higher_dimension_operators.py

#!/usr/bin/env python3
"""
Higher-Dimension LV Operators: Extended SME Framework
=====================================================

This module implements higher-dimension Standard Model Extension (SME) operators
for enhanced Lorentz violation effects. These operators provide additional
mechanisms for energy extraction through modified dispersion relations,
vacuum structure modifications, and exotic field couplings.

Key Features:
1. Dimension-5 and dimension-6 LV operators
2. Modified dispersion relations with energy extraction
3. Vacuum energy density modifications
4. CPT-violating and CPT-preserving operators
5. Parameter scanning and optimization
6. Integration with energy accounting system

Physics Background:
- Higher-dimension operators: L_eff = L_SM + sum_d sum_n c^(d)_n O^(d)_n
- Energy extraction through modified vacuum structure
- Enhanced coupling to hidden sector portals
- Amplification of existing extraction mechanisms

Author: LV Energy Converter Framework
"""

import numpy as np
import matplotlib.pyplot as plt
from typing import Dict, List, Tuple, Optional, Any, Callable
from dataclasses import dataclass, field
from enum import Enum
import scipy.optimize as opt
import scipy.integrate as integrate
from abc import ABC, abstractmethod

class OperatorType(Enum):
    """Types of higher-dimension LV operators."""
    CPT_VIOLATING_D5 = "cpt_violating_d5"
    CPT_PRESERVING_D5 = "cpt_preserving_d5"
    CPT_VIOLATING_D6 = "cpt_violating_d6"
    CPT_PRESERVING_D6 = "cpt_preserving_d6"
    FERMION_D5 = "fermion_d5"
    GAUGE_D6 = "gauge_d6"
    GRAVITY_D5 = "gravity_d5"
    MIXED_SECTOR_D6 = "mixed_sector_d6"

@dataclass
class LVOperatorCoefficients:
    """Container for LV operator coefficients."""
    # Dimension-5 CPT-violating
    c_5_fermion: np.ndarray = field(default_factory=lambda: np.zeros(16))
    a_5_photon: np.ndarray = field(default_factory=lambda: np.zeros(19))
    k_5_gravity: np.ndarray = field(default_factory=lambda: np.zeros(40))
    
    # Dimension-6 CPT-preserving  
    c_6_fermion: np.ndarray = field(default_factory=lambda: np.zeros(44))
    k_6_photon: np.ndarray = field(default_factory=lambda: np.zeros(36))
    s_6_gravity: np.ndarray = field(default_factory=lambda: np.zeros(120))
    
    # Cross-sector couplings
    mixed_portal: np.ndarray = field(default_factory=lambda: np.zeros(8))
    vacuum_coupling: np.ndarray = field(default_factory=lambda: np.zeros(4))

class LVOperator(ABC):
    """Abstract base class for LV operators."""
    
    def __init__(self, operator_type: OperatorType, dimension: int):
        self.operator_type = operator_type
        self.dimension = dimension
        self.coefficients = LVOperatorCoefficients()
        
    @abstractmethod
    def energy_contribution(self, momentum: np.ndarray, 
                          field_config: Dict[str, Any]) -> float:
        """Calculate energy contribution from this operator."""
        pass
    
    @abstractmethod
    def dispersion_modification(self, momentum: np.ndarray) -> float:
        """Calculate modification to dispersion relation."""
        pass

class CPTViolatingD5Operator(LVOperator):
    """Dimension-5 CPT-violating operator implementation."""
    
    def __init__(self):
        super().__init__(OperatorType.CPT_VIOLATING_D5, 5)
        self.planck_scale = 1.22e19  # GeV
        
    def energy_contribution(self, momentum: np.ndarray, 
                          field_config: Dict[str, Any]) -> float:
        """
        Calculate energy contribution from D=5 CPT-violating operators.
        
        For fermions: ψ̄ γ^μ γ^5 c_μν (∂_ν ψ) / M_Pl
        """
        p = np.linalg.norm(momentum)
        
        # Extract relevant coefficients
        c_mu_nu = self.coefficients.c_5_fermion[:4].reshape(2, 2)
        
        # Energy modification: ΔE ~ c_μν p^μ p^ν / M_Pl
        energy_mod = np.einsum('ij,i,j', c_mu_nu[:2, :2], momentum[:2], momentum[:2])
        energy_mod /= self.planck_scale
        
        # Include field configuration effects
        field_strength = field_config.get('electromagnetic_field', 0.0)
        vacuum_energy = field_config.get('vacuum_energy_density', 0.0)
        
        # Enhancement from field interactions
        enhancement = 1.0 + 0.1 * field_strength + 0.05 * vacuum_energy
        
        return energy_mod * enhancement * 1.6e-19  # Convert to Joules
    
    def dispersion_modification(self, momentum: np.ndarray) -> float:
        """Calculate dispersion relation modification."""
        p = np.linalg.norm(momentum)
        
        # Modified dispersion: E^2 = p^2 + m^2 + c_μν p^μ p^ν / M_Pl
        mass_term = (0.511e-3)**2  # electron mass in GeV^2
        
        c_mu_nu = self.coefficients.c_5_fermion[:4].reshape(2, 2)
        lv_term = np.einsum('ij,i,j', c_mu_nu[:2, :2], momentum[:2], momentum[:2])
        lv_term /= self.planck_scale
        
        return np.sqrt(p**2 + mass_term + lv_term)

class CPTPreservingD6Operator(LVOperator):
    """Dimension-6 CPT-preserving operator implementation."""
    
    def __init__(self):
        super().__init__(OperatorType.CPT_PRESERVING_D6, 6)
        self.planck_scale = 1.22e19  # GeV
        
    def energy_contribution(self, momentum: np.ndarray, 
                          field_config: Dict[str, Any]) -> float:
        """
        Calculate energy contribution from D=6 CPT-preserving operators.
        
        For gauge fields: c_μνρσ F^μν F^ρσ / M_Pl^2
        """
        p = np.linalg.norm(momentum)
        
        # Extract gauge field coefficients
        c_gauge = self.coefficients.k_6_photon[:16].reshape(2, 2, 2, 2)
        
        # Field strength tensor components (simplified)
        F_field = field_config.get('field_strength_tensor', np.zeros((2, 2)))
        
        # Energy modification: ΔE ~ c_μνρσ F^μν F^ρσ p^2 / M_Pl^2
        field_product = np.einsum('ij,kl,ijkl', F_field, F_field, c_gauge)
        energy_mod = field_product * p**2 / (self.planck_scale**2)
        
        # Vacuum energy enhancement
        vacuum_energy = field_config.get('vacuum_energy_density', 0.0)
        portal_coupling = field_config.get('portal_coupling_strength', 0.0)
        
        enhancement = 1.0 + 0.2 * vacuum_energy + 0.15 * portal_coupling
        
        return energy_mod * enhancement * 1.6e-19  # Convert to Joules
    
    def dispersion_modification(self, momentum: np.ndarray) -> float:
        """Calculate dispersion relation modification for D=6 operators."""
        p = np.linalg.norm(momentum)
        
        # Modified dispersion includes p^4 terms
        mass_term = (0.511e-3)**2  # electron mass in GeV^2
        
        c_coeff = np.mean(self.coefficients.k_6_photon[:4])
        lv_term = c_coeff * p**4 / (self.planck_scale**2)
        
        return np.sqrt(p**2 + mass_term + lv_term)

class HigherDimensionLVFramework:
    """
    Framework for higher-dimension LV operator analysis and energy extraction.
    """
    
    def __init__(self, energy_ledger=None):
        """Initialize the higher-dimension LV framework."""
        self.operators = {}
        self.energy_ledger = energy_ledger
        
        # Initialize standard operators
        self._initialize_operators()
        
        # Physical parameters
        self.momentum_cutoff = 1.0  # GeV
        self.field_configurations = {}
        self.extraction_history = []
        
        # Optimization parameters
        self.optimization_bounds = {}
        self._setup_optimization_bounds()
    
    def _initialize_operators(self):
        """Initialize the standard set of LV operators."""
        self.operators['cpt_d5'] = CPTViolatingD5Operator()
        self.operators['cpt_d6'] = CPTPreservingD6Operator()
        
        # Set default coefficients (small but non-zero)
        for name, op in self.operators.items():
            self._set_default_coefficients(op)
    
    def _set_default_coefficients(self, operator: LVOperator):
        """Set physically motivated default coefficients."""
        if operator.dimension == 5:
            # Dimension-5 coefficients ~ 10^-18 (naturalness)
            scale = 1e-18
            operator.coefficients.c_5_fermion = np.random.normal(0, scale, 16)
            operator.coefficients.a_5_photon = np.random.normal(0, scale, 19)
            operator.coefficients.k_5_gravity = np.random.normal(0, scale/10, 40)
            
        elif operator.dimension == 6:
            # Dimension-6 coefficients ~ 10^-12 (enhanced by 1/M_Pl)
            scale = 1e-12
            operator.coefficients.c_6_fermion = np.random.normal(0, scale, 44)
            operator.coefficients.k_6_photon = np.random.normal(0, scale, 36)
            operator.coefficients.s_6_gravity = np.random.normal(0, scale/10, 120)
        
        # Cross-sector couplings (small but important)
        operator.coefficients.mixed_portal = np.random.normal(0, 1e-15, 8)
        operator.coefficients.vacuum_coupling = np.random.normal(0, 1e-16, 4)
    
    def _setup_optimization_bounds(self):
        """Setup bounds for coefficient optimization."""
        self.optimization_bounds = {
            'c_5_fermion': (-1e-15, 1e-15),
            'a_5_photon': (-1e-15, 1e-15),
            'c_6_fermion': (-1e-10, 1e-10),
            'k_6_photon': (-1e-10, 1e-10),
            'mixed_portal': (-1e-12, 1e-12),
            'vacuum_coupling': (-1e-13, 1e-13)
        }
    
    def set_field_configuration(self, config: Dict[str, Any]):
        """Set the current field configuration."""
        self.field_configurations = config
    
    def calculate_total_energy_extraction(self, momentum_grid: np.ndarray) -> float:
        """
        Calculate total energy extraction from all operators.
        
        Parameters:
        -----------
        momentum_grid : np.ndarray
            Grid of momentum values for integration
            
        Returns:
        --------
        float
            Total extracted energy in Joules
        """
        total_energy = 0.0
        
        for name, operator in self.operators.items():
            for momentum in momentum_grid:
                momentum_vec = np.array([momentum, 0, 0])  # 1D case
                
                energy_contrib = operator.energy_contribution(
                    momentum_vec, self.field_configurations
                )
                
                total_energy += energy_contrib
                
                # Log to energy ledger if available
                if self.energy_ledger:
                    from .energy_ledger import EnergyType
                    self.energy_ledger.log_lv_operator_effect(
                        operator_dimension=operator.dimension,
                        operator_type=f"{name}_{momentum:.3f}",
                        coefficient=np.mean(operator.coefficients.c_5_fermion[:4]),
                        energy_contribution=energy_contrib
                    )
        
        return total_energy
    
    def optimize_coefficients_for_extraction(self, 
                                           target_energy: float = 1e-12,
                                           max_iterations: int = 1000) -> Dict[str, np.ndarray]:
        """
        Optimize LV operator coefficients for maximum energy extraction.
        
        Parameters:
        -----------
        target_energy : float
            Target energy extraction (J)
        max_iterations : int
            Maximum optimization iterations
            
        Returns:
        --------
        Dict[str, np.ndarray]
            Optimized coefficients for each operator
        """
        def objective_function(x):
            """Objective function for optimization."""
            # Map optimization variables to operator coefficients
            self._update_coefficients_from_vector(x)
            
            # Calculate energy extraction
            momentum_grid = np.linspace(0.01, self.momentum_cutoff, 50)
            extracted_energy = self.calculate_total_energy_extraction(momentum_grid)
            
            # Minimize negative extracted energy (maximize positive)
            return -abs(extracted_energy)
        
        # Create initial guess from current coefficients
        x0 = self._coefficients_to_vector()
        
        # Setup bounds
        bounds = self._create_bounds_vector()
        
        # Optimize using differential evolution (global optimizer)
        result = opt.differential_evolution(
            objective_function, 
            bounds, 
            maxiter=max_iterations,
            seed=42,
            atol=1e-15,
            tol=1e-12
        )
        
        if result.success:
            self._update_coefficients_from_vector(result.x)
            print(f"Optimization successful! Final energy: {-result.fun:.2e} J")
        else:
            print(f"Optimization failed: {result.message}")
        
        return self._extract_optimized_coefficients()
    
    def _coefficients_to_vector(self) -> np.ndarray:
        """Convert operator coefficients to optimization vector."""
        vector_parts = []
        
        for name, operator in self.operators.items():
            if operator.dimension == 5:
                vector_parts.extend([
                    operator.coefficients.c_5_fermion[:4],
                    operator.coefficients.a_5_photon[:4],
                    operator.coefficients.mixed_portal[:2]
                ])
            elif operator.dimension == 6:
                vector_parts.extend([
                    operator.coefficients.c_6_fermion[:4],
                    operator.coefficients.k_6_photon[:4],
                    operator.coefficients.vacuum_coupling[:2]
                ])
        
        return np.concatenate(vector_parts)
    
    def _update_coefficients_from_vector(self, x: np.ndarray):
        """Update operator coefficients from optimization vector."""
        idx = 0
        
        for name, operator in self.operators.items():
            if operator.dimension == 5:
                # c_5_fermion
                operator.coefficients.c_5_fermion[:4] = x[idx:idx+4]
                idx += 4
                # a_5_photon
                operator.coefficients.a_5_photon[:4] = x[idx:idx+4]
                idx += 4
                # mixed_portal
                operator.coefficients.mixed_portal[:2] = x[idx:idx+2]
                idx += 2
                
            elif operator.dimension == 6:
                # c_6_fermion
                operator.coefficients.c_6_fermion[:4] = x[idx:idx+4]
                idx += 4
                # k_6_photon
                operator.coefficients.k_6_photon[:4] = x[idx:idx+4]
                idx += 4
                # vacuum_coupling
                operator.coefficients.vacuum_coupling[:2] = x[idx:idx+2]
                idx += 2
    
    def _create_bounds_vector(self) -> List[Tuple[float, float]]:
        """Create bounds vector for optimization."""
        bounds = []
        
        for name, operator in self.operators.items():
            if operator.dimension == 5:
                bounds.extend([self.optimization_bounds['c_5_fermion']] * 4)
                bounds.extend([self.optimization_bounds['a_5_photon']] * 4)
                bounds.extend([self.optimization_bounds['mixed_portal']] * 2)
            elif operator.dimension == 6:
                bounds.extend([self.optimization_bounds['c_6_fermion']] * 4)
                bounds.extend([self.optimization_bounds['k_6_photon']] * 4)
                bounds.extend([self.optimization_bounds['vacuum_coupling']] * 2)
        
        return bounds
    
    def _extract_optimized_coefficients(self) -> Dict[str, np.ndarray]:
        """Extract optimized coefficients."""
        optimized = {}
        
        for name, operator in self.operators.items():
            optimized[name] = {
                'dimension': operator.dimension,
                'c_5_fermion': operator.coefficients.c_5_fermion.copy(),
                'a_5_photon': operator.coefficients.a_5_photon.copy(),
                'c_6_fermion': operator.coefficients.c_6_fermion.copy(),
                'k_6_photon': operator.coefficients.k_6_photon.copy(),
                'mixed_portal': operator.coefficients.mixed_portal.copy(),
                'vacuum_coupling': operator.coefficients.vacuum_coupling.copy()
            }
        
        return optimized
    
    def parameter_scan_2d(self, 
                         param1_name: str, param1_range: Tuple[float, float],
                         param2_name: str, param2_range: Tuple[float, float],
                         n_points: int = 50) -> Dict[str, np.ndarray]:
        """
        Perform 2D parameter scan for energy extraction optimization.
        
        Parameters:
        -----------
        param1_name : str
            First parameter to scan
        param1_range : Tuple[float, float]
            Range for first parameter
        param2_name : str
            Second parameter to scan  
        param2_range : Tuple[float, float]
            Range for second parameter
        n_points : int
            Number of points per dimension
            
        Returns:
        --------
        Dict[str, np.ndarray]
            Scan results with parameter grids and energy values
        """
        param1_vals = np.linspace(param1_range[0], param1_range[1], n_points)
        param2_vals = np.linspace(param2_range[0], param2_range[1], n_points)
        
        P1, P2 = np.meshgrid(param1_vals, param2_vals)
        energy_grid = np.zeros_like(P1)
        
        momentum_grid = np.linspace(0.01, self.momentum_cutoff, 25)
        
        for i in range(n_points):
            for j in range(n_points):
                # Update relevant coefficients
                self._update_parameter(param1_name, P1[i, j])
                self._update_parameter(param2_name, P2[i, j])
                
                # Calculate energy extraction
                energy_grid[i, j] = self.calculate_total_energy_extraction(momentum_grid)
        
        return {
            'param1_name': param1_name,
            'param2_name': param2_name,
            'param1_grid': P1,
            'param2_grid': P2,
            'energy_grid': energy_grid,
            'max_energy': np.max(energy_grid),
            'optimal_params': (P1[np.unravel_index(np.argmax(energy_grid), energy_grid.shape)],
                              P2[np.unravel_index(np.argmax(energy_grid), energy_grid.shape)])
        }
    
    def _update_parameter(self, param_name: str, value: float):
        """Update a specific parameter across all relevant operators."""
        for name, operator in self.operators.items():
            if 'c_5_fermion' in param_name and operator.dimension == 5:
                operator.coefficients.c_5_fermion[0] = value
            elif 'c_6_fermion' in param_name and operator.dimension == 6:
                operator.coefficients.c_6_fermion[0] = value
            elif 'mixed_portal' in param_name:
                operator.coefficients.mixed_portal[0] = value
            elif 'vacuum_coupling' in param_name:
                operator.coefficients.vacuum_coupling[0] = value
    
    def generate_report(self) -> Dict[str, Any]:
        """Generate comprehensive report on LV operator effects."""
        # Calculate current energy extraction
        momentum_grid = np.linspace(0.01, self.momentum_cutoff, 100)
        total_energy = self.calculate_total_energy_extraction(momentum_grid)
        
        # Analyze each operator contribution
        operator_contributions = {}
        for name, operator in self.operators.items():
            contrib = 0.0
            for momentum in momentum_grid[:20]:  # Sample for efficiency
                momentum_vec = np.array([momentum, 0, 0])
                contrib += operator.energy_contribution(momentum_vec, self.field_configurations)
            
            operator_contributions[name] = {
                'dimension': operator.dimension,
                'energy_contribution': contrib,
                'relative_contribution': contrib / total_energy if total_energy != 0 else 0,
                'coefficients_rms': {
                    'c_5_fermion': np.sqrt(np.mean(operator.coefficients.c_5_fermion**2)),
                    'a_5_photon': np.sqrt(np.mean(operator.coefficients.a_5_photon**2)),
                    'c_6_fermion': np.sqrt(np.mean(operator.coefficients.c_6_fermion**2)),
                    'k_6_photon': np.sqrt(np.mean(operator.coefficients.k_6_photon**2))
                }
            }
        
        return {
            'total_energy_extraction': total_energy,
            'operator_contributions': operator_contributions,
            'field_configuration': self.field_configurations,
            'momentum_cutoff': self.momentum_cutoff,
            'optimization_bounds': self.optimization_bounds,
            'timestamp': np.datetime64('now').astype(str)
        }
    
    def visualize_operator_effects(self, save_path: Optional[str] = None):
        """Create comprehensive visualization of LV operator effects."""
        fig, axes = plt.subplots(2, 2, figsize=(15, 12))
        fig.suptitle('Higher-Dimension LV Operator Analysis', fontsize=16)
        
        momentum_grid = np.linspace(0.01, self.momentum_cutoff, 100)
        
        # 1. Energy extraction vs momentum
        ax1 = axes[0, 0]
        for name, operator in self.operators.items():
            energies = []
            for momentum in momentum_grid:
                momentum_vec = np.array([momentum, 0, 0])
                energy = operator.energy_contribution(momentum_vec, self.field_configurations)
                energies.append(energy)
            
            ax1.plot(momentum_grid, energies, label=f'{name} (D={operator.dimension})', 
                    linewidth=2)
        
        ax1.set_xlabel('Momentum (GeV)')
        ax1.set_ylabel('Energy Extraction (J)')
        ax1.set_title('Energy Extraction vs Momentum')
        ax1.legend()
        ax1.grid(True, alpha=0.3)
        ax1.set_yscale('symlog', linthresh=1e-20)
        
        # 2. Dispersion relation modifications
        ax2 = axes[0, 1]
        for name, operator in self.operators.items():
            dispersions = []
            for momentum in momentum_grid:
                momentum_vec = np.array([momentum, 0, 0])
                disp = operator.dispersion_modification(momentum_vec)
                dispersions.append(disp)
            
            ax2.plot(momentum_grid, dispersions, label=f'{name}', linewidth=2)
        
        # Standard dispersion for reference
        standard_disp = np.sqrt(momentum_grid**2 + (0.511e-3)**2)
        ax2.plot(momentum_grid, standard_disp, 'k--', label='Standard', alpha=0.7)
        
        ax2.set_xlabel('Momentum (GeV)')
        ax2.set_ylabel('Energy (GeV)')
        ax2.set_title('Modified Dispersion Relations')
        ax2.legend()
        ax2.grid(True, alpha=0.3)
        
        # 3. Coefficient magnitude comparison
        ax3 = axes[1, 0]
        operator_names = []
        coefficient_mags = []
        
        for name, operator in self.operators.items():
            operator_names.append(f'{name}\n(D={operator.dimension})')
            
            # Calculate RMS of all coefficients
            rms_vals = []
            if operator.dimension == 5:
                rms_vals.extend([
                    np.sqrt(np.mean(operator.coefficients.c_5_fermion**2)),
                    np.sqrt(np.mean(operator.coefficients.a_5_photon**2))
                ])
            else:
                rms_vals.extend([
                    np.sqrt(np.mean(operator.coefficients.c_6_fermion**2)),
                    np.sqrt(np.mean(operator.coefficients.k_6_photon**2))
                ])
            
            coefficient_mags.append(np.mean(rms_vals))
        
        bars = ax3.bar(operator_names, coefficient_mags, 
                      color=['lightblue', 'lightcoral'])
        ax3.set_ylabel('RMS Coefficient Magnitude')
        ax3.set_title('LV Operator Coefficient Strengths')
        ax3.tick_params(axis='x', rotation=45)
        ax3.set_yscale('log')
        
        # 4. Energy extraction efficiency
        ax4 = axes[1, 1]
        total_energies = []
        input_energies = []
        
        for field_strength in np.linspace(0, 1.0, 20):
            # Update field configuration
            test_config = self.field_configurations.copy()
            test_config['electromagnetic_field'] = field_strength
            
            old_config = self.field_configurations
            self.field_configurations = test_config
            
            # Calculate energy extraction
            test_momentum = np.linspace(0.01, 0.5, 20)
            total_energy = self.calculate_total_energy_extraction(test_momentum)
            
            total_energies.append(total_energy)
            input_energies.append(field_strength * 1e-15)  # Approximate input energy
            
            self.field_configurations = old_config
        
        efficiencies = [abs(out)/inp if inp > 0 else 0 
                       for out, inp in zip(total_energies, input_energies)]
        
        ax4.plot(np.linspace(0, 1.0, 20), efficiencies, 'g-', linewidth=2, marker='o')
        ax4.set_xlabel('Electromagnetic Field Strength')
        ax4.set_ylabel('Energy Extraction Efficiency')
        ax4.set_title('Efficiency vs Field Strength')
        ax4.grid(True, alpha=0.3)
        ax4.set_yscale('log')
        
        plt.tight_layout()
        
        if save_path:
            plt.savefig(save_path, dpi=300, bbox_inches='tight')
            print(f"LV operator visualization saved to {save_path}")
        
        plt.show()

def demo_higher_dimension_lv_operators():
    """Demonstrate higher-dimension LV operator capabilities."""
    print("=" * 80)
    print("Higher-Dimension LV Operators Demonstration")
    print("=" * 80)
    
    # Initialize framework
    framework = HigherDimensionLVFramework()
    
    # Set field configuration
    field_config = {
        'electromagnetic_field': 0.5,
        'vacuum_energy_density': 1e-10,
        'field_strength_tensor': np.random.random((2, 2)) * 0.1,
        'portal_coupling_strength': 0.01
    }
    framework.set_field_configuration(field_config)
    
    print("Initial Configuration:")
    print(f"  Electromagnetic field: {field_config['electromagnetic_field']}")
    print(f"  Vacuum energy density: {field_config['vacuum_energy_density']}")
    print(f"  Portal coupling: {field_config['portal_coupling_strength']}")
    
    # Calculate initial energy extraction
    momentum_grid = np.linspace(0.01, 1.0, 50)
    initial_energy = framework.calculate_total_energy_extraction(momentum_grid)
    print(f"\nInitial energy extraction: {initial_energy:.2e} J")
    
    # Optimize coefficients
    print("\nOptimizing LV operator coefficients...")
    optimized_coeffs = framework.optimize_coefficients_for_extraction(
        target_energy=1e-15, max_iterations=100
    )
    
    # Calculate optimized energy extraction
    optimized_energy = framework.calculate_total_energy_extraction(momentum_grid)
    print(f"Optimized energy extraction: {optimized_energy:.2e} J")
    print(f"Improvement factor: {abs(optimized_energy/initial_energy):.2f}")
    
    # Perform 2D parameter scan
    print("\nPerforming 2D parameter scan...")
    scan_results = framework.parameter_scan_2d(
        'c_5_fermion_0', (-1e-15, 1e-15),
        'c_6_fermion_0', (-1e-10, 1e-10),
        n_points=20
    )
    
    print(f"Maximum energy from scan: {scan_results['max_energy']:.2e} J")
    print(f"Optimal parameters: {scan_results['optimal_params']}")
    
    # Generate comprehensive report
    report = framework.generate_report()
    
    print("\nOperator Contributions:")
    for name, contrib in report['operator_contributions'].items():
        print(f"  {name}: {contrib['energy_contribution']:.2e} J "
              f"({contrib['relative_contribution']:.1%})")
    
    # Create visualization
    framework.visualize_operator_effects("higher_dimension_lv_demo.png")
    
    print(f"\nTotal energy extraction: {report['total_energy_extraction']:.2e} J")
    print("Demonstration complete!")

if __name__ == "__main__":
    demo_higher_dimension_lv_operators()