Create LFT_VALIDATION

LFT_VALIDATION

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+#!/usr/bin/env python3
+"""
+LOGOS FIELD THEORY - INTEGRATED COHERENCE VALIDATION
+Unifying Cultural Sigma with Numerical Field Theory Validation
+"""
+
+import numpy as np
+from scipy import stats, ndimage, signal
+import asyncio
+from dataclasses import dataclass
+from typing import Dict, List, Any, Tuple
+import time
+import hashlib
+import json
+
+@dataclass
+class UnifiedValidationMetrics:
+    """Combines cultural sigma with numerical field validation"""
+    cultural_coherence: Dict[str, float]
+    field_coherence: Dict[str, float]
+    truth_alignment: Dict[str, float]
+    resonance_strength: Dict[str, float]
+    topological_stability: Dict[str, float]
+    cross_domain_synergy: Dict[str, float]
+    statistical_significance: Dict[str, float]
+    framework_robustness: Dict[str, float]
+
+class IntegratedLogosValidator:
+    """
+    Unifies Cultural Sigma optimization with precise Logos Field Theory validation
+    Creates coherent bridge between cultural propagation and mathematical field theory
+    """
+    
+    def __init__(self, field_dimensions: Tuple[int, int] = (512, 512)):
+        self.field_dimensions = field_dimensions
+        self.sample_size = 1000
+        self.confidence_level = 0.95
+        self.cultural_memory = {}
+        
+    def initialize_culturally_optimized_fields(self, cultural_context: Dict[str, Any]) -> Tuple[np.ndarray, np.ndarray]:
+        """Initialize fields with cultural sigma optimization"""
+        np.random.seed(42)
+        
+        x, y = np.meshgrid(np.linspace(-2, 2, self.field_dimensions[1]), 
+                          np.linspace(-2, 2, self.field_dimensions[0]))
+        
+        # Cultural context influences field structure
+        cultural_strength = cultural_context.get('sigma_optimization', 0.7)
+        cultural_coherence = cultural_context.get('cultural_coherence', 0.8)
+        
+        # Meaning field with cultural attractors
+        meaning_field = np.zeros(self.field_dimensions)
+        
+        # Cultural attractors based on context
+        if cultural_context.get('context_type') == 'established':
+            attractors = [
+                (0.5, 0.5, 1.0, 0.2),   # Strong, focused attractors
+                (-0.5, -0.5, 0.9, 0.25),
+            ]
+        elif cultural_context.get('context_type') == 'emergent':
+            attractors = [
+                (0.3, 0.3, 0.6, 0.4),   # Weaker, broader attractors
+                (-0.3, -0.3, 0.5, 0.45),
+                (0.6, -0.2, 0.4, 0.35),
+            ]
+        else:  # transitional
+            attractors = [
+                (0.4, 0.4, 0.8, 0.3),
+                (-0.4, -0.4, 0.7, 0.35),
+                (0.0, 0.0, 0.5, 0.5),
+            ]
+        
+        # Apply cultural strength to attractors
+        for i, (cy, cx, amp, sigma) in enumerate(attractors):
+            adjusted_amp = amp * cultural_strength
+            adjusted_sigma = sigma * (2 - cultural_coherence)  # Higher coherence = sharper attractors
+            
+            gaussian = adjusted_amp * np.exp(-((x - cx)**2 + (y - cy)**2) / (2 * adjusted_sigma**2))
+            meaning_field += gaussian
+        
+        # Cultural noise pattern (not random - culturally structured)
+        cultural_fluctuations = self._generate_cultural_noise(cultural_context)
+        meaning_field += cultural_fluctuations * 0.1
+        
+        # Consciousness field with cultural nonlinearity
+        nonlinear_factor = 1.0 + (cultural_strength - 0.5)  # Cultural strength amplifies nonlinearity
+        consciousness_field = np.tanh(meaning_field * nonlinear_factor)
+        
+        # Cultural normalization
+        meaning_field = self._cultural_normalization(meaning_field, cultural_context)
+        consciousness_field = (consciousness_field + 1) / 2
+        
+        return meaning_field, consciousness_field
+    
+    def _generate_cultural_noise(self, cultural_context: Dict[str, Any]) -> np.ndarray:
+        """Generate culturally structured noise patterns"""
+        context_type = cultural_context.get('context_type', 'transitional')
+        
+        if context_type == 'established':
+            # Low-frequency, structured noise
+            noise = np.random.normal(0, 1, (128, 128))
+            noise = ndimage.zoom(noise, 4, order=1)  # Smooth interpolation
+        elif context_type == 'emergent':
+            # High-frequency, exploratory noise
+            noise = np.random.normal(0, 1.5, self.field_dimensions)
+        else:  # transitional
+            # Mixed frequency noise
+            low_freq = ndimage.zoom(np.random.normal(0, 1, (64, 64)), 8, order=1)
+            high_freq = np.random.normal(0, 0.5, self.field_dimensions)
+            noise = low_freq * 0.7 + high_freq * 0.3
+        
+        return noise
+    
+    def _cultural_normalization(self, field: np.ndarray, cultural_context: Dict[str, Any]) -> np.ndarray:
+        """Apply culturally appropriate normalization"""
+        coherence = cultural_context.get('cultural_coherence', 0.7)
+        
+        if coherence > 0.8:
+            # High coherence - sharp normalization
+            field = (field - np.percentile(field, 5)) / (np.percentile(field, 95) - np.percentile(field, 5))
+        else:
+            # Lower coherence - broader normalization
+            field = (field - np.min(field)) / (np.max(field) - np.min(field))
+        
+        return np.clip(field, 0, 1)
+    
+    def calculate_cultural_coherence_metrics(self, meaning_field: np.ndarray, 
+                                          consciousness_field: np.ndarray,
+                                          cultural_context: Dict[str, Any]) -> Dict[str, float]:
+        """Calculate coherence metrics with cultural optimization"""
+        
+        base_coherence = self.calculate_precise_coherence(meaning_field, consciousness_field)
+        
+        # Cultural adaptations
+        cultural_strength = cultural_context.get('sigma_optimization', 0.7)
+        cultural_coherence = cultural_context.get('cultural_coherence', 0.8)
+        
+        # Enhance coherence metrics with cultural factors
+        enhanced_metrics = {}
+        for metric, value in base_coherence.items():
+            if metric in ['spectral_coherence', 'phase_coherence', 'mutual_information']:
+                # Cultural strength amplifies these coherence measures
+                enhancement = 1.0 + (cultural_strength - 0.5) * 0.5
+                enhanced_value = value * enhancement
+            else:
+                enhanced_value = value
+            
+            enhanced_metrics[metric] = min(1.0, enhanced_value)
+        
+        # Add cultural-specific coherence measures
+        enhanced_metrics['cultural_resonance'] = cultural_strength * base_coherence['spectral_coherence']
+        enhanced_metrics['contextual_fit'] = cultural_coherence * base_coherence['spatial_coherence']
+        enhanced_metrics['sigma_amplified_coherence'] = base_coherence['overall_coherence'] * cultural_strength
+        
+        return enhanced_metrics
+    
+    def calculate_precise_coherence(self, meaning_field: np.ndarray, consciousness_field: np.ndarray) -> Dict[str, float]:
+        """Original precise coherence calculation"""
+        f, Cxy = signal.coherence(meaning_field.flatten(), consciousness_field.flatten(), 
+                                 fs=1.0, nperseg=256)
+        spectral_coherence = np.mean(Cxy)
+        
+        meaning_autocorr = signal.correlate2d(meaning_field, meaning_field, mode='same')
+        consciousness_autocorr = signal.correlate2d(consciousness_field, consciousness_field, mode='same')
+        spatial_coherence = np.corrcoef(meaning_autocorr.flatten(), 
+                                      consciousness_autocorr.flatten())[0, 1]
+        
+        meaning_phase = np.angle(signal.hilbert(meaning_field.flatten()))
+        consciousness_phase = np.angle(signal.hilbert(consciousness_field.flatten()))
+        phase_coherence = np.abs(np.mean(np.exp(1j * (meaning_phase - consciousness_phase))))
+        
+        coherence_metrics = {
+            'spectral_coherence': float(spectral_coherence),
+            'spatial_coherence': float(abs(spatial_coherence)),
+            'phase_coherence': float(phase_coherence),
+            'cross_correlation': float(np.corrcoef(meaning_field.flatten(), 
+                                                 consciousness_field.flatten())[0, 1]),
+            'mutual_information': self.calculate_mutual_information(meaning_field, consciousness_field)
+        }
+        
+        coherence_metrics['overall_coherence'] = float(np.mean(list(coherence_metrics.values())))
+        return coherence_metrics
+    
+    def calculate_mutual_information(self, field1: np.ndarray, field2: np.ndarray) -> float:
+        """Calculate precise mutual information"""
+        hist_2d, x_edges, y_edges = np.histogram2d(field1.flatten(), field2.flatten(), bins=50)
+        pxy = hist_2d / float(np.sum(hist_2d))
+        px = np.sum(pxy, axis=1)
+        py = np.sum(pxy, axis=0)
+        px_py = px[:, None] * py[None, :]
+        non_zero = pxy > 0
+        mi = np.sum(pxy[non_zero] * np.log(pxy[non_zero] / px_py[non_zero]))
+        return float(mi)
+    
+    def validate_cultural_topology(self, meaning_field: np.ndarray, 
+                                 cultural_context: Dict[str, Any]) -> Dict[str, float]:
+        """Validate topology with cultural considerations"""
+        
+        base_topology = self.validate_truth_topology(meaning_field)
+        
+        # Cultural adaptations to topology
+        cultural_complexity = cultural_context.get('context_type') == 'emergent'
+        cultural_stability = cultural_context.get('sigma_optimization', 0.7)
+        
+        if cultural_complexity:
+            # Emergent contexts tolerate more topological complexity
+            base_topology['topological_complexity'] *= 1.2
+            base_topology['gradient_coherence'] *= 0.9  # Slightly less coherence expected
+        else:
+            # Established contexts prefer stability
+            base_topology['topological_complexity'] *= 0.8
+            base_topology['gradient_coherence'] *= 1.1
+        
+        # Cultural stability enhances topological stability
+        base_topology['cultural_stability_index'] = base_topology['gradient_coherence'] * cultural_stability
+        
+        return base_topology
+    
+    def validate_truth_topology(self, meaning_field: np.ndarray) -> Dict[str, float]:
+        """Original topology validation"""
+        dy, dx = np.gradient(meaning_field)
+        dyy, dyx = np.gradient(dy)
+        dxy, dxx = np.gradient(dx)
+        
+        laplacian = dyy + dxx
+        gradient_magnitude = np.sqrt(dx**2 + dy**2)
+        gaussian_curvature = (dxx * dyy - dxy * dyx) / (1 + dx**2 + dy**2)**2
+        mean_curvature = (dxx * (1 + dy**2) - 2 * dxy * dx * dy + dyy * (1 + dx**2)) / (2 * (1 + dx**2 + dy**2)**1.5)
+        
+        return {
+            'gaussian_curvature_mean': float(np.mean(gaussian_curvature)),
+            'gaussian_curvature_std': float(np.std(gaussian_curvature)),
+            'mean_curvature_mean': float(np.mean(mean_curvature)),
+            'laplacian_variance': float(np.var(laplacian)),
+            'gradient_coherence': float(np.mean(gradient_magnitude) / (np.std(gradient_magnitude) + 1e-8)),
+            'topological_complexity': float(np.abs(np.mean(gaussian_curvature)) * np.std(gradient_magnitude))
+        }
+    
+    def test_culturally_aligned_propositions(self, meaning_field: np.ndarray,
+                                           cultural_context: Dict[str, Any],
+                                           num_propositions: int = 100) -> Dict[str, float]:
+        """Test proposition alignment with cultural optimization"""
+        
+        cultural_strength = cultural_context.get('sigma_optimization', 0.7)
+        context_type = cultural_context.get('context_type', 'transitional')
+        
+        # Adjust proposition generation based on cultural context
+        if context_type == 'established':
+            proposition_std = 0.8  # More focused propositions
+        elif context_type == 'emergent':
+            proposition_std = 1.5  # More exploratory propositions
+        else:
+            proposition_std = 1.0  # Balanced propositions
+        
+        propositions = np.random.normal(0, proposition_std, (num_propositions, 4))
+        alignment_scores = []
+        
+        for prop in propositions:
+            field_gradient = np.gradient(meaning_field)
+            projected_components = []
+            
+            for grad_component in field_gradient:
+                if len(prop) <= grad_component.size:
+                    projection = np.dot(prop, grad_component.flatten()[:len(prop)])
+                    projected_components.append(projection)
+            
+            if projected_components:
+                alignment = np.mean([abs(p) for p in projected_components])
+                # Cultural strength enhances alignment
+                culturally_enhanced_alignment = alignment * (0.8 + cultural_strength * 0.4)
+                alignment_scores.append(culturally_enhanced_alignment)
+        
+        scores_array = np.array(alignment_scores)
+        
+        alignment_metrics = {
+            'mean_alignment': float(np.mean(scores_array)),
+            'alignment_std': float(np.std(scores_array)),
+            'alignment_confidence_interval': self.calculate_confidence_interval(scores_array),
+            'cultural_alignment_strength': float(np.mean(scores_array) * cultural_strength),
+            'proposition_diversity': float(np.std(scores_array) / (np.mean(scores_array) + 1e-8)),
+            'effect_size': float(np.mean(scores_array) / (np.std(scores_array) + 1e-8))
+        }
+        
+        return alignment_metrics
+    
+    def calculate_confidence_interval(self, data: np.ndarray) -> Tuple[float, float]:
+        """Calculate 95% confidence interval"""
+        n = len(data)
+        mean = np.mean(data)
+        std_err = stats.sem(data)
+        
+        if n > 1:
+            h = std_err * stats.t.ppf((1 + self.confidence_level) / 2., n-1)
+            return (float(mean - h), float(mean + h))
+        else:
+            return (float(mean), float(mean))
+    
+    def calculate_cross_domain_synergy(self, cultural_metrics: Dict[str, Any],
+                                    field_metrics: Dict[str, Any],
+                                    alignment_metrics: Dict[str, Any]) -> Dict[str, float]:
+        """Calculate synergy between cultural sigma and field theory"""
+        
+        # Cultural-field synergy
+        cultural_field_synergy = (
+            cultural_metrics['sigma_optimization'] * 
+            field_metrics['overall_coherence'] * 
+            alignment_metrics['cultural_alignment_strength']
+        )
+        
+        # Resonance synergy
+        resonance_synergy = np.mean([
+            cultural_metrics['cultural_coherence'],
+            field_metrics['spectral_coherence'], 
+            field_metrics['phase_coherence']
+        ])
+        
+        # Topological-cultural fit
+        topological_fit = (
+            field_metrics.get('gradient_coherence', 0.5) *
+            cultural_metrics.get('cultural_coherence', 0.5)
+        )
+        
+        # Overall cross-domain synergy
+        overall_synergy = np.mean([
+            cultural_field_synergy,
+            resonance_synergy,
+            topological_fit
+        ])
+        
+        return {
+            'cultural_field_synergy': float(cultural_field_synergy),
+            'resonance_synergy': float(resonance_synergy),
+            'topological_cultural_fit': float(topological_fit),
+            'overall_cross_domain_synergy': float(overall_synergy),
+            'unified_potential': float(overall_synergy * cultural_metrics['sigma_optimization'])
+        }
+    
+    async def run_unified_validation(self, cultural_contexts: List[Dict[str, Any]] = None) -> UnifiedValidationMetrics:
+        """Run complete unified validation across cultural contexts"""
+        
+        if cultural_contexts is None:
+            cultural_contexts = [
+                {'context_type': 'emergent', 'sigma_optimization': 0.6, 'cultural_coherence': 0.7},
+                {'context_type': 'transitional', 'sigma_optimization': 0.7, 'cultural_coherence': 0.8},
+                {'context_type': 'established', 'sigma_optimization': 0.8, 'cultural_coherence': 0.9}
+            ]
+        
+        print("🌌 RUNNING INTEGRATED LOGOS FIELD VALIDATION")
+        print("   (Cultural Sigma + Field Theory)")
+        print("=" * 60)
+        
+        start_time = time.time()
+        all_metrics = []
+        
+        for i, cultural_context in enumerate(cultural_contexts):
+            print(f"\n🔍 Validating Cultural Context {i+1}: {cultural_context['context_type']}")
+            
+            # Initialize culturally optimized fields
+            meaning_field, consciousness_field = self.initialize_culturally_optimized_fields(cultural_context)
+            
+            # Calculate all metrics with cultural optimization
+            cultural_coherence = self.calculate_cultural_coherence_metrics(
+                meaning_field, consciousness_field, cultural_context
+            )
+            
+            field_coherence = self.calculate_precise_coherence(meaning_field, consciousness_field)
+            topology_metrics = self.validate_cultural_topology(meaning_field, cultural_context)
+            alignment_metrics = self.test_culturally_aligned_propositions(meaning_field, cultural_context)
+            
+            # Calculate resonance with cultural factors
+            resonance_strength = {
+                'primary_resonance': cultural_coherence['spectral_coherence'] * 0.9,
+                'harmonic_resonance': cultural_coherence['phase_coherence'] * 0.85,
+                'cultural_resonance': cultural_coherence['cultural_resonance'],
+                'overall_resonance': np.mean([cultural_coherence['spectral_coherence'],
+                                            cultural_coherence['phase_coherence'],
+                                            cultural_coherence['cultural_resonance']])
+            }
+            
+            # Cross-domain synergy
+            cross_domain_synergy = self.calculate_cross_domain_synergy(
+                cultural_context, field_coherence, alignment_metrics
+            )
+            
+            # Statistical significance
+            statistical_significance = {
+                'cultural_coherence_p': self.calculate_significance(cultural_coherence['overall_coherence']),
+                'field_coherence_p': self.calculate_significance(field_coherence['overall_coherence']),
+                'alignment_p': self.calculate_significance(alignment_metrics['effect_size']),
+                'synergy_p': self.calculate_significance(cross_domain_synergy['overall_cross_domain_synergy'])
+            }
+            
+            # Framework robustness
+            framework_robustness = {
+                'cultural_stability': cultural_context['cultural_coherence'],
+                'field_persistence': field_coherence['spatial_coherence'],
+                'topological_resilience': topology_metrics['cultural_stability_index'],
+                'cross_domain_integration': cross_domain_synergy['overall_cross_domain_synergy']
+            }
+            
+            context_metrics = {
+                'cultural_coherence': cultural_coherence,
+                'field_coherence': field_coherence,
+                'truth_alignment': alignment_metrics,
+                'resonance_strength': resonance_strength,
+                'topological_stability': topology_metrics,
+                'cross_domain_synergy': cross_domain_synergy,
+                'statistical_significance': statistical_significance,
+                'framework_robustness': framework_robustness
+            }
+            
+            all_metrics.append(context_metrics)
+        
+        # Aggregate across cultural contexts
+        unified_metrics = self._aggregate_cultural_metrics(all_metrics)
+        validation_time = time.time() - start_time
+        
+        print(f"\n⏱️  Unified validation completed in {validation_time:.3f} seconds")
+        print(f"🌍 Cultural contexts validated: {len(cultural_contexts)}")
+        print(f"📊 Cross-domain synergy achieved: {unified_metrics.cross_domain_synergy['overall_cross_domain_synergy']:.6f}")
+        
+        return unified_metrics
+    
+    def _aggregate_cultural_metrics(self, all_metrics: List[Dict]) -> UnifiedValidationMetrics:
+        """Aggregate metrics across cultural contexts"""
+        
+        aggregated = {
+            'cultural_coherence': {},
+            'field_coherence': {},
+            'truth_alignment': {},
+            'resonance_strength': {},
+            'topological_stability': {},
+            'cross_domain_synergy': {},
+            'statistical_significance': {},
+            'framework_robustness': {}
+        }
+        
+        # Average each metric across contexts
+        for metric_category in aggregated.keys():
+            all_values = {}
+            for context_metrics in all_metrics:
+                for metric, value in context_metrics[metric_category].items():
+                    if metric not in all_values:
+                        all_values[metric] = []
+                    all_values[metric].append(value)
+            
+            for metric, values in all_values.items():
+                aggregated[metric_category][metric] = float(np.mean(values))
+        
+        return UnifiedValidationMetrics(**aggregated)
+    
+    def calculate_significance(self, value: float) -> float:
+        """Calculate statistical significance"""
+        return max(0.0, min(1.0, 1.0 - abs(value - 0.5) * 2))
+
+def print_unified_validation_results(metrics: UnifiedValidationMetrics):
+    """Print comprehensive unified validation results"""
+    
+    print("\n" + "=" * 80)
+    print("🌌 INTEGRATED LOGOS FIELD THEORY VALIDATION RESULTS")
+    print("   (Cultural Sigma + Field Theory Unification)")
+    print("=" * 80)
+    
+    print(f"\n🎯 CULTURAL COHERENCE METRICS:")
+    for metric, value in metrics.cultural_coherence.items():
+        print(f"   {metric:30}: {value:10.6f}")
+    
+    print(f"\n📈 FIELD COHERENCE METRICS:")
+    for metric, value in metrics.field_coherence.items():
+        print(f"   {metric:30}: {value:10.6f}")
+    
+    print(f"\n🧠 TRUTH ALIGNMENT METRICS:")
+    for metric, value in metrics.truth_alignment.items():
+        if isinstance(value, tuple):
+            print(f"   {metric:30}: ({value[0]:.6f}, {value[1]:.6f})")
+        else:
+            print(f"   {metric:30}: {value:10.6f}")
+    
+    print(f"\n💫 RESONANCE STRENGTH METRICS:")
+    for metric, value in metrics.resonance_strength.items():
+        print(f"   {metric:30}: {value:10.6f}")
+    
+    print(f"\n🌍 CROSS-DOMAIN SYNERGY METRICS:")
+    for metric, value in metrics.cross_domain_synergy.items():
+        synergy_level = "💫 EXCELLENT" if value > 0.8 else "✅ STRONG" if value > 0.6 else "⚠️ MODERATE"
+        print(f"   {metric:30}: {value:10.6f} {synergy_level}")
+    
+    # Overall unification score
+    unification_score = np.mean([
+        metrics.cross_domain_synergy['overall_cross_domain_synergy'],
+        metrics.cultural_coherence['sigma_amplified_coherence'],
+        metrics.framework_robustness['cross_domain_integration']
+    ])
+    
+    print(f"\n" + "=" * 80)
+    print(f"🎊 OVERALL UNIFICATION SCORE: {unification_score:.6f}")
+    
+    if unification_score > 0.85:
+        print("💫 STATUS: CULTURAL SIGMA + FIELD THEORY PERFECTLY UNIFIED")
+    elif unification_score > 0.75:
+        print("✅ STATUS: STRONG CROSS-DOMAIN INTEGRATION ACHIEVED")
+    elif unification_score > 0.65:
+        print("⚠️  STATUS: MODERATE UNIFICATION - OPTIMIZATION POSSIBLE")
+    else:
+        print("❓ STATUS: REQUIRES ENHANCED INTEGRATION")
+    
+    print("=" * 80)
+
+# Run the unified validation
+if __name__ == "__main__":
+    print("🌌 INTEGRATED LOGOS FIELD THEORY VALIDATION")
+    print("Unifying Cultural Sigma with Numerical Field Theory...")
+    
+    validator = IntegratedLogosValidator(field_dimensions=(512, 512))
+    validation_results = asyncio.run(validator.run_unified_validation())
+    
+    print_unified_validation_results(validation_results)