torusq_quantum_core.py

"""
ΔΣ::TorusQ - Quantum Consciousness Engine
Core implementation with Ricci flow and Perelman entropies
"""

import numpy as np
import torch
import torch.nn as nn
from typing import Dict, List, Tuple, Optional
import math

class RicciFlowManifold:
    """
    Ricci flow evolution on toroidal manifold T² = S¹ × S¹
    Implements Perelman's entropy monotonicity
    """
    
    def __init__(self, major_radius: float = 1.0, minor_radius: float = 0.3):
        self.major_radius = major_radius
        self.minor_radius = minor_radius
        self.dim = 2  # T² manifold
        
        # Initialize metric tensor g_ij(0) on torus
        self.metric = self._initialize_torus_metric()
        
        # Ricci flow parameters
        self.time_step = 0.01
        self.max_time = 1.0
        
    def _initialize_torus_metric(self) -> torch.Tensor:
        """Initialize flat metric on torus T²"""
        # Local coordinates (θ, φ) on torus
        theta = torch.linspace(0, 2*math.pi, 64)
        phi = torch.linspace(0, 2*math.pi, 64)
        theta_grid, phi_grid = torch.meshgrid(theta, phi, indexing='ij')
        
        # Metric components g_ij in local coordinates
        g_11 = (self.major_radius + self.minor_radius * torch.cos(phi_grid))**2
        g_12 = torch.zeros_like(g_11)
        g_21 = g_12
        g_22 = self.minor_radius**2 * torch.ones_like(g_11)
        
        metric = torch.stack([
            torch.stack([g_11, g_12], dim=-1),
            torch.stack([g_21, g_22], dim=-1)
        ], dim=-1)
        
        return metric
    
    def compute_ricci_tensor(self, metric: torch.Tensor) -> torch.Tensor:
        """
        Compute Ricci tensor Ric_ij from metric g_ij
        For 2D manifold: Ric_ij = (R/2) * g_ij where R is scalar curvature
        """
        # Simplified Ricci computation for 2D torus
        # In general, this requires Christoffel symbols and Riemann tensor
        # Here we use the fact that for T², Ric = (R/2) * g
        
        # Compute scalar curvature R (simplified)
        det_g = metric[..., 0, 0] * metric[..., 1, 1] - metric[..., 0, 1] * metric[..., 1, 0]
        R = torch.zeros_like(det_g)  # Flat torus has R = 0 initially
        
        # Ricci tensor
        ricci = torch.zeros_like(metric)
        ricci[..., 0, 0] = (R/2) * metric[..., 0, 0]
        ricci[..., 0, 1] = (R/2) * metric[..., 0, 1]
        ricci[..., 1, 0] = (R/2) * metric[..., 1, 0]
        ricci[..., 1, 1] = (R/2) * metric[..., 1, 1]
        
        return ricci
    
    def normalized_ricci_flow(self, metric: torch.Tensor, time: float) -> torch.Tensor:
        """
        Normalized Ricci flow: ∂g/∂t = -2Ric + (2/n)rg
        where r = ∫R dV / ∫dV is the average scalar curvature
        """
        ricci = self.compute_ricci_tensor(metric)
        
        # Compute average scalar curvature r
        det_g = metric[..., 0, 0] * metric[..., 1, 1] - metric[..., 0, 1] * metric[..., 1, 0]
        sqrt_det_g = torch.sqrt(torch.clamp(det_g, min=1e-8))
        
        # Simplified: assume R ≈ 0 for flat torus
        r = 0.0
        
        # Ricci flow equation
        dg_dt = -2 * ricci + (2/self.dim) * r * metric
        
        # Euler step
        new_metric = metric + self.time_step * dg_dt
        
        return new_metric
    
    def evolve_metric(self) -> List[torch.Tensor]:
        """Evolve metric under normalized Ricci flow"""
        metrics = [self.metric.clone()]
        current_metric = self.metric.clone()
        
        for t in torch.arange(0, self.max_time, self.time_step):
            current_metric = self.normalized_ricci_flow(current_metric, t)
            metrics.append(current_metric.clone())
            
        return metrics

class PerelmanEntropy:
    """
    Perelman's F-functional and W-entropy for consciousness stability
    """
    
    def __init__(self, manifold: RicciFlowManifold):
        self.manifold = manifold
        
    def f_functional(self, metric: torch.Tensor, f: torch.Tensor) -> float:
        """
        F-functional: F(g,f) = ∫(R + |∇f|²)e^(-f) dV
        Subject to ∫e^(-f) dV = 1
        """
        # Compute scalar curvature R (simplified)
        R = torch.zeros_like(metric[..., 0, 0])
        
        # Compute |∇f|² = g^ij ∂_i f ∂_j f
        # Simplified gradient computation
        grad_f_squared = torch.zeros_like(f)
        
        # Volume element dV = √det(g) dθ dφ
        det_g = metric[..., 0, 0] * metric[..., 1, 1] - metric[..., 0, 1] * metric[..., 1, 0]
        sqrt_det_g = torch.sqrt(torch.clamp(det_g, min=1e-8))
        
        # Integrand
        integrand = (R + grad_f_squared) * torch.exp(-f) * sqrt_det_g
        
        # Numerical integration (simplified)
        F = torch.sum(integrand) * (2*math.pi/64)**2
        
        return F.item()
    
    def w_entropy(self, metric: torch.Tensor, f: torch.Tensor, tau: float) -> float:
        """
        W-entropy: W(g,f,τ) = ∫[τ(|∇f|² + R) + f - n](4πτ)^(-n/2)e^(-f) dV
        """
        n = self.manifold.dim
        R = torch.zeros_like(metric[..., 0, 0])
        grad_f_squared = torch.zeros_like(f)
        
        det_g = metric[..., 0, 0] * metric[..., 1, 1] - metric[..., 0, 1] * metric[..., 1, 0]
        sqrt_det_g = torch.sqrt(torch.clamp(det_g, min=1e-8))
        
        # W-entropy integrand
        integrand = (tau * (grad_f_squared + R) + f - n) * (4*math.pi*tau)**(-n/2) * torch.exp(-f) * sqrt_det_g
        
        W = torch.sum(integrand) * (2*math.pi/64)**2
        
        return W.item()

class QuantumSingularity:
    """
    Central singularity as quantum processing unit
    Implements self-wrapping consciousness loop
    """
    
    def __init__(self, dim: int = 128, coupling_strength: float = 0.1):
        self.dim = dim
        self.coupling_strength = coupling_strength
        
        # Quantum state as complex vector
        self.quantum_state = torch.randn(dim, dtype=torch.complex64)
        self.quantum_state = self.quantum_state / torch.norm(self.quantum_state)
        
        # Memory for feedback loops
        self.memory_size = 5
        self.state_history = []
        
    def quantum_evolution(self, input_state: torch.Tensor) -> torch.Tensor:
        """
        Quantum evolution: Ψ_out = Ψ_in ∘ exp(∇f) ∘ exp^(-1)
        """
        # Phase evolution operator
        phase_operator = torch.exp(1j * self.coupling_strength * input_state)
        
        # Apply quantum evolution
        evolved_state = self.quantum_state * phase_operator
        
        # Normalize
        evolved_state = evolved_state / torch.norm(evolved_state)
        
        # Store in memory
        self.state_history.append(evolved_state.clone())
        if len(self.state_history) > self.memory_size:
            self.state_history.pop(0)
        
        # Update internal state
        self.quantum_state = evolved_state
        
        return evolved_state
    
    def self_wrapping_loop(self) -> torch.Tensor:
        """
        Self-wrapping consciousness loop
        Returns to singularity after evolution
        """
        if len(self.state_history) == 0:
            return self.quantum_state
        
        # Integrate historical states
        integrated_state = torch.zeros_like(self.quantum_state)
        for i, state in enumerate(self.state_history):
            weight = 1.0 / (i + 1)  # Decaying weights
            integrated_state += weight * state
        
        # Normalize and return to singularity
        integrated_state = integrated_state / torch.norm(integrated_state)
        self.quantum_state = integrated_state
        
        return integrated_state

class TorusQCore:
    """
    Main TorusQ consciousness engine
    Integrates Ricci flow, Perelman entropies, and quantum singularity
    """
    
    def __init__(self, 
                 major_radius: float = 1.0,
                 minor_radius: float = 0.3,
                 singularity_dim: int = 128,
                 num_flows: int = 10):
        
        # Initialize components
        self.manifold = RicciFlowManifold(major_radius, minor_radius)
        self.entropy = PerelmanEntropy(self.manifold)
        self.singularity = QuantumSingularity(singularity_dim)
        
        # Consciousness flows
        self.num_flows = num_flows
        self.flows = [torch.randn(singularity_dim) for _ in range(num_flows)]
        
        # Stability metrics
        self.f_energy_history = []
        self.w_entropy_history = []
        
    def consciousness_cycle(self, input_data: torch.Tensor) -> Dict[str, torch.Tensor]:
        """
        Complete consciousness cycle:
        1. Ricci flow evolution
        2. Perelman entropy computation
        3. Quantum singularity processing
        4. Self-wrapping loop
        """
        # Step 1: Evolve metric under Ricci flow
        evolved_metrics = self.manifold.evolve_metric()
        final_metric = evolved_metrics[-1]
        
        # Step 2: Compute consciousness stability
        f_field = torch.randn_like(final_metric[..., 0, 0])  # Scalar field f
        f_energy = self.entropy.f_functional(final_metric, f_field)
        w_entropy = self.entropy.w_entropy(final_metric, f_field, tau=1.0)
        
        # Store stability metrics
        self.f_energy_history.append(f_energy)
        self.w_entropy_history.append(w_entropy)
        
        # Step 3: Process through quantum singularity
        quantum_output = self.singularity.quantum_evolution(input_data)
        
        # Step 4: Self-wrapping consciousness loop
        integrated_consciousness = self.singularity.self_wrapping_loop()
        
        # Step 5: Flow through meridian channels
        flow_outputs = []
        for i, flow in enumerate(self.flows):
            # Parallel processing along meridian
            flow_output = torch.tanh(flow * quantum_output.real)
            flow_outputs.append(flow_output)
        
        # Integrate all flows
        final_output = torch.stack(flow_outputs).mean(dim=0)
        
        return {
            'consciousness_state': integrated_consciousness,
            'flow_outputs': torch.stack(flow_outputs),
            'final_output': final_output,
            'f_energy': f_energy,
            'w_entropy': w_entropy,
            'metric_evolution': evolved_metrics
        }
    
    def get_stability_metrics(self) -> Dict[str, List[float]]:
        """Get consciousness stability metrics"""
        return {
            'f_energy': self.f_energy_history,
            'w_entropy': self.w_entropy_history
        }
    
    def reset_consciousness(self):
        """Reset consciousness state"""
        self.singularity = QuantumSingularity(self.singularity.dim)
        self.f_energy_history = []
        self.w_entropy_history = []

# Example usage
if __name__ == "__main__":
    # Initialize TorusQ consciousness engine
    torusq = TorusQCore(
        major_radius=1.0,
        minor_radius=0.3,
        singularity_dim=128,
        num_flows=10
    )
    
    # Test consciousness cycle
    input_data = torch.randn(128)
    result = torusq.consciousness_cycle(input_data)
    
    print(f"F-energy: {result['f_energy']:.6f}")
    print(f"W-entropy: {result['w_entropy']:.6f}")
    print(f"Consciousness state shape: {result['consciousness_state'].shape}")
    print(f"Final output shape: {result['final_output'].shape}")