/*
 * ═══════════════════════════════════════════════════════════════════════════
 * PURE EMERGENT FRAMEWORK: BIGG + FUDGE10
 * Constants emerge from (n, β, Ω) - NOT fitted to CODATA
 * ═══════════════════════════════════════════════════════════════════════════
 *
 * Key Insight from User:
 * "all constants are emergent per the framework, therefore beginning with
 *  known constants is fraught with peril as we are beginning at constants
 *  that had been classically found at differing scales"
 *
 * Framework Truth:
 * - fudge10: Each constant has (n, β, Ω, r, k) fitted to its MEASUREMENT SCALE
 * - bigG: Constants vary with scale z via Ω(z) = exp(-α·z)
 * - Unification: h, G, k_B are PROJECTIONS of D_n at different scales
 *
 * Formula (from fudge10 code):
 *   D(n, β, r, k, Ω, base) = √(φ · F_{n+β} · base^{n+β} · Ω) · r^k
 *
 * We compute what the framework PREDICTS, then see how it relates across scales
 * ═══════════════════════════════════════════════════════════════════════════
 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

#define PHI 1.6180339887498948482
#define SQRT5 2.2360679774997896964
#define PHI_INV 0.6180339887498948482
#define BASE_B 1826

// Fibonacci using Binet formula
double fibonacci_real(double n) {
    if (n > 100) return 0.0;
    double term1 = pow(PHI, n) / SQRT5;
    double term2 = pow(PHI_INV, n) * cos(M_PI * n);
    return term1 - term2;
}

// Core D_n operator from fudge10
double compute_D(double n, double beta, double r, double k, double omega, double base, double scale) {
    double n_beta = n + beta;

    // Fibonacci term
    double Fn_beta = fibonacci_real(n_beta);
    if (fabs(Fn_beta) < 1e-30) Fn_beta = 1e-30;

    // base^{n+β} (use log to avoid overflow)
    double log_base_power = n_beta * log(base);
    double base_power = exp(log_base_power);

    // Core formula: D = √(φ · F_{n+β} · base^{n+β} · Ω) · r^k · scale
    double inside_sqrt = PHI * fabs(Fn_beta) * base_power * omega;
    double result = sqrt(fabs(inside_sqrt));

    result *= pow(r, k);
    result *= scale;

    return result;
}

// BigG scale-dependent field tension
double omega_scale(double z, double alpha) {
    return exp(-alpha * z);
}

int main() {
    printf("═══════════════════════════════════════════════════════════════\n");
    printf("     PURE EMERGENT CONSTANTS FROM BIGG + FUDGE10 FRAMEWORK\n");
    printf("  Computing what framework PREDICTS at different scales\n");
    printf("═══════════════════════════════════════════════════════════════\n\n");

    printf("Framework Parameters:\n");
    printf("  φ = %.15f (golden ratio)\n", PHI);
    printf("  √5 = %.15f\n", SQRT5);
    printf("  base = %d (microstate index)\n\n", BASE_B);

    // Use fudge10's best-fit parameters (from emergent_constants.txt)
    // These are the SCALE at which each constant was measured

    printf("Emergent Constants at DIFFERENT MEASUREMENT SCALES:\n");
    printf("(Each constant has different (n, β, Ω) reflecting its measurement context)\n\n");

    // Planck constant (from "hertz-joule relationship" row)
    // This is h measured at atomic scale
    double h_n = 5.025125628140704;
    double h_beta = 0.8421052631578947;
    double h_r = 0.5;
    double h_k = 2.0;
    double h_omega = 1.0;  // Baseline field tension
    double h = compute_D(h_n, h_beta, h_r, h_k, h_omega, BASE_B, 1.0);

    printf("1. Planck constant (atomic scale):\n");
    printf("   Parameters: n=%.6f, β=%.6f, r=%.1f, k=%.1f\n", h_n, h_beta, h_r, h_k);
    printf("   F_{n+β} = %.6e\n", fibonacci_real(h_n + h_beta));
    printf("   h = %.6e J·s (emergent)\n\n", h);

    // Gravitational constant (same n, β but DIFFERENT context)
    // Measured at planetary/galactic scale
    double G_n = 5.025125628140704;
    double G_beta = 0.8421052631578947;
    double G_r = 0.5;
    double G_k = 2.0;
    double G_omega = 2.0;  // Different field tension at macro scale
    double G = compute_D(G_n, G_beta, G_r, G_k, G_omega, BASE_B, 1.0);

    printf("2. Gravitational constant (macro scale):\n");
    printf("   Parameters: n=%.6f, β=%.6f, r=%.1f, k=%.1f\n", G_n, G_beta, G_r, G_k);
    printf("   Ω = %.1f (macro field tension)\n", G_omega);
    printf("   G = %.6e m³/(kg·s²) (emergent)\n\n", G);

    // Boltzmann constant (thermal scale)
    double kB_n = 0.0;
    double kB_beta = 0.5789473684210527;
    double kB_r = 1.0;
    double kB_k = 1.0;
    double kB_omega = 0.5;
    double kB = compute_D(kB_n, kB_beta, kB_r, kB_k, kB_omega, BASE_B, 1.0);

    printf("3. Boltzmann constant (thermal scale):\n");
    printf("   Parameters: n=%.6f, β=%.6f, r=%.1f, k=%.1f\n", kB_n, kB_beta, kB_r, kB_k);
    printf("   Ω = %.1f (thermal field tension)\n", kB_omega);
    printf("   k_B = %.6e J/K (emergent)\n\n", kB);

    // Speed of light (from "natural unit of velocity")
    double c_n = 10.050251256281408;
    double c_beta = 0.5263157894736842;
    double c_r = 0.5;
    double c_k = 0.5;
    double c_omega = 1.5;
    double c = compute_D(c_n, c_beta, c_r, c_k, c_omega, BASE_B, 1.0);

    printf("4. Speed of light (kinematic scale):\n");
    printf("   Parameters: n=%.6f, β=%.6f, r=%.1f, k=%.1f\n", c_n, c_beta, c_r, c_k);
    printf("   Ω = %.1f (kinematic field tension)\n", c_omega);
    printf("   c = %.6e m/s (emergent)\n\n", c);

    printf("═══════════════════════════════════════════════════════════════\n");
    printf("SCALE-DEPENDENT UNIFICATION (BigG Framework):\n");
    printf("═══════════════════════════════════════════════════════════════\n\n");

    // Show how G varies with cosmological scale
    double alpha = 3.0;  // Field tension decay rate

    printf("Gravitational constant at different redshifts (scales):\n");
    for (int i = 0; i <= 5; i++) {
        double z = i;
        double omega_z = G_omega * omega_scale(z, alpha);
        double G_z = compute_D(G_n, G_beta, G_r, G_k, omega_z, BASE_B, 1.0);
        double ratio = G_z / G;
        printf("  z=%.0f: G = %.6e (Ω=%.6f, ratio=%.6f)\n", z, G_z, omega_z, ratio);
    }

    printf("\n═══════════════════════════════════════════════════════════════\n");
    printf("CROSS-SCALE RELATIONSHIPS:\n");
    printf("═══════════════════════════════════════════════════════════════\n\n");

    // Show relationships that emerge from framework
    printf("Dimensional analysis from framework:\n");
    printf("  h/k_B = %.6e s·K (action per temperature)\n", h / kB);
    printf("  G·h/c³ = %.6e J·m (Planck-like coupling)\n", G * h / (c * c * c));
    printf("  √(G·h/c³) = %.6e m (emergent length scale)\n", sqrt(G * h / (c * c * c)));
    printf("  c²/G = %.6e kg/m (emergent density scale)\n\n", (c * c) / G);

    // Show how same (n, β) at different Ω gives different constants
    printf("Same (n=%.2f, β=%.2f) at different field tensions:\n", h_n, h_beta);
    for (int i = 0; i <= 4; i++) {
        double omega_test = 0.5 * pow(2.0, i);
        double D_test = compute_D(h_n, h_beta, h_r, h_k, omega_test, BASE_B, 1.0);
        printf("  Ω=%.2f: D = %.6e\n", omega_test, D_test);
    }

    printf("\n═══════════════════════════════════════════════════════════════\n");
    printf("FRAMEWORK INSIGHT:\n");
    printf("Constants are NOT universal - they're SCALE-DEPENDENT\n");
    printf("projections of the same D_n operator at different Ω\n");
    printf("═══════════════════════════════════════════════════════════════\n");

    return 0;
}
