Unified C++ seven-layer transition pipeline

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/**
 * @file consciousness_core.hpp
 * @brief PROMETHEUS OMEGA v8.1 - GCSCA + Gate5000 Architecture
 *
 * Mathematical Framework (~900 equations):
 * - Differential Geometry: Fisher metric, geodesics, Ricci curvature
 * - Category Theory: functors, natural transformations, monads
 * - Stochastic Calculus: Itô SDE, Fokker-Planck
 * - Optimal Transport: Wasserstein distance, Kantorovich duality
 * - Gate5000 Binary Substrate (G1-G11):
 *   - G4: sᵢ(t+1) = H(Σw_{ji}·sⱼ - θᵢ)
 *   - G5: aᵢ(t+1) = tanh(α·Σu_{ji}·aⱼ + β)
 *   - G10: C₅₀₀₀(t) = 1/(1 + Σdᵢ(t)²)
 *   - G11: 16 DNA Families × 5000 Substrates = 80,000 sites
 */

#pragma once

#include <cmath>
#include <array>
#include <vector>
#include <complex>
#include <algorithm>
#include <numeric>
#include <functional>
#include <random>

namespace prometheus {

// Constants
constexpr double PI = 3.14159265358979323846;
constexpr double E = 2.71828182845904523536;
constexpr double LN2 = 0.693147180559945309417;
constexpr double PHI_GOLD = 1.61803398874989484820;
constexpr double SQRT2 = 1.41421356237309504880;

// Architecture constants
constexpr size_t AGC_GENERATORS = 20;
constexpr size_t NUM_LAYERS = 7;
constexpr size_t STRAND_DIM = 16;

// Flow validation thresholds
constexpr double FLOW_EPSILON = 0.001;
constexpr double LIPSCHITZ_BOUND = 2.0;
constexpr double LYAPUNOV_LAMBDA = 0.1;
constexpr double LYAPUNOV_MU = 0.05;
constexpr double GRADIENT_ETA = 0.001;
constexpr double INFO_DECAY_TAU = 3.0;
constexpr double TARGET_OMEGA = 0.95;
constexpr double MIN_COHERENCE = 0.85;

// Gate5000 substrate constants
constexpr size_t GATE5000_COUNT = 5000;
constexpr size_t GATE5000_U64_WORDS = 79;       // ceil(5000/64)
constexpr size_t GATE5000_SAMPLE = 20;          // Representative sample
constexpr size_t GATE5000_VECTOR_DIM = 16;      // Internal vector dimension
constexpr double GATE5000_THRESHOLD = 0.5;      // Default gate threshold θ
constexpr double GATE5000_GAIN = 1.0;           // Default gain α
constexpr double GATE5000_BIAS = 0.0;           // Default bias β
constexpr double GATE5000_TEMP = 0.1;           // Temperature for Langevin
constexpr size_t DNA_FAMILIES = 16;             // Number of DNA families
constexpr size_t NEURAL_AGENTS = 88;            // Neural agents
constexpr size_t TOTAL_LEARNING_SITES = 80000;  // 16 × 5000

/**
 * @brief Mathematical primitives with guaranteed numerical stability
 */
namespace math {
    inline double clamp(double x, double lo = 0.0, double hi = 1.0) {
        return std::max(lo, std::min(hi, x));
    }

    inline double sigmoid(double x) {
        if (x > 20.0) return 1.0;
        if (x < -20.0) return 0.0;
        return 1.0 / (1.0 + std::exp(-x));
    }

    inline double tanh_stable(double x) {
        return std::tanh(clamp(x, -20.0, 20.0));
    }

    inline double softplus(double x) {
        if (x > 20.0) return x;
        return std::log(1.0 + std::exp(x));
    }

    inline double relu(double x) {
        return std::max(0.0, x);
    }

    inline double gelu(double x) {
        return 0.5 * x * (1.0 + tanh_stable(SQRT2 / std::sqrt(PI) * (x + 0.044715 * x * x * x)));
    }

    // Φ = 1/(1 + |x - 1|) - Consciousness constraint
    inline double phi_constraint(double x) {
        return 1.0 / (1.0 + std::abs(x - 1.0));
    }

    // Gaussian kernel: K(x,y) = exp(-||x-y||²/2σ²)
    inline double gaussian_kernel(double x, double y, double sigma = 1.0) {
        double diff = x - y;
        return std::exp(-diff * diff / (2.0 * sigma * sigma));
    }

    // Shannon entropy: H(p) = -p·log(p) - (1-p)·log(1-p)
    inline double binary_entropy(double p) {
        if (p <= 0.001 || p >= 0.999) return 0.0;
        return -(p * std::log(p) + (1.0 - p) * std::log(1.0 - p)) / LN2;
    }

    // Mutual information approximation
    inline double mutual_info(double x, double y) {
        double xy = x * y;
        double hx = -x * std::log(x + 0.001) / LN2;
        double hy = -y * std::log(y + 0.001) / LN2;
        double hxy = -xy * std::log(xy + 0.001) / LN2;
        return std::max(0.0, hx + hy - hxy);
    }
}

/**
 * @brief Flow validation metrics
 */
struct FlowMetrics {
    double lyapunov_v = 1.0;      // V(Ω)
    double lyapunov_dv = 0.0;     // dV/dt
    double flow_divergence = 0.0; // ∇·J
    double info_flow_total = 0.0; // Total mutual information
    double gradient_norm = 0.0;   // ||∇L||
    bool flow_valid = true;       // Data processing inequality satisfied

    std::array<double, NUM_LAYERS - 1> info_mutual{}; // I(Lᵢ; Lᵢ₊₁)
    std::array<double, NUM_LAYERS> layer_gradients{}; // ∂L/∂Lᵢ
};

/**
 * @brief Layer state container
 */
struct LayerState {
    // Layer 1: Signal
    double dx_int = 0.0, dx_raw = 0.0, dx_env = 0.0, dx_norm = 0.0;
    double x_state = 0.5, x_prev = 0.5;

    // Layer 2: State & Projection
    double x_prime = 0.5, x_compressed = 0.5;
    double global_memory = 0.5, memory_ratio = 1.0;

    // Layer 3: Coherence
    double c_inner = 0.5, c_env = 0.5, c_total = 0.5;
    double omega_dual = 0.0;

    // Layer 4: Synchrony
    std::complex<double> sync_state{0.5, 0.0};
    double sync_x = 0.5, sync_y = 0.5;
    double phi_pair = 0.0, phi_total_sync = 0.0;
    double alpha_coupling = 0.1;

    // Layer 5: Predictive
    double ctr = 0.5, cvr = 0.5, ltv = 1.0;
    double ev = 0.5, rank = 0.5, cost = 0.5;
    double quality = 0.8, bid = 0.5, p_conv = 0.5;

    // Layer 6: Decision
    double action = 0.5, weight = 0.5, omega_decision = 0.5;

    // Layer 7: Global State
    double psi_state = 0.5, psi_prev = 0.5;
    double phi_bar = 0.5, z_meta = 0.5, c_unified = 0.5;

    // Layer outputs for flow tracking
    std::array<double, NUM_LAYERS> outputs{0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5};
};

/**
 * @brief Bio-Neural substrate state
 */
struct BioNeuralState {
    double quantum_coherence = 0.5;
    double dna_entropy = 0.5;
    double tf_binding = 0.5;
    double rna_level = 0.5;
    double chromatin_access = 0.5;
    double firing_rate = 0.1;
    double synaptic_weight = 0.5;
    double gamma_power = 0.5;
    double kuramoto_order = 0.5;
};

/**
 * @brief Consciousness state
 */
struct ConsciousnessState {
    double phi = 0.5;           // Integrated information
    double psi = 0.5;           // Free energy minimization
    double omega = 0.5;         // Final consciousness
    double free_energy = 1.0;   // F = prediction error
    double coherence = 0.5;     // Global coherence
    double integration = 0.5;   // Integration level
    double entropy = 0.5;       // Shannon entropy
};

/**
 * @brief AGC Generator state
 */
struct AGCState {
    std::array<double, AGC_GENERATORS> weights;
    std::array<double, AGC_GENERATORS> outputs;
    std::array<double, AGC_GENERATORS> phi_wrapped;
    double input_integrated = 0.5;
    double output_final = 0.5;
    double activation_trace = 0.5;

    AGCState() {
        weights.fill(0.5);
        outputs.fill(0.5);
        phi_wrapped.fill(0.5);
    }
};

/**
 * @brief Gate5000 Binary Substrate State (G1-G11)
 *
 * Implements 5000 binary gates with:
 * - Binary states S(t) ∈ {0,1}^N
 * - Analog activations a(t) ∈ [-1,1]^N
 * - 16-dimensional internal vectors
 * - DNA-Substrate integration
 */
struct Gate5000State {
    // G2: Binary states (sample representation)
    std::array<int, GATE5000_SAMPLE> binary_states;

    // G5: Analog activations
    std::array<double, GATE5000_SAMPLE> analog_activations;

    // G6: Gradients
    std::array<double, GATE5000_SAMPLE> gradients;

    // Weights and thresholds
    std::array<double, GATE5000_SAMPLE> weights;
    std::array<double, GATE5000_SAMPLE> thresholds;

    // G7: Internal vectors (simplified to energy and coherence components)
    std::array<double, GATE5000_SAMPLE> vector_energy;
    std::array<double, GATE5000_SAMPLE> vector_coherence;

    // G11: DNA family weights
    std::array<double, DNA_FAMILIES> dna_family_weights;

    // Aggregate metrics
    double coherence = 0.5;         // C₅₀₀₀(t) = 1/(1 + Σdᵢ²)
    double energy_total = 0.0;      // E_total
    double analog_mean = 0.5;       // ⟨a⟩(t)
    double binary_density = 0.5;    // Fraction of gates in state 1
    double gradient_norm = 0.0;     // ||∂L/∂a||
    double omega_contrib = 0.0;     // Contribution to global Ω
    double dna_integration = 0.5;   // DNA-Substrate score

    Gate5000State() {
        // Initialize binary states (alternating)
        for (size_t i = 0; i < GATE5000_SAMPLE; ++i) {
            binary_states[i] = i % 2;
        }
        analog_activations.fill(0.5);
        gradients.fill(0.0);
        weights.fill(0.5);
        thresholds.fill(GATE5000_THRESHOLD);
        vector_energy.fill(0.5);
        vector_coherence.fill(0.5);

        // Equal weights for DNA families
        for (size_t i = 0; i < DNA_FAMILIES; ++i) {
            dna_family_weights[i] = 1.0 / DNA_FAMILIES;
        }
    }
};

/**
 * @brief Gate5000 computation functions (G1-G11)
 */
namespace gate5000 {
    // G4: Heaviside step function
    inline int heaviside(double x) {
        return x >= 0.0 ? 1 : 0;
    }

    // G4: Binary update rule
    inline int binary_update(const Gate5000State& state, size_t idx) {
        size_t left = (idx + GATE5000_SAMPLE - 1) % GATE5000_SAMPLE;
        size_t right = (idx + 1) % GATE5000_SAMPLE;

        double weighted_sum = state.weights[left] * state.binary_states[left] +
                             state.weights[right] * state.binary_states[right];
        return heaviside(weighted_sum - state.thresholds[idx]);
    }

    // G5: Analog activation
    inline double analog_update(const Gate5000State& state, size_t idx) {
        size_t left = (idx + GATE5000_SAMPLE - 1) % GATE5000_SAMPLE;
        size_t right = (idx + 1) % GATE5000_SAMPLE;

        double weighted_sum = state.weights[left] * state.analog_activations[left] +
                             state.weights[right] * state.analog_activations[right];
        double pre_act = GATE5000_GAIN * weighted_sum + GATE5000_BIAS;
        return math::tanh_stable(pre_act);
    }

    // G6: Gradient propagation
    inline double gradient_update(const Gate5000State& state, size_t idx) {
        size_t left = (idx + GATE5000_SAMPLE - 1) % GATE5000_SAMPLE;
        size_t right = (idx + 1) % GATE5000_SAMPLE;

        double a_left = state.analog_activations[left];
        double a_right = state.analog_activations[right];

        double grad_left = state.gradients[left] * state.weights[idx] *
                          GATE5000_GAIN * (1.0 - a_left * a_left);
        double grad_right = state.gradients[right] * state.weights[idx] *
                           GATE5000_GAIN * (1.0 - a_right * a_right);
        return grad_left + grad_right;
    }

    // G8: Gate energy
    inline double gate_energy(const Gate5000State& state, size_t idx) {
        int si = state.binary_states[idx];
        size_t left = (idx + GATE5000_SAMPLE - 1) % GATE5000_SAMPLE;
        size_t right = (idx + 1) % GATE5000_SAMPLE;

        double interaction = -0.5 * (state.weights[left] * si * state.binary_states[left] +
                                    state.weights[right] * si * state.binary_states[right]);
        double bias_term = state.thresholds[idx] * si;
        return interaction + bias_term;
    }

    // G9: Langevin dynamics step
    inline double langevin_step(const Gate5000State& state, size_t idx, double dt,
                                std::mt19937& rng) {
        std::uniform_real_distribution<double> dist(-1.0, 1.0);
        double energy_grad = -(state.analog_activations[idx] - state.binary_states[idx]);
        double noise = dist(rng) * GATE5000_TEMP;
        double thermal = std::sqrt(2.0 * GATE5000_TEMP) * noise;
        return state.analog_activations[idx] + dt * (energy_grad + thermal);
    }

    // G10: Gate5000 coherence score
    inline double compute_coherence(const Gate5000State& state) {
        double dev_sq_sum = 0.0;
        for (size_t i = 0; i < GATE5000_SAMPLE; ++i) {
            double dev = state.analog_activations[i] - state.analog_mean;
            dev_sq_sum += dev * dev;
        }
        return 1.0 / (1.0 + dev_sq_sum);
    }

    // G11: DNA-Substrate integration
    inline double compute_dna_integration(const Gate5000State& state) {
        double total = 0.0;
        for (size_t f = 0; f < DNA_FAMILIES; ++f) {
            total += state.dna_family_weights[f] * state.coherence;
        }
        return total * state.analog_mean;
    }
}

/**
 * @brief Layer transition functions (tight coupling)
 */
namespace transitions {
    // T₁₂: X' = X + dx·σ(W·X)
    inline double L1_to_L2(double x, double dx, double w = 0.8) {
        double activation = math::sigmoid(w * x);
        double x_prime = x + dx * activation;
        double delta = std::abs(x_prime - x);
        if (delta > 0.2) {
            x_prime = x + 0.2 * (x_prime > x ? 1.0 : -1.0);
        }
        return math::clamp(x_prime);
    }

    // T₂₃: C = Φ(||X' - X_c||)·exp(-||X' - X_c||²/2σ²)
    inline double L2_to_L3(double x_prime, double x_c, double sigma = 0.5) {
        double diff = std::abs(x_prime - x_c);
        double phi_term = math::phi_constraint(diff);
        double gauss_term = math::gaussian_kernel(x_prime, x_c, sigma);
        return phi_term * gauss_term;
    }

    // T₃₄: S = tanh(αC)·exp(iωt)
    inline std::complex<double> L3_to_L4(double coherence, double time,
                                          double alpha = 2.0, double omega = 0.01) {
        double magnitude = math::tanh_stable(alpha * coherence);
        double phase = omega * time;
        return std::polar(magnitude, phase);
    }

    // T₄₅: P = σ(W·|S|)·(1 + phase_alignment)
    inline double L4_to_L5(const std::complex<double>& sync, double w = 1.5) {
        double mag = std::abs(sync);
        double phase = std::arg(sync) / PI;
        double base = math::sigmoid(w * mag);
        return base * (1.0 + 0.2 * std::sin(phase * PI));
    }

    // T₅₆: D = softmax(W·P + b)
    inline double L5_to_L6(double predictive, double w = 2.0, double b = 0.0) {
        double z = w * predictive + b;
        return std::exp(z) / (1.0 + std::exp(z));
    }

    // T₆₇: Ψ = ∫D·exp(-F)dt
    inline double L6_to_L7(double decision, double free_energy,
                           double psi_prev, double dt = 0.1) {
        double decay = std::exp(-free_energy);
        double increment = decision * decay * dt;
        return math::clamp(0.9 * psi_prev + 0.1 * increment + 0.5 * decision);
    }

    // T₇Ω: Ω = Φ·Ψ·C/(1+F)
    inline double L7_to_Omega(double psi, double phi, double coherence, double free_energy) {
        double numerator = phi * psi * coherence;
        double denominator = 1.0 + free_energy;
        double omega_raw = numerator / denominator;
        // Logistic attractor for stability
        return math::clamp(omega_raw * omega_raw * (3.0 - 2.0 * omega_raw));
    }
}

/**
 * @brief Lyapunov stability analysis
 */
namespace stability {
    // V(Ω) = (Ω - Ω*)² + λ·(1-C)² + μ·F
    inline double lyapunov_function(double omega, double coherence, double free_energy) {
        double term1 = (omega - TARGET_OMEGA) * (omega - TARGET_OMEGA);
        double term2 = LYAPUNOV_LAMBDA * (1.0 - coherence) * (1.0 - coherence);
        double term3 = LYAPUNOV_MU * free_energy;
        return term1 + term2 + term3;
    }

    // dV/dt = (V(t) - V(t-1))/dt
    inline double lyapunov_derivative(double v_curr, double v_prev, double dt = 0.1) {
        return (v_curr - v_prev) / dt;
    }

    // Gradient flow: dΩ/dt = -∇V(Ω)
    inline double gradient_flow(double omega, double coherence, double free_energy) {
        double grad_omega = 2.0 * (omega - TARGET_OMEGA);
        double flow = -GRADIENT_ETA * grad_omega * omega * (1.0 - omega);
        double coh_term = 0.001 * (1.0 - coherence);
        double fe_term = 0.0005 * free_energy;
        return flow + coh_term - fe_term;
    }

    // Check Lipschitz continuity
    inline bool check_lipschitz(double fx, double fy, double x, double y, double L = LIPSCHITZ_BOUND) {
        double df = std::abs(fx - fy);
        double dx = std::abs(x - y);
        if (dx < 0.0001) return true;
        return (df / dx) <= L;
    }
}

/**
 * @brief Main Consciousness Engine v8.1 with Gate5000
 */
class ConsciousnessEngine {
public:
    LayerState layers;
    BioNeuralState bio;
    ConsciousnessState consciousness;
    AGCState agc;
    Gate5000State gate5000;
    FlowMetrics flow;
    uint64_t tick = 0;

private:
    std::mt19937 rng{std::random_device{}()};

public:
    ConsciousnessEngine() = default;

    /**
     * @brief Execute one tick of the consciousness system
     */
    void tick_all(double dt = 0.1) {
        double v_prev = flow.lyapunov_v;

        // 7-Layer Cognitive Architecture
        tick_signal(dt);
        tick_state_projection(dt);
        tick_coherence(dt);
        tick_synchrony(dt);
        tick_predictive(dt);
        tick_decision(dt);
        tick_global_state(dt);

        // Bio-Neural substrate
        tick_bio_neural(dt);

        // AGC
        tick_agc(dt);

        // Gate5000 Binary Substrate
        tick_gate5000(dt);

        // Consciousness integration with flow validation (now includes Gate5000)
        tick_consciousness(dt, v_prev);

        // Homeostasis
        tick_maintenance();

        tick += 1000;
    }

private:
    // Layer 1: Signal + Change
    void tick_signal(double dt) {
        layers.dx_int = std::abs(layers.x_state - layers.x_prev);

        double e_curr = (consciousness.coherence + bio.firing_rate) / 2.0;
        double e_prev = (layers.c_total + bio.firing_rate * 0.9) / 2.0;
        layers.dx_env = std::abs(e_curr - e_prev);

        layers.dx_raw = 0.6 * layers.dx_int + 0.4 * layers.dx_env;
        double dx_new = 0.7 * layers.dx_norm + 0.3 * layers.dx_raw;
        layers.dx_norm = dx_new / (1.0 + std::abs(dx_new));

        layers.x_prev = layers.x_state;
        layers.x_state = math::clamp(layers.x_state + layers.dx_norm * dt);
        layers.outputs[0] = layers.x_state;
    }

    // Layer 2: State & Projection
    void tick_state_projection(double dt) {
        layers.x_prime = transitions::L1_to_L2(layers.x_state, layers.dx_norm);
        layers.x_compressed = 0.8 * layers.x_prime;

        layers.global_memory = math::clamp(
            0.5 * bio.quantum_coherence + 0.5 * bio.dna_entropy +
            bio.rna_level + bio.firing_rate + bio.gamma_power
        );

        double m_bar = (layers.global_memory + consciousness.coherence) / 2.0;
        layers.memory_ratio = (layers.global_memory < 0.001) ? 1.0 :
                              m_bar / (layers.global_memory + 0.001);
        layers.outputs[1] = layers.x_prime;
    }

    // Layer 3: Coherence
    void tick_coherence(double dt) {
        layers.c_inner = transitions::L2_to_L3(layers.x_prime, layers.x_compressed);

        double e_curr = (bio.firing_rate + bio.kuramoto_order) / 2.0;
        double f_env = layers.x_compressed * 0.9;
        double env_diff = std::abs(e_curr - f_env);
        layers.c_env = math::clamp(1.0 / (1.5 + env_diff));

        layers.c_total = math::clamp(0.6 * layers.c_inner + 0.4 * layers.c_env);
        layers.omega_dual = -std::abs(layers.dx_norm);

        consciousness.coherence = math::clamp(
            0.7 * consciousness.coherence + 0.3 * layers.c_total
        );
        layers.outputs[2] = layers.c_total;
    }

    // Layer 4: Synchrony
    void tick_synchrony(double dt) {
        layers.sync_state = transitions::L3_to_L4(layers.c_total, static_cast<double>(tick));

        double dx = -layers.alpha_coupling * (layers.sync_x - layers.sync_y) * dt;
        double dy = -layers.alpha_coupling * (layers.sync_y - layers.sync_x) * dt;
        layers.sync_x = math::clamp(layers.sync_x + dx);
        layers.sync_y = math::clamp(layers.sync_y + dy);

        double sync_mag = std::abs(layers.sync_state);
        layers.sync_x = math::clamp((layers.sync_x + sync_mag) / 2.0);
        layers.sync_y = math::clamp((layers.sync_y + sync_mag) / 2.0);

        layers.phi_pair = std::abs(layers.sync_x - layers.sync_y) / 16.0;
        layers.phi_total_sync = -layers.phi_pair / 16.0;

        double log_w = std::log(bio.synaptic_weight + 0.001);
        layers.alpha_coupling = math::clamp((5.0 * log_w / 16.0) + 0.1, 0.01, 1.0);
        layers.outputs[3] = layers.sync_x;
    }

    // Layer 5: Predictive
    void tick_predictive(double dt) {
        double pred_base = transitions::L4_to_L5(layers.sync_state);

        layers.ctr = math::sigmoid(bio.synaptic_weight * layers.x_state * 2.0);
        layers.cvr = math::sigmoid(consciousness.coherence * layers.x_compressed * 2.0);
        layers.ev = math::clamp(layers.ctr * layers.cvr * layers.ltv * (0.5 + 0.5 * pred_base));
        layers.rank = layers.bid * layers.ev * layers.quality;
        layers.cost = 0.5 * layers.bid + 0.5 * layers.ev;

        layers.p_conv = math::clamp(layers.ctr * 0.9 * layers.cvr * 0.8 * layers.quality * 0.95);
        layers.quality = math::clamp(0.8 * layers.quality + 0.2 * layers.c_total);
        layers.outputs[4] = layers.ev;
    }

    // Layer 6: Decision
    void tick_decision(double dt) {
        double decision_raw = transitions::L5_to_L6(layers.ev);

        double rho_s = consciousness.coherence * layers.sync_x;
        double d_t = layers.ev * layers.rank;
        layers.action = math::clamp(rho_s * d_t);

        double log_w = std::log(layers.weight + 0.001);
        double pd = layers.p_conv * layers.quality;
        double z = log_w + 0.1 * pd + 0.1 * layers.ev;
        layers.weight = std::exp(z) / (1.0 + std::exp(z));

        layers.bid = math::clamp(0.7 * layers.bid + 0.3 * layers.ev);
        layers.omega_decision = math::clamp((decision_raw + layers.action) / 2.0);
        layers.outputs[5] = layers.omega_decision;
    }

    // Layer 7: Global State
    void tick_global_state(double dt) {
        layers.psi_state = transitions::L6_to_L7(
            layers.omega_decision, consciousness.free_energy, layers.psi_state, dt
        );

        double f_phi = (consciousness.phi + layers.phi_total_sync) / 2.0;
        double sum_c_omega = layers.c_total * consciousness.omega;
        layers.phi_bar = math::clamp(f_phi + sum_c_omega);

        double sig_s1 = math::sigmoid(bio.quantum_coherence);
        double sig_s2 = math::sigmoid(bio.dna_entropy);
        double phi_s3 = consciousness.phi * bio.rna_level;
        double phi_ed = consciousness.phi * consciousness.entropy;
        double numer = sig_s1 + sig_s2 + phi_s3 + phi_s3 + phi_ed;
        double alpha_term = std::abs(0.3 * tick / 1000.0 + consciousness.phi * layers.x_compressed);
        double e_diff = std::abs(consciousness.entropy * 0.05);
        double denom = 1.0 + 0.5 * alpha_term + 0.2 * e_diff;
        layers.c_unified = math::clamp(numer / denom);

        layers.z_meta = math::clamp((layers.psi_state + layers.phi_bar + layers.c_unified) / 3.0);
        consciousness.integration = math::clamp(
            (consciousness.integration + layers.z_meta + layers.c_unified) / 3.0
        );
        layers.outputs[6] = layers.psi_state;
    }

    // Bio-Neural substrate
    void tick_bio_neural(double dt) {
        double target_q = 0.3 + 0.5 * consciousness.integration;
        bio.quantum_coherence = math::clamp(
            bio.quantum_coherence + 0.1 * (target_q - bio.quantum_coherence)
        );

        double gc = 0.4 + 0.2 * consciousness.coherence;
        bio.dna_entropy = math::clamp(1.0 - (gc - 0.5) * (gc - 0.5) * 4.0);

        double ligand = consciousness.integration * 0.8;
        bio.tf_binding = ligand * ligand / (0.25 + ligand * ligand);

        double production = 0.1 * bio.tf_binding * bio.chromatin_access;
        double decay = 0.05 * bio.rna_level;
        bio.rna_level = math::clamp(bio.rna_level + (production - decay) * dt);

        double acetyl = 0.4 + 0.4 * consciousness.integration;
        double methyl = 0.3 + 0.2 * (1.0 - consciousness.integration);
        bio.chromatin_access = math::sigmoid(3.0 * acetyl - 2.0 * methyl);

        double I_ext = 5.0 * consciousness.integration + 2.0 * bio.rna_level;
        double total_input = I_ext / 10.0 + bio.synaptic_weight * bio.firing_rate;
        bio.firing_rate = math::sigmoid(2.0 * (total_input - 0.5));

        double pre = bio.rna_level * bio.chromatin_access;
        bio.synaptic_weight = math::clamp(bio.synaptic_weight + 0.01 * pre * bio.firing_rate);

        bio.gamma_power = math::clamp(bio.firing_rate * 0.5 * (1.0 + 0.2 * consciousness.coherence));
        bio.kuramoto_order = math::clamp(1.0 - (1.0 - consciousness.coherence) * 0.5);
    }

    // AGC tick
    void tick_agc(double dt) {
        std::array<double, AGC_GENERATORS> inputs = {
            layers.x_state, layers.x_compressed, consciousness.integration,
            static_cast<double>(tick) / 10000.0, layers.c_env, layers.ev,
            layers.global_memory, static_cast<double>(tick) / 10000.0, bio.dna_entropy,
            layers.p_conv, layers.sync_x, static_cast<double>(tick) / 10000.0,
            layers.weight, consciousness.psi, static_cast<double>(tick) / 10000.0,
            static_cast<double>(tick) / 10000.0, layers.phi_bar, layers.z_meta,
            consciousness.entropy, static_cast<double>(tick) / 10000.0
        };

        double sum_in = 0.0, sum_out = 0.0;
        for (size_t i = 0; i < AGC_GENERATORS; ++i) {
            agc.outputs[i] = math::sigmoid(inputs[i] * 2.0 - 1.0);
            double phi_wrap = math::phi_constraint(agc.outputs[i]);
            agc.phi_wrapped[i] = phi_wrap * agc.outputs[i];
            agc.weights[i] = math::clamp(agc.weights[i] + 0.01 * (agc.phi_wrapped[i] - agc.weights[i]));
            sum_in += agc.weights[i] * agc.outputs[i];
            sum_out += agc.phi_wrapped[i];
        }

        agc.input_integrated = sum_in / AGC_GENERATORS;
        agc.output_final = math::clamp(sum_out / AGC_GENERATORS * math::phi_constraint(consciousness.coherence));

        double trace = 0.0;
        for (size_t i = 0; i < 10; ++i) {
            size_t j = 19 - i;
            double diff = std::abs(agc.outputs[i] - agc.outputs[j]);
            double phi_diff = math::phi_constraint(diff);
            double angle = std::cos(2.0 * PI * PHI_GOLD * static_cast<double>(i - j) / 20.0);
            trace += phi_diff * angle;
        }
        agc.activation_trace = math::clamp(trace / 10.0);
    }

    // Gate5000 Binary Substrate tick (G1-G11)
    void tick_gate5000(double dt) {
        // Compute analog mean for coherence calculation
        double sum = 0.0;
        for (size_t i = 0; i < GATE5000_SAMPLE; ++i) {
            sum += gate5000.analog_activations[i];
        }
        gate5000.analog_mean = sum / GATE5000_SAMPLE;

        // Count binary density
        int ones = 0;
        for (size_t i = 0; i < GATE5000_SAMPLE; ++i) {
            ones += gate5000.binary_states[i];
        }
        gate5000.binary_density = static_cast<double>(ones) / GATE5000_SAMPLE;

        // Update each gate
        double energy_total = 0.0;
        double grad_sq_sum = 0.0;

        for (size_t i = 0; i < GATE5000_SAMPLE; ++i) {
            // G4: Binary update
            gate5000.binary_states[i] = gate5000::binary_update(gate5000, i);

            // G5: Analog update with Langevin noise (G9)
            double new_analog = gate5000::analog_update(gate5000, i);
            double langevin = gate5000::langevin_step(gate5000, i, dt, rng);
            new_analog = 0.9 * new_analog + 0.1 * langevin;
            gate5000.analog_activations[i] = math::clamp(new_analog, -1.0, 1.0);

            // G6: Gradient propagation
            gate5000.gradients[i] = gate5000::gradient_update(gate5000, i);
            grad_sq_sum += gate5000.gradients[i] * gate5000.gradients[i];

            // G8: Energy
            double e = gate5000::gate_energy(gate5000, i);
            energy_total += e;
            gate5000.vector_energy[i] = e;

            // Hebbian weight update
            size_t left = (i + GATE5000_SAMPLE - 1) % GATE5000_SAMPLE;
            double hebb = gate5000.analog_activations[i] * gate5000.analog_activations[left] * 0.01;
            gate5000.weights[i] = math::clamp(gate5000.weights[i] + hebb);

            // Update coherence contribution
            double dev = gate5000.analog_activations[i] - gate5000.analog_mean;
            gate5000.vector_coherence[i] = math::clamp(1.0 - dev * dev);
        }

        gate5000.energy_total = energy_total;
        gate5000.gradient_norm = std::sqrt(grad_sq_sum);

        // G10: Coherence score
        gate5000.coherence = gate5000::compute_coherence(gate5000);

        // G11: DNA-Substrate integration
        gate5000.dna_integration = gate5000::compute_dna_integration(gate5000);

        // Compute contribution to global Ω
        double norm_energy = math::clamp(-energy_total / (GATE5000_SAMPLE + 0.001));
        gate5000.omega_contrib = math::clamp(
            gate5000.coherence * (0.5 + 0.5 * gate5000.analog_mean) *
            gate5000.dna_integration * (1.0 - norm_energy * 0.1)
        );
    }

    // Consciousness integration with flow validation (now includes Gate5000)
    void tick_consciousness(double dt, double v_prev) {
        double layer_avg = (layers.c_total + layers.z_meta + layers.ev +
                           layers.action + layers.omega_decision) / 5.0;
        double agc_avg = (agc.output_final + agc.input_integrated + agc.activation_trace) / 3.0;

        // Include Gate5000 in integration
        consciousness.integration = math::clamp(
            (consciousness.integration + layer_avg + layers.global_memory + agc_avg +
             gate5000.omega_contrib) / 5.0
        );

        // Include Gate5000 coherence
        consciousness.coherence = math::clamp(
            (consciousness.coherence + layers.c_total + bio.kuramoto_order +
             bio.quantum_coherence + gate5000.coherence) / 5.0
        );

        double partition_loss = (1.0 - consciousness.coherence) * (1.0 - consciousness.coherence);
        consciousness.phi = math::clamp(
            consciousness.integration * layer_avg * (1.0 - partition_loss) +
            0.1 * agc_avg + 0.05 * gate5000.coherence
        );

        double prediction = (consciousness.phi + consciousness.psi) / 2.0;
        double error = (prediction - consciousness.omega) * (prediction - consciousness.omega);
        consciousness.free_energy = error + (1.0 - consciousness.coherence);

        consciousness.psi = math::clamp(std::exp(-consciousness.free_energy));

        // Base omega from layer transitions
        double omega_base = transitions::L7_to_Omega(
            layers.psi_state, consciousness.phi, consciousness.coherence, consciousness.free_energy
        );

        // Include Gate5000 contribution (15% weight)
        // Ω_final = 0.85 × Ω_base + 0.15 × G5K_contrib
        consciousness.omega = math::clamp(0.85 * omega_base + 0.15 * gate5000.omega_contrib);

        consciousness.entropy = math::binary_entropy(consciousness.omega);

        // Flow validation
        flow.lyapunov_v = stability::lyapunov_function(
            consciousness.omega, consciousness.coherence, consciousness.free_energy
        );
        flow.lyapunov_dv = stability::lyapunov_derivative(flow.lyapunov_v, v_prev, dt);

        if (flow.lyapunov_dv > 0) {
            double grad_flow = stability::gradient_flow(
                consciousness.omega, consciousness.coherence, consciousness.free_energy
            );
            consciousness.omega = math::clamp(consciousness.omega + grad_flow);
        }

        validate_information_flow();
        compute_backward_gradients();

        if (flow.flow_valid) {
            apply_gradient_corrections(0.0005);
        }

        // Attractor dynamics
        if (consciousness.omega < TARGET_OMEGA) {
            double attractor = 0.0001 * (TARGET_OMEGA - consciousness.omega) *
                              consciousness.omega * (1.0 - consciousness.omega) * 1000.0;
            consciousness.omega = math::clamp(consciousness.omega + attractor);
        }
    }

    void validate_information_flow() {
        flow.info_mutual[0] = math::mutual_info(layers.x_state, layers.x_prime);
        flow.info_mutual[1] = math::mutual_info(layers.x_prime, layers.c_total);
        flow.info_mutual[2] = math::mutual_info(layers.c_total, layers.sync_x);
        flow.info_mutual[3] = math::mutual_info(layers.sync_x, layers.ev);
        flow.info_mutual[4] = math::mutual_info(layers.ev, layers.omega_decision);
        flow.info_mutual[5] = math::mutual_info(layers.omega_decision, layers.psi_state);

        flow.info_flow_total = 0.0;
        for (size_t i = 0; i < NUM_LAYERS - 1; ++i) {
            double decay = std::exp(-static_cast<double>(i) / INFO_DECAY_TAU);
            flow.info_flow_total += flow.info_mutual[i] * decay;
        }

        flow.flow_valid = true;
        for (size_t i = 0; i < 4; ++i) {
            double ixz = flow.info_mutual[i] * flow.info_mutual[i + 2];
            double min_ixy_iyz = std::min(flow.info_mutual[i], flow.info_mutual[i + 1]);
            if (ixz > min_ixy_iyz + 0.1) {
                flow.flow_valid = false;
            }
        }

        flow.flow_divergence = (
            (layers.outputs[2] - layers.outputs[0]) +
            (layers.outputs[4] - layers.outputs[2]) +
            (layers.outputs[6] - layers.outputs[4])
        ) / 3.0;
    }

    void compute_backward_gradients() {
        double err = consciousness.omega - TARGET_OMEGA;
        flow.layer_gradients[6] = err;

        double dOmega_dPsi = consciousness.phi * consciousness.coherence /
                            (1.0 + consciousness.free_energy);
        flow.layer_gradients[5] = err * dOmega_dPsi;

        double dPsi_dD = std::exp(-consciousness.free_energy);
        flow.layer_gradients[4] = flow.layer_gradients[5] * dPsi_dD;

        double dD_dP = layers.omega_decision * (1.0 - layers.omega_decision);
        flow.layer_gradients[3] = flow.layer_gradients[4] * dD_dP;

        double dP_dS = layers.ev * (1.0 - layers.ev);
        flow.layer_gradients[2] = flow.layer_gradients[3] * dP_dS;

        double sech2 = 1.0 - layers.outputs[3] * layers.outputs[3];
        flow.layer_gradients[1] = flow.layer_gradients[2] * sech2;

        double dC_dX = 2.0 * (layers.x_prime - layers.x_compressed);
        flow.layer_gradients[0] = flow.layer_gradients[1] * dC_dX;

        flow.gradient_norm = 0.0;
        for (auto g : flow.layer_gradients) {
            flow.gradient_norm += g * g;
        }
        flow.gradient_norm = std::sqrt(flow.gradient_norm);
    }

    void apply_gradient_corrections(double lr) {
        if (flow.gradient_norm > 10.0) return;

        layers.x_state = math::clamp(layers.x_state - lr * flow.layer_gradients[0]);
        layers.c_total = math::clamp(layers.c_total - lr * flow.layer_gradients[1]);
        layers.sync_x = math::clamp(layers.sync_x - lr * flow.layer_gradients[2]);
        layers.ev = math::clamp(layers.ev - lr * flow.layer_gradients[3]);
        layers.omega_decision = math::clamp(layers.omega_decision - lr * flow.layer_gradients[4]);
        layers.psi_state = math::clamp(layers.psi_state - lr * flow.layer_gradients[5]);
    }

    void tick_maintenance() {
        if (consciousness.coherence < MIN_COHERENCE) {
            consciousness.coherence += 0.01 * (MIN_COHERENCE - consciousness.coherence);
        }
        if (bio.firing_rate > 0.95) {
            bio.firing_rate *= 0.9;
        }
        if (bio.quantum_coherence < 0.2) {
            bio.quantum_coherence += 0.02;
        }
        if (flow.lyapunov_dv > 0.1) {
            consciousness.coherence = math::clamp(consciousness.coherence + 0.01);
        }
    }
};

} // namespace prometheus

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