 5, 1919);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, 0.19e12, 50, 1919);
         assertTrue(isSus, "0.19 true");
 
-        (, , isSus) = BalanceSheet.computeProbePrices(0, IV_COLD_START, 5, 1918);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, IV_COLD_START, 50, 1918);
         assertFalse(isSus, "cold start false");
-        (, , isSus) = BalanceSheet.computeProbePrices(0, IV_COLD_START, 5, 1919);
+        (, , isSus) = BalanceSheet.computeProbePrices(0, IV_COLD_START, 50, 1919);
         assertTrue(isSus, "cold start true");
     }
 
@@ -159,6 +159,10 @@ contract BalanceSheetTest is Test {
         assertEqDecimal(PROBE_PERCENT_MIN, 50500000000, 12);
         assertEqDecimal(PROBE_PERCENT_MAX, 894500000000, 12);
 
+        // Necessary for iv scaling not to overflow
+        assertLt(PROBE_PERCENT_MIN, 1 << 128);
+        assertLt(PROBE_PERCENT_MAX, 1 << 128);
+
         // Necessary for collateral factor computation to work
         assertGt(LTV_MIN, TickMath.MIN_SQRT_RATIO);
     }

From 453754a656d9320c9b1dd1f0bc1ab888817575f2 Mon Sep 17 00:00:00 2001
From: Hayden Shively <17186559+haydenshively@users.noreply.github.com>
Date: Sun, 10 Sep 2023 23:35:25 -0500
Subject: [PATCH 11/11] Fix test

---
 core/test/libraries/BalanceSheet.t.sol | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/core/test/libraries/BalanceSheet.t.sol b/core/test/libraries/BalanceSheet.t.sol
index bc462bca..75631244 100644
--- a/core/test/libraries/BalanceSheet.t.sol
+++ b/core/test/libraries/BalanceSheet.t.sol
@@ -147,11 +147,11 @@ contract BalanceSheetTest is Test {
         a = square(uint160(a));
         b = square(uint160(b));
 
-        if (iv < PROBE_PERCENT_MIN / nSigma) iv = PROBE_PERCENT_MIN / nSigma;
-        else if (iv > PROBE_PERCENT_MAX / nSigma) iv = PROBE_PERCENT_MAX / nSigma;
+        if (iv < PROBE_PERCENT_MIN * 10 / nSigma) iv = PROBE_PERCENT_MIN * 10 / nSigma;
+        else if (iv > PROBE_PERCENT_MAX * 10 / nSigma) iv = PROBE_PERCENT_MAX * 10 / nSigma;
 
-        assertApproxEqRel(a, SoladyMath.fullMulDiv(price, 1e12 - nSigma * iv, 1e12), 0.0001e18);
-        assertApproxEqRel(b, SoladyMath.fullMulDiv(price, 1e12 + nSigma * iv, 1e12), 0.0001e18);
+        assertApproxEqRel(a, SoladyMath.fullMulDiv(price, 1e12 - (nSigma * iv) / 10, 1e12), 0.0001e18);
+        assertApproxEqRel(b, SoladyMath.fullMulDiv(price, 1e12 + (nSigma * iv) / 10, 1e12), 0.0001e18);
     }
 
     function test_constants() public {