harb/onchain/src/Optimizer.sol

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.19;

import { Kraiken } from "./Kraiken.sol";
import { Stake } from "./Stake.sol";

import { Initializable } from "@openzeppelin/proxy/utils/Initializable.sol";
import { UUPSUpgradeable } from "@openzeppelin/proxy/utils/UUPSUpgradeable.sol";

/**
 * @title Optimizer
 * @notice This contract (formerly Sentimenter) calculates a "sentiment" value and liquidity parameters
 *         based on the tax rate and the percentage of Kraiken staked.
 * @dev It is upgradeable using UUPS. Only the admin (set during initialization) can upgrade.
 *
 * Key features:
 * - Analyzes staking sentiment (% staked, average tax rate)
 * - Returns four key parameters for liquidity management:
 *   1. capitalInefficiency (0 to 1e18): Capital buffer level
 *   2. anchorShare (0 to 1e18): % of non-floor ETH in anchor
 *   3. anchorWidth (0 to 100): Anchor position width %
 *   4. discoveryDepth (0 to 1e18): Discovery liquidity density (2x-10x)
 * - Upgradeable for future algorithm improvements
 *
 * AnchorWidth Price Ranges:
 * The anchor position's price range depends on anchorWidth value:
 * - anchorWidth = 10: ±9% range (0.92x to 1.09x current price)
 * - anchorWidth = 40: ±33% range (0.75x to 1.34x current price)
 * - anchorWidth = 50: ±42% range (0.70x to 1.43x current price)
 * - anchorWidth = 80: ±74% range (0.57x to 1.75x current price)
 * - anchorWidth = 100: -50% to +100% range (0.50x to 2.00x current price)
 *
 * The formula: anchorSpacing = TICK_SPACING + (34 * anchorWidth * TICK_SPACING / 100)
 * creates a non-linear price range due to Uniswap V3's tick-based system
 */
contract Optimizer is Initializable, UUPSUpgradeable {
    Kraiken private kraiken;
    Stake private stake;

    /// @dev Reverts if the caller is not the admin.
    error UnauthorizedAccount(address account);

    /**
     * @notice Initialize the Optimizer.
     * @param _kraiken The address of the Kraiken token.
     * @param _stake The address of the Stake contract.
     */
    function initialize(address _kraiken, address _stake) public initializer {
        // Set the admin for upgradeability (using ERC1967Upgrade _changeAdmin)
        _changeAdmin(msg.sender);
        kraiken = Kraiken(_kraiken);
        stake = Stake(_stake);
    }

    modifier onlyAdmin() {
        _checkAdmin();
        _;
    }

    function _checkAdmin() internal view virtual {
        if (_getAdmin() != msg.sender) {
            revert UnauthorizedAccount(msg.sender);
        }
    }

    function _authorizeUpgrade(address newImplementation) internal override onlyAdmin { }

    /**
     * @notice Calculates the sentiment based on the average tax rate and the percentage staked.
     * @param averageTaxRate The average tax rate (as returned by the Stake contract).
     * @param percentageStaked The percentage (in 1e18 precision) of the authorized stake that is currently staked.
     * @return sentimentValue A value in the range 0 to 1e18 where 1e18 represents the worst sentiment.
     */
    function calculateSentiment(uint256 averageTaxRate, uint256 percentageStaked) public pure returns (uint256 sentimentValue) {
        // Ensure percentageStaked doesn't exceed 100%
        require(percentageStaked <= 1e18, "Invalid percentage staked");

        // deltaS is the "slack" available below full staking
        uint256 deltaS = 1e18 - percentageStaked;

        if (percentageStaked > 92e16) {
            // If more than 92% of the authorized stake is in use, the sentiment drops rapidly.
            // Penalty is computed as: (deltaS^3 * averageTaxRate) / (20 * 1e48)
            uint256 penalty = (deltaS * deltaS * deltaS * averageTaxRate) / (20 * 1e48);
            sentimentValue = penalty / 2;
        } else {
            // For lower staked percentages, sentiment decreases roughly linearly.
            // Ensure we don't underflow if percentageStaked approaches 92%
            uint256 scaledStake = (percentageStaked * 1e18) / (92e16);
            uint256 baseSentiment = scaledStake >= 1e18 ? 0 : 1e18 - scaledStake;
            // Apply a penalty based on the average tax rate.
            if (averageTaxRate <= 1e16) {
                sentimentValue = baseSentiment;
            } else if (averageTaxRate <= 5e16) {
                uint256 ratePenalty = ((averageTaxRate - 1e16) * baseSentiment) / (4e16);
                sentimentValue = baseSentiment > ratePenalty ? baseSentiment - ratePenalty : 0;
            } else {
                // For very high tax rates, sentiment is maximally poor.
                sentimentValue = 1e18;
            }
        }
        return sentimentValue;
    }

    /**
     * @notice Returns the current sentiment.
     * @return sentiment A number (with 1e18 precision) representing the staker sentiment.
     */
    function getSentiment() external view returns (uint256 sentiment) {
        uint256 percentageStaked = stake.getPercentageStaked();
        uint256 averageTaxRate = stake.getAverageTaxRate();
        sentiment = calculateSentiment(averageTaxRate, percentageStaked);
    }

    /**
     * @notice Calculates the optimal anchor width based on staking metrics.
     * @param percentageStaked The percentage of tokens staked (0 to 1e18)
     * @param averageTaxRate The average tax rate across all stakers (0 to 1e18)
     * @return anchorWidth The calculated anchor width (10 to 80)
     *
     * @dev This function implements a staking-based approach to determine anchor width:
     *
     * Base Strategy:
     * - Start with base width of 40% (balanced default)
     *
     * Staking Adjustment (-20% to +20%):
     * - High staking (>70%) indicates bullish confidence → narrow anchor for fee optimization
     * - Low staking (<30%) indicates bearish/uncertainty → wide anchor for safety
     * - Inverse relationship: higher staking = lower width adjustment
     *
     * Tax Rate Adjustment (-10% to +30%):
     * - High tax rates signal expected volatility → wider anchor to reduce rebalancing
     * - Low tax rates signal expected stability → narrower anchor for fee collection
     * - Direct relationship: higher tax = higher width adjustment
     *
     * The Harberger tax mechanism acts as a decentralized prediction market where:
     * - Tax rates reflect holders' expectations of being "snatched" (volatility)
     * - Staking percentage reflects overall market confidence
     *
     * Final width is clamped between 10 (minimum safe) and 80 (maximum effective)
     */
    function _calculateAnchorWidth(uint256 percentageStaked, uint256 averageTaxRate) internal pure returns (uint24) {
        // Base width: 40% is our neutral starting point
        int256 baseWidth = 40;

        // Staking adjustment: -20% to +20% based on staking percentage
        // Formula: 20 - (percentageStaked * 40 / 1e18)
        // High staking (1e18) → -20 adjustment → narrower width
        // Low staking (0) → +20 adjustment → wider width
        int256 stakingAdjustment = 20 - int256(percentageStaked * 40 / 1e18);

        // Tax rate adjustment: -10% to +30% based on average tax rate
        // Formula: (averageTaxRate * 40 / 1e18) - 10
        // High tax (1e18) → +30 adjustment → wider width for volatility
        // Low tax (0) → -10 adjustment → narrower width for stability
        int256 taxAdjustment = int256(averageTaxRate * 40 / 1e18) - 10;

        // Combine all adjustments
        int256 totalWidth = baseWidth + stakingAdjustment + taxAdjustment;

        // Clamp to safe bounds (10 to 80)
        // Below 10%: rebalancing costs exceed benefits
        // Above 80%: capital efficiency degrades significantly
        if (totalWidth < 10) {
            return 10;
        }
        if (totalWidth > 80) {
            return 80;
        }

        return uint24(uint256(totalWidth));
    }

    /**
     * @notice Returns liquidity parameters for the liquidity manager.
     * @return capitalInefficiency Calculated as (1e18 - sentiment). Capital buffer level (0-1e18)
     * @return anchorShare         Set equal to the sentiment. % of non-floor ETH in anchor (0-1e18)
     * @return anchorWidth         Dynamically adjusted based on staking metrics. Anchor position width % (1-100)
     * @return discoveryDepth      Set equal to the sentiment.
     *
     * @dev AnchorWidth Strategy:
     * The anchorWidth parameter controls the price range of the anchor liquidity position.
     * - anchorWidth = 50: Price range from 0.70x to 1.43x current price
     * - anchorWidth = 100: Price range from 0.50x to 2.00x current price
     *
     * We use staking metrics as a decentralized prediction market:
     * - High staking % → Bullish sentiment → Narrower width (30-50%) for fee optimization
     * - Low staking % → Bearish/uncertain → Wider width (60-80%) for defensive positioning
     * - High avg tax rate → Expects volatility → Wider anchor to reduce rebalancing
     * - Low avg tax rate → Expects stability → Narrower anchor for fee collection
     */
    function getLiquidityParams() external view returns (uint256 capitalInefficiency, uint256 anchorShare, uint24 anchorWidth, uint256 discoveryDepth) {
        uint256 percentageStaked = stake.getPercentageStaked();
        uint256 averageTaxRate = stake.getAverageTaxRate();
        uint256 sentiment = calculateSentiment(averageTaxRate, percentageStaked);

        // Ensure sentiment doesn't exceed 1e18 to prevent underflow
        // Cap sentiment at 1e18 if it somehow exceeds it
        if (sentiment > 1e18) {
            sentiment = 1e18;
        }
        capitalInefficiency = 1e18 - sentiment;
        anchorShare = sentiment;

        // Calculate dynamic anchorWidth based on staking metrics
        anchorWidth = _calculateAnchorWidth(percentageStaked, averageTaxRate);

        discoveryDepth = sentiment;
    }
}