""" 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}")