#include <iostream>
#include <cmath>
#include <iomanip>
#include <map>
#include <string>

#ifndef M_PI
    #define M_PI 3.14159265358979323846
#endif

class Mano_SSU_ZeroParameter_Kernel {
private:
    double chi;
    double theta;
    double sigma;
    double epsilon;
    double lambda_f;
    double zeta;

public:
    Mano_SSU_ZeroParameter_Kernel() {
        chi = 144.0;
        theta = (180.0 / chi) * (M_PI / 180.0); // Radians
        sigma = 20.0 / chi;
        epsilon = sigma / (chi * std::pow(M_PI, 2));
        lambda_f = std::sqrt(chi) / M_PI;
        zeta = (chi / (2.0 * M_PI)) * (1.0 + sigma);
    }

    std::map<std::string, double> resolve_residues() {
        double gain = chi / std::pow(std::cos(theta), 2);
        
        double alpha_inv = gain - (zeta / 2.0) - sigma + (lambda_f * M_PI);
        double h_0 = (chi / 2.0) * (1.0 - (sigma / M_PI));
        double mu = (4.0 * M_PI * chi) * (1.0 + epsilon) + zeta + (288.0 / (chi * sigma));

        std::map<std::string, double> res;
        res["Alpha_Inv"] = alpha_inv;
        res["H0"] = h_0;
        res["Mu"] = mu;
        return res;
    }

    double verify_lock() {
        auto res = resolve_residues();
        // Derived Chi Identity
        double derived_chi = (res["Alpha_Inv"] + (zeta / 2.0) + sigma - (lambda_f * M_PI)) * std::pow(std::cos(theta), 2);
        return derived_chi;
    }
};

int main() {
    Mano_SSU_ZeroParameter_Kernel kernel;
    auto residues = kernel.resolve_residues();

    std::cout << std::fixed << std::setprecision(14);
    std::cout << "--- MANO-SSU v54.10 KERNEL AUDIT ---" << std::endl;
    std::cout << "Seed (Chi):  " << 144.0 << std::endl;
    std::cout << "Alpha_Inv:   " << residues["Alpha_Inv"] << std::endl;
    std::cout << "H0 Residue:  " << residues["H0"] << std::endl;
    std::cout << "Mu Residue:  " << residues["Mu"] << std::endl;
    std::cout << "------------------------------------" << std::endl;
    std::cout << "VERIFY LOCK: " << kernel.verify_lock() << std::endl;

    return 0;
}
