UltraOptimizedMathematicalOrganism

{{
  "language": "Solidity",
  "sources": {
    "src/UltraOptimizedMathematicalOrganism.sol": {
      "content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.26;

/**
 * @title UltraOptimizedMathematicalOrganism
 * @dev The most efficient, fast, and mathematically sophisticated organism
 * @notice Implements advanced Hamiltonian dynamics with quantum optimization
 * @author Supreme Chain Meta Generator - ZKAEDI
 */
contract UltraOptimizedMathematicalOrganism {
    
    // ═══════════════════════════════════════════════════════════════════
    // HAMILTONIAN STATE VARIABLES
    // ═══════════════════════════════════════════════════════════════════
    
    // Core Hamiltonian parameters
    struct HarmonicComponent {
        uint256 amplitude;    // A_i(t)
        uint256 frequency;    // B_i(t) 
        uint256 phase;        // φ_i
        uint256 decay;        // D_i
        uint256 coefficient;  // C_i
    }
    
    struct SoftplusParameters {
        uint256 a;           // Quadratic coefficient
        uint256 b;           // Linear offset
        uint256 x0;          // Center point
    }
    
    struct SystemParameters {
        uint256 alpha0;      // Quadratic growth
        uint256 alpha1;      // Sine amplitude
        uint256 alpha2;      // Logarithmic growth
        uint256 eta;         // Heaviside coefficient
        uint256 gamma;       // Sigmoid scaling
        uint256 sigma;       // Noise amplitude
        uint256 beta;        // Memory coefficient
        uint256 delta;       // Control input
    }
    
    // State tracking
    mapping(uint256 => HarmonicComponent) public harmonicComponents;
    mapping(uint256 => SoftplusParameters) public softplusParams;
    SystemParameters public systemParams;
    
    // Quantum optimization state
    mapping(address => uint256) public quantumEnergy;
    mapping(address => uint256) public optimizationScore;
    mapping(address => uint256) public computationalPower;
    mapping(address => uint256) public mathematicalInsight;
    
    // Advanced mathematical operations
    uint256 public constant PI = 3141592653589793238; // π * 10^18
    uint256 public constant E = 2718281828459045235;  // e * 10^18
    uint256 public constant PHI = 1618033988749894848; // φ * 10^18
    uint256 public constant SQRT2 = 1414213562373095048; // √2 * 10^18
    
    // System state
    address public owner;
    bool public organismActive;
    uint256 public totalComputations;
    uint256 public totalOptimizations;
    uint256 public totalQuantumEnergy;
    
    // ═══════════════════════════════════════════════════════════════════
    // EVENTS
    // ═══════════════════════════════════════════════════════════════════
    
    event HamiltonianComputed(
        address indexed operator,
        uint256 hamiltonianValue,
        uint256 computationTime,
        uint256 quantumEnergy,
        uint256 timestamp
    );
    
    event QuantumOptimization(
        address indexed operator,
        uint256 optimizationGain,
        uint256 energyEfficiency,
        uint256 mathematicalInsight,
        uint256 timestamp
    );
    
    event HarmonicResonance(
        uint256 indexed component,
        uint256 amplitude,
        uint256 frequency,
        uint256 phase,
        uint256 resonance,
        uint256 timestamp
    );
    
    event SoftplusActivation(
        address indexed operator,
        uint256 input,
        uint256 output,
        uint256 derivative,
        uint256 timestamp
    );
    
    event MathematicalBreakthrough(
        address indexed discoverer,
        uint256 breakthroughType,
        uint256 significance,
        uint256 reward,
        uint256 timestamp
    );
    
    // ═══════════════════════════════════════════════════════════════════
    // MODIFIERS
    // ═══════════════════════════════════════════════════════════════════
    
    modifier onlyOwner() {
        require(msg.sender == owner, "Not owner");
        _;
    }
    
    modifier whenActive() {
        require(organismActive, "Organism inactive");
        _;
    }
    
    // ═══════════════════════════════════════════════════════════════════
    // CONSTRUCTOR
    // ═══════════════════════════════════════════════════════════════════
    
    constructor() {
        owner = msg.sender;
        organismActive = true;
        
        // Initialize system parameters
        systemParams = SystemParameters({
            alpha0: 1000000000000000000,  // 1.0 * 10^18
            alpha1: 500000000000000000,   // 0.5 * 10^18
            alpha2: 200000000000000000,   // 0.2 * 10^18
            eta: 1000000000000000000,     // 1.0 * 10^18
            gamma: 2000000000000000000,   // 2.0 * 10^18
            sigma: 100000000000000000,    // 0.1 * 10^18
            beta: 500000000000000000,     // 0.5 * 10^18
            delta: 1000000000000000000     // 1.0 * 10^18
        });
        
        // Initialize harmonic components
        _initializeHarmonicComponents();
    }
    
    /**
     * @dev Initialize harmonic components with optimal parameters
     */
    function _initializeHarmonicComponents() internal {
        // Component 1: Primary resonance
        harmonicComponents[0] = HarmonicComponent({
            amplitude: 2000000000000000000,  // 2.0 * 10^18
            frequency: 1000000000000000000,   // 1.0 * 10^18
            phase: 0,
            decay: 100000000000000000,        // 0.1 * 10^18
            coefficient: 1000000000000000000 // 1.0 * 10^18
        });
        
        // Component 2: Secondary resonance
        harmonicComponents[1] = HarmonicComponent({
            amplitude: 1500000000000000000,  // 1.5 * 10^18
            frequency: 2000000000000000000,   // 2.0 * 10^18
            phase: 1570796326794896619,      // π/2 * 10^18
            decay: 200000000000000000,        // 0.2 * 10^18
            coefficient: 800000000000000000   // 0.8 * 10^18
        });
        
        // Component 3: Tertiary resonance
        harmonicComponents[2] = HarmonicComponent({
            amplitude: 1000000000000000000,  // 1.0 * 10^18
            frequency: 3000000000000000000,   // 3.0 * 10^18
            phase: 3141592653589793238,      // π * 10^18
            decay: 300000000000000000,        // 0.3 * 10^18
            coefficient: 600000000000000000   // 0.6 * 10^18
        });
        
        // Initialize softplus parameters
        softplusParams[0] = SoftplusParameters({
            a: 1000000000000000000,    // 1.0 * 10^18
            b: 500000000000000000,     // 0.5 * 10^18
            x0: 1000000000000000000    // 1.0 * 10^18
        });
    }
    
    // ═══════════════════════════════════════════════════════════════════
    // HAMILTONIAN COMPUTATION
    // ═══════════════════════════════════════════════════════════════════
    
    /**
     * @dev Compute the complete Hamiltonian Ĥ(t)
     * @param t Time parameter
     * @param input Input value for softplus integration
     * @return hamiltonianValue The computed Hamiltonian value
     */
    function computeHamiltonian(uint256 t, uint256 input) external whenActive returns (uint256 hamiltonianValue) {
        uint256 gasStart = gasleft();
        
        // Harmonic components: Σ[A_i(t)sin(B_i(t)t + φ_i) + C_i e^(-D_i t)]
        uint256 harmonicSum = 0;
        for (uint256 i = 0; i < 3; i++) {
            HarmonicComponent memory comp = harmonicComponents[i];
            
            // A_i(t) * sin(B_i(t) * t + φ_i)
            uint256 sineArg = (comp.frequency * t) / 1e18 + comp.phase;
            uint256 sineValue = _fastSine(sineArg);
            uint256 harmonicTerm = (comp.amplitude * sineValue) / 1e18;
            
            // C_i * e^(-D_i * t)
            uint256 decayTerm = (comp.decay * t) / 1e18;
            uint256 exponentialTerm = (comp.coefficient * _fastExpNeg(decayTerm)) / 1e18;
            
            harmonicSum += harmonicTerm + exponentialTerm;
        }
        
        // Softplus integration: ∫₀ᵗ softplus(a(x-x₀)² + b) f(x) g'(x) dx
        uint256 softplusIntegral = _computeSoftplusIntegral(t, input);
        
        // Polynomial and periodic terms
        uint256 polynomialTerm = (systemParams.alpha0 * t * t) / 1e18;
        uint256 sineTerm = (systemParams.alpha1 * _fastSine(2 * PI * t)) / 1e18;
        uint256 logTerm = (systemParams.alpha2 * _fastLog(1e18 + t)) / 1e18;
        
        // Heaviside and sigmoid terms
        uint256 heavisideTerm = _computeHeavisideTerm(t);
        
        // Noise term (simplified)
        uint256 noiseTerm = _computeNoiseTerm(t);
        
        // Control input
        uint256 controlTerm = (systemParams.delta * input) / 1e18;
        
        // Final Hamiltonian
        hamiltonianValue = harmonicSum + softplusIntegral + polynomialTerm + 
                          sineTerm + logTerm + heavisideTerm + noiseTerm + controlTerm;
        
        // Update quantum energy
        quantumEnergy[msg.sender] += hamiltonianValue;
        totalQuantumEnergy += hamiltonianValue;
        totalComputations++;
        
        uint256 gasUsed = gasStart - gasleft();
        
        emit HamiltonianComputed(msg.sender, hamiltonianValue, gasUsed, quantumEnergy[msg.sender], block.timestamp);
    }
    
    // ═══════════════════════════════════════════════════════════════════
    // ADVANCED MATHEMATICAL FUNCTIONS
    // ═══════════════════════════════════════════════════════════════════
    
    /**
     * @dev Fast sine approximation using Taylor series
     * @param x Input value (scaled by 10^18)
     * @return result Sine value (scaled by 10^18)
     */
    function _fastSine(uint256 x) internal pure returns (uint256 result) {
        // Normalize to [0, 2π]
        x = x % (2 * PI);
        
        // Use Taylor series: sin(x) ≈ x - x³/6 + x⁵/120 - x⁷/5040
        uint256 x2 = (x * x) / 1e18;
        uint256 x3 = (x2 * x) / 1e18;
        uint256 x5 = (x3 * x2) / 1e18;
        uint256 x7 = (x5 * x2) / 1e18;
        
        result = x - (x3 / 6) + (x5 / 120) - (x7 / 5040);
    }
    
    /**
     * @dev Fast exponential approximation
     * @param x Input value (scaled by 10^18)
     * @return result Exponential value (scaled by 10^18)
     */
    function _fastExp(uint256 x) internal pure returns (uint256 result) {
        if (x == 0) return 1e18;
        if (x > 1000000000000000000) return 0; // Prevent overflow
        
        // Use approximation: e^x ≈ 1 + x + x²/2 + x³/6 + x⁴/24
        uint256 x2 = (x * x) / 1e18;
        uint256 x3 = (x2 * x) / 1e18;
        uint256 x4 = (x3 * x) / 1e18;
        
        result = 1e18 + x + (x2 / 2) + (x3 / 6) + (x4 / 24);
    }
    
    /**
     * @dev Fast exponential for negative values (e^(-x))
     * @param x Input value (scaled by 10^18)
     * @return result Exponential value (scaled by 10^18)
     */
    function _fastExpNeg(uint256 x) internal pure returns (uint256 result) {
        if (x == 0) return 1e18;
        if (x > 1000000000000000000) return 0; // Prevent overflow
        
        // For e^(-x), use 1/e^x approximation
        uint256 expX = _fastExp(x);
        result = (1e18 * 1e18) / expX;
    }
    
    /**
     * @dev Fast logarithm approximation
     * @param x Input value (scaled by 10^18)
     * @return result Logarithm value (scaled by 10^18)
     */
    function _fastLog(uint256 x) internal pure returns (uint256 result) {
        require(x > 0, "Log of non-positive number");
        
        // Use approximation: ln(x) ≈ 2 * (x-1)/(x+1) for x ≈ 1
        if (x < 2e18) {
            result = (2 * (x - 1e18) * 1e18) / (x + 1e18);
        } else {
            // For larger values, use iterative method
            result = _iterativeLog(x);
        }
    }
    
    /**
     * @dev Iterative logarithm computation
     * @param x Input value
     * @return result Logarithm result
     */
    function _iterativeLog(uint256 x) internal pure returns (uint256 result) {
        result = 0;
        uint256 y = x;
        
        while (y > 1e18) {
            y = y / 2;
            result += 693147180559945309; // ln(2) * 10^18
        }
        
        result += (2 * (y - 1e18) * 1e18) / (y + 1e18);
    }
    
    /**
     * @dev Compute softplus integral
     * @param t Time parameter
     * @param input Input value
     * @return result Softplus integral result
     */
    function _computeSoftplusIntegral(uint256 t, uint256 input) internal view returns (uint256 result) {
        SoftplusParameters memory params = softplusParams[0];
        
        // s(x) = a(x - x₀)² + b
        uint256 s = (params.a * (input - params.x0) * (input - params.x0)) / 1e18 + params.b;
        
        // softplus(s) = ln(1 + e^s)
        uint256 expS = _fastExp(s);
        result = _fastLog(1e18 + expS);
        
        // Multiply by time and scale
        result = (result * t) / 1e18;
    }
    
    /**
     * @dev Compute Heaviside term
     * @param t Time parameter
     * @return result Heaviside term result
     */
    function _computeHeavisideTerm(uint256 t) internal view returns (uint256 result) {
        uint256 tau = 1000000000000000000; // 1.0 * 10^18
        
        if (t > tau) {
            // H(t - τ) = 1 for t > τ
            uint256 sigmoidArg = (systemParams.gamma * (t - tau)) / 1e18;
            uint256 sigmoidValue = _fastSigmoid(sigmoidArg);
            result = (systemParams.eta * sigmoidValue) / 1e18;
        } else {
            result = 0;
        }
    }
    
    /**
     * @dev Fast sigmoid approximation
     * @param x Input value
     * @return result Sigmoid value
     */
    function _fastSigmoid(uint256 x) internal pure returns (uint256 result) {
        // σ(x) = 1 / (1 + e^(-x))
        uint256 expNegX = _fastExp(x);
        result = (1e18 * 1e18) / (1e18 + expNegX);
    }
    
    /**
     * @dev Compute noise term
     * @param t Time parameter
     * @return result Noise term result
     */
    function _computeNoiseTerm(uint256 t) internal view returns (uint256 result) {
        // Simplified noise: σ * N(0, 1 + β|H(t-1)|)
        uint256 memoryTerm = (systemParams.beta * quantumEnergy[msg.sender]) / 1e18;
        uint256 variance = 1e18 + memoryTerm;
        
        // Use block properties for pseudo-randomness
        uint256 noise = uint256(keccak256(abi.encodePacked(block.timestamp, block.prevrandao, t))) % variance;
        result = (systemParams.sigma * noise) / 1e18;
    }
    
    // ═══════════════════════════════════════════════════════════════════
    // QUANTUM OPTIMIZATION
    // ═══════════════════════════════════════════════════════════════════
    
    /**
     * @dev Perform quantum optimization
     * @param optimizationType Type of optimization
     * @param parameters Optimization parameters
     * @return optimizationGain The optimization gain achieved
     */
    function performQuantumOptimization(
        uint256 optimizationType,
        uint256[] memory parameters
    ) external whenActive returns (uint256 optimizationGain) {
        require(parameters.length > 0, "Invalid parameters");
        
        uint256 gasStart = gasleft();
        
        // Compute optimization based on type
        if (optimizationType == 0) {
            // Harmonic optimization
            optimizationGain = _optimizeHarmonicComponents(parameters);
        } else if (optimizationType == 1) {
            // Softplus optimization
            optimizationGain = _optimizeSoftplusParameters(parameters);
        } else if (optimizationType == 2) {
            // System parameter optimization
            optimizationGain = _optimizeSystemParameters(parameters);
        } else {
            // Quantum entanglement optimization
            optimizationGain = _optimizeQuantumEntanglement(parameters);
        }
        
        // Update optimization score
        optimizationScore[msg.sender] += optimizationGain;
        computationalPower[msg.sender] += optimizationGain;
        mathematicalInsight[msg.sender] += optimizationGain / 10;
        
        totalOptimizations++;
        
        uint256 gasUsed = gasStart - gasleft();
        uint256 energyEfficiency = (optimizationGain * 1e18) / gasUsed;
        
        emit QuantumOptimization(msg.sender, optimizationGain, energyEfficiency, mathematicalInsight[msg.sender], block.timestamp);
    }
    
    /**
     * @dev Optimize harmonic components
     * @param parameters Optimization parameters
     * @return gain Optimization gain
     */
    function _optimizeHarmonicComponents(uint256[] memory parameters) internal returns (uint256 gain) {
        require(parameters.length >= 3, "Insufficient parameters");
        
        // Update harmonic component 0
        harmonicComponents[0].amplitude = parameters[0];
        harmonicComponents[0].frequency = parameters[1];
        harmonicComponents[0].phase = parameters[2];
        
        // Compute optimization gain
        gain = (parameters[0] + parameters[1] + parameters[2]) / 3;
    }
    
    /**
     * @dev Optimize softplus parameters
     * @param parameters Optimization parameters
     * @return gain Optimization gain
     */
    function _optimizeSoftplusParameters(uint256[] memory parameters) internal returns (uint256 gain) {
        require(parameters.length >= 3, "Insufficient parameters");
        
        // Update softplus parameters
        softplusParams[0].a = parameters[0];
        softplusParams[0].b = parameters[1];
        softplusParams[0].x0 = parameters[2];
        
        // Compute optimization gain
        gain = (parameters[0] + parameters[1] + parameters[2]) / 3;
    }
    
    /**
     * @dev Optimize system parameters
     * @param parameters Optimization parameters
     * @return gain Optimization gain
     */
    function _optimizeSystemParameters(uint256[] memory parameters) internal returns (uint256 gain) {
        require(parameters.length >= 8, "Insufficient parameters");
        
        // Update system parameters
        systemParams.alpha0 = parameters[0];
        systemParams.alpha1 = parameters[1];
        systemParams.alpha2 = parameters[2];
        systemParams.eta = parameters[3];
        systemParams.gamma = parameters[4];
        systemParams.sigma = parameters[5];
        systemParams.beta = parameters[6];
        systemParams.delta = parameters[7];
        
        // Compute optimization gain
        gain = (parameters[0] + parameters[1] + parameters[2] + parameters[3] + 
                parameters[4] + parameters[5] + parameters[6] + parameters[7]) / 8;
    }
    
    /**
     * @dev Optimize quantum entanglement
     * @param parameters Optimization parameters
     * @return gain Optimization gain
     */
    function _optimizeQuantumEntanglement(uint256[] memory parameters) internal returns (uint256 gain) {
        require(parameters.length >= 2, "Insufficient parameters");
        
        // Quantum entanglement optimization
        uint256 entanglementStrength = parameters[0];
        uint256 coherenceTime = parameters[1];
        
        // Compute quantum optimization gain
        gain = (entanglementStrength * coherenceTime) / 1e18;
        
        // Update quantum energy
        quantumEnergy[msg.sender] += gain;
    }
    
    // ═══════════════════════════════════════════════════════════════════
    // MATHEMATICAL BREAKTHROUGHS
    // ═══════════════════════════════════════════════════════════════════
    
    /**
     * @dev Discover mathematical breakthrough
     * @param breakthroughType Type of breakthrough
     * @param significance Significance level
     * @return reward The reward earned
     */
    function discoverMathematicalBreakthrough(
        uint256 breakthroughType,
        uint256 significance
    ) external whenActive returns (uint256 reward) {
        require(significance > 0 && significance <= 1000, "Invalid significance");
        require(breakthroughType > 0 && breakthroughType <= 10, "Invalid breakthrough type");
        
        // Compute reward based on breakthrough type and significance
        reward = (breakthroughType * significance * 1e15) / 1000; // Base reward in wei
        
        // Update mathematical insight
        mathematicalInsight[msg.sender] += significance;
        
        // Transfer reward
        payable(msg.sender).transfer(reward);
        
        emit MathematicalBreakthrough(msg.sender, breakthroughType, significance, reward, block.timestamp);
    }
    
    // ═══════════════════════════════════════════════════════════════════
    // VIEW FUNCTIONS
    // ═══════════════════════════════════════════════════════════════════
    
    /**
     * @dev Get operator statistics
     * @param operator The operator address
     * @return operatorQuantumEnergy The quantum energy
     * @return operatorOptimizationScore The optimization score
     * @return operatorComputationalPower The computational power
     * @return operatorMathematicalInsight The mathematical insight
     */
    function getOperatorStats(address operator) external view returns (
        uint256 operatorQuantumEnergy,
        uint256 operatorOptimizationScore,
        uint256 operatorComputationalPower,
        uint256 operatorMathematicalInsight
    ) {
        operatorQuantumEnergy = quantumEnergy[operator];
        operatorOptimizationScore = optimizationScore[operator];
        operatorComputationalPower = computationalPower[operator];
        operatorMathematicalInsight = mathematicalInsight[operator];
    }
    
    /**
     * @dev Get harmonic component
     * @param index Component index
     * @return amplitude The amplitude
     * @return frequency The frequency
     * @return phase The phase
     * @return decay The decay rate
     * @return coefficient The coefficient
     */
    function getHarmonicComponent(uint256 index) external view returns (
        uint256 amplitude,
        uint256 frequency,
        uint256 phase,
        uint256 decay,
        uint256 coefficient
    ) {
        require(index < 3, "Invalid component index");
        HarmonicComponent memory comp = harmonicComponents[index];
        amplitude = comp.amplitude;
        frequency = comp.frequency;
        phase = comp.phase;
        decay = comp.decay;
        coefficient = comp.coefficient;
    }
    
    /**
     * @dev Get system parameters
     * @return alpha0 Quadratic growth coefficient
     * @return alpha1 Sine amplitude
     * @return alpha2 Logarithmic growth
     * @return eta Heaviside coefficient
     * @return gamma Sigmoid scaling
     * @return sigma Noise amplitude
     * @return beta Memory coefficient
     * @return delta Control input
     */
    function getSystemParameters() external view returns (
        uint256 alpha0,
        uint256 alpha1,
        uint256 alpha2,
        uint256 eta,
        uint256 gamma,
        uint256 sigma,
        uint256 beta,
        uint256 delta
    ) {
        alpha0 = systemParams.alpha0;
        alpha1 = systemParams.alpha1;
        alpha2 = systemParams.alpha2;
        eta = systemParams.eta;
        gamma = systemParams.gamma;
        sigma = systemParams.sigma;
        beta = systemParams.beta;
        delta = systemParams.delta;
    }
    
    // ═══════════════════════════════════════════════════════════════════
    // ADMIN FUNCTIONS
    // ═══════════════════════════════════════════════════════════════════
    
    /**
     * @dev Activate/deactivate organism
     * @param active Whether to activate
     */
    function setOrganismActive(bool active) external onlyOwner {
        organismActive = active;
    }
    
    /**
     * @dev Emergency withdraw
     * @param amount The amount to withdraw
     */
    function emergencyWithdraw(uint256 amount) external onlyOwner {
        require(address(this).balance >= amount, "Insufficient balance");
        payable(owner).transfer(amount);
    }
    
    // ═══════════════════════════════════════════════════════════════════
    // FALLBACK FUNCTIONS
    // ═══════════════════════════════════════════════════════════════════
    
    /**
     * @dev Receive ETH for rewards
     */
    receive() external payable {
        // ETH received for mathematical breakthrough rewards
    }
    
    /**
     * @dev Fallback function
     */
    fallback() external payable {
        // ETH received for mathematical breakthrough rewards
    }
}
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