"""TNFR Unified Field Prototype - Mathematical Unification Framework

This module implements the discoveries from TETRAD_MATHEMATICAL_AUDIT_2025.md:
unified complex fields, conservation laws, and emergent field candidates.

EXPERIMENTAL STATUS: Research prototype based on mathematical analysis.
Not yet promoted to canonical - requires extensive validation.

New Fields Discovered:
----------------------
1. Complex Geometric Field Ψ = K_φ + i·J_φ (geometry-transport unification)
2. Chirality Field χ (handedness detection)
3. Symmetry Breaking Field 𝒮 (phase transition indicator)
4. Coherence Coupling Field 𝒞 (multi-scale connector)

Tensor Invariants:
-----------------
1. Energy Density ℰ (quadratic field combinations)
2. Action Density 𝒜 (bilinear field interactions)
3. Topological Charge 𝒬 (topological invariant)

Conservation Laws:
-----------------
1. Structural Continuity: ∂ρ/∂t + ∇·𝐉 = 0
2. Flux Conservation: Incompressibility conditions

Physics Foundation:
------------------
Based on the fundamental duality discovered between K_φ (geometric curvature)
and J_φ (phase current) showing correlation r ≈ -0.85 to -0.997, suggesting
they are dual aspects of a single complex geometric object.
"""

from __future__ import annotations

import numpy as np
from typing import Dict, Tuple, Any, Optional
import math

from ..constants.canonical import PHI  # Golden ratio constant

try:
    import networkx as nx
except ImportError:
    nx = None

# Import canonical fields
try:
    from ..physics.canonical import (
        compute_structural_potential,
        compute_phase_gradient, 
        compute_phase_curvature
    )
    from ..physics.extended import (
        compute_phase_current,
        compute_dnfr_flux
    )
except ImportError:
    # Standalone usage - define minimal interfaces
    def compute_structural_potential(G, alpha=PHI):
        """Minimal implementation for prototype.""" 
        return {n: 0.1 for n in G.nodes()}
    
    def compute_phase_gradient(G):
        """Minimal implementation for prototype."""
        return {n: 0.1 for n in G.nodes()}
        
    def compute_phase_curvature(G):
        """Minimal implementation for prototype."""
        return {n: 0.1 for n in G.nodes()}
        
    def compute_phase_current(G):
        """Minimal implementation for prototype."""
        return {n: -0.1 for n in G.nodes()}
        
    def compute_dnfr_flux(G):
        """Minimal implementation for prototype."""
        return {n: 0.05 for n in G.nodes()}


# ============================================================================
# UNIFIED COMPLEX FIELDS
# ============================================================================

def compute_complex_geometric_field(G: Any) -> Dict[Any, complex]:
    """Compute unified complex geometric field Ψ = K_φ + i·J_φ.
    
    DISCOVERY: K_φ (curvature) and J_φ (current) show strong anticorrelation
    (r ≈ -0.85 to -0.997), indicating they are dual aspects of a single
    complex geometric object.
    
    Physics Interpretation:
    - Real part (K_φ): Static geometric confinement
    - Imaginary part (J_φ): Dynamic transport flow
    - Magnitude |Ψ|: Total geometric-transport intensity
    - Phase arg(Ψ): Balance between geometry and transport
    
    Parameters
    ----------
    G : NetworkX graph
        Network with 'theta'/'phase' attributes on nodes
        
    Returns
    -------
    Dict[node_id, complex]
        Complex field values Ψ(i) = K_φ(i) + i·J_φ(i)
        
    Examples
    --------
    >>> G = nx.watts_strogatz_graph(10, k=3, p=0.2)
    >>> # Initialize phases
    >>> for i, n in enumerate(G.nodes()):
    ...     G.nodes[n]['theta'] = 2*np.pi*i/10
    >>> psi = compute_complex_geometric_field(G)
    >>> magnitude = {n: abs(psi[n]) for n in G.nodes()}
    >>> phase_angle = {n: np.angle(psi[n]) for n in G.nodes()}
    """
    # Get constituent fields
    k_phi = compute_phase_curvature(G)
    j_phi = compute_phase_current(G)
    
    # Construct complex field
    psi = {}
    for node in G.nodes():
        psi[node] = complex(k_phi[node], j_phi[node])
    
    return psi


def compute_field_magnitude(complex_field: Dict[Any, complex]) -> Dict[Any, float]:
    """Compute magnitude |Ψ| of complex field."""
    return {node: abs(value) for node, value in complex_field.items()}


def compute_field_phase(complex_field: Dict[Any, complex]) -> Dict[Any, float]:
    """Compute phase angle arg(Ψ) of complex field."""
    return {node: np.angle(value) for node, value in complex_field.items()}


# ============================================================================
# EMERGENT FIELD CANDIDATES 
# ============================================================================

def compute_chirality_field(G: Any) -> Dict[Any, float]:
    """Compute chirality field χ = |∇φ|·K_φ - J_φ·J_ΔNFR.
    
    Physics: Detects "handedness" (left/right asymmetry) in TNFR structures.
    High |χ| indicates chiral patterns, broken mirror symmetry.
    
    Applications:
    - Detect spiral vs anti-spiral patterns
    - Identify symmetry-breaking events
    - Classify topological defects
    
    Parameters
    ---------- 
    G : NetworkX graph
        Network with phase and delta_nfr attributes
        
    Returns
    -------
    Dict[node_id, float]
        Chirality field values χ(i)
    """
    grad_phi = compute_phase_gradient(G)
    k_phi = compute_phase_curvature(G) 
    j_phi = compute_phase_current(G)
    j_dnfr = compute_dnfr_flux(G)
    
    chirality = {}
    for node in G.nodes():
        chirality[node] = (grad_phi[node] * k_phi[node] - 
                          j_phi[node] * j_dnfr[node])
    
    return chirality


def compute_symmetry_breaking_field(G: Any) -> Dict[Any, float]:
    """Compute symmetry breaking field 𝒮 = (|∇φ|² - K_φ²) + (J_φ² - J_ΔNFR²).
    
    Physics: Quantifies imbalance between conjugate field pairs.
    Detects when symmetries are broken and system reorganizing.
    
    Applications:
    - Phase transition detection
    - Identify reorganization events  
    - Predict instabilities
    
    Parameters
    ----------
    G : NetworkX graph
        Network with phase and delta_nfr attributes
        
    Returns
    -------
    Dict[node_id, float]
        Symmetry breaking field 𝒮(i)
    """
    grad_phi = compute_phase_gradient(G)
    k_phi = compute_phase_curvature(G)
    j_phi = compute_phase_current(G)
    j_dnfr = compute_dnfr_flux(G)
    
    symmetry_breaking = {}
    for node in G.nodes():
        term1 = grad_phi[node]**2 - k_phi[node]**2
        term2 = j_phi[node]**2 - j_dnfr[node]**2
        symmetry_breaking[node] = term1 + term2
        
    return symmetry_breaking


def compute_coherence_coupling_field(G: Any) -> Dict[Any, float]:
    """Compute coherence coupling field 𝒞 = Φ_s · |Ψ|.
    
    Physics: Connects global structural potential with local geometry-transport
    intensity. Predicts multi-scale coupling strength.
    
    Applications:
    - Multi-scale stability prediction
    - Hierarchical coupling analysis
    - Global-local interaction strength
    
    Parameters
    ----------
    G : NetworkX graph
        Network with phase and delta_nfr attributes
        
    Returns
    -------
    Dict[node_id, float]  
        Coherence coupling field 𝒞(i)
    """
    phi_s = compute_structural_potential(G)
    psi = compute_complex_geometric_field(G)
    
    coherence_coupling = {}
    for node in G.nodes():
        coherence_coupling[node] = phi_s[node] * abs(psi[node])
        
    return coherence_coupling


# ============================================================================
# TENSOR INVARIANTS
# ============================================================================

def compute_energy_density(G: Any) -> Dict[Any, float]:
    """Compute field energy density ℰ = Φ_s² + |∇φ|² + K_φ² + J_φ² + J_ΔNFR².
    
    Physics: Analogous to electromagnetic energy density. 
    Quadratic in all field components, gauge-invariant.
    
    Conservation: Should be conserved under field evolution.
    """
    phi_s = compute_structural_potential(G)
    grad_phi = compute_phase_gradient(G)
    k_phi = compute_phase_curvature(G)
    j_phi = compute_phase_current(G)  
    j_dnfr = compute_dnfr_flux(G)
    
    energy_density = {}
    for node in G.nodes():
        energy_density[node] = (
            phi_s[node]**2 + grad_phi[node]**2 + k_phi[node]**2 + 
            j_phi[node]**2 + j_dnfr[node]**2
        )
        
    return energy_density


def compute_action_density(G: Any) -> Dict[Any, float]:
    """Compute field action density 𝒜 = Φ_s·|∇φ| + K_φ·J_φ + |∇φ|·J_ΔNFR.
    
    Physics: Bilinear field interactions. Captures coupling between
    different field components.
    
    Variational: Related to Lagrangian action principle.
    """
    phi_s = compute_structural_potential(G)
    grad_phi = compute_phase_gradient(G)
    k_phi = compute_phase_curvature(G) 
    j_phi = compute_phase_current(G)
    j_dnfr = compute_dnfr_flux(G)
    
    action_density = {}
    for node in G.nodes():
        action_density[node] = (
            phi_s[node] * grad_phi[node] + 
            k_phi[node] * j_phi[node] + 
            grad_phi[node] * j_dnfr[node]
        )
        
    return action_density


def compute_topological_charge(G: Any) -> Dict[Any, float]:
    """Compute topological charge 𝒬 = |∇φ|·J_φ - K_φ·J_ΔNFR.
    
    Physics: Topological invariant analogous to electric charge.
    Characterizes topological defects and vortex structures.
    
    Conservation: Should be conserved under continuous deformations.
    """
    grad_phi = compute_phase_gradient(G)
    k_phi = compute_phase_curvature(G)
    j_phi = compute_phase_current(G)
    j_dnfr = compute_dnfr_flux(G)
    
    topological_charge = {}
    for node in G.nodes():
        topological_charge[node] = (
            grad_phi[node] * j_phi[node] - 
            k_phi[node] * j_dnfr[node]
        )
        
    return topological_charge


# ============================================================================
# CONSERVATION LAWS
# ============================================================================

def compute_charge_density(G: Any) -> Dict[Any, float]:
    """Compute structural charge density ρ = Φ_s + K_φ.
    
    Physics: "Source" term in conservation equation ∂ρ/∂t + ∇·𝐉 = 0.
    Combines global potential with local geometric curvature.
    """
    phi_s = compute_structural_potential(G)
    k_phi = compute_phase_curvature(G)
    
    charge_density = {}
    for node in G.nodes():
        charge_density[node] = phi_s[node] + k_phi[node]
        
    return charge_density


def compute_current_vector(G: Any) -> Dict[Any, Tuple[float, float]]:
    """Compute current vector 𝐉 = (J_φ, J_ΔNFR).
    
    Physics: "Flux" term in conservation equation ∂ρ/∂t + ∇·𝐉 = 0.
    Two-component vector capturing phase and potential transport.
    """
    j_phi = compute_phase_current(G)
    j_dnfr = compute_dnfr_flux(G)
    
    current_vector = {}
    for node in G.nodes():
        current_vector[node] = (j_phi[node], j_dnfr[node])
        
    return current_vector


def test_conservation_balance(G: Any) -> Dict[str, float]:
    """Test structural conservation law ∂ρ/∂t + ∇·𝐉 ≈ 0.
    
    Returns statistical measures of conservation violation.
    Perfect conservation → all measures ≈ 0.
    """
    charge_density = compute_charge_density(G)
    current_vector = compute_current_vector(G)
    
    # Discrete approximation of divergence
    nodes = list(G.nodes())
    balance_violations = []
    
    for node in nodes:
        neighbors = list(G.neighbors(node))
        if not neighbors:
            continue
            
        # Gradient of charge density (proxy for ∂ρ/∂t)
        charge_grad = sum(charge_density[nb] - charge_density[node] 
                         for nb in neighbors) / len(neighbors)
        
        # Divergence of current vector
        j_phi_div = sum(current_vector[nb][0] - current_vector[node][0]
                       for nb in neighbors) / len(neighbors)
        j_dnfr_div = sum(current_vector[nb][1] - current_vector[node][1] 
                        for nb in neighbors) / len(neighbors)
        
        # Conservation balance: should be ≈ 0
        balance = charge_grad + j_phi_div + j_dnfr_div
        balance_violations.append(balance)
    
    if balance_violations:
        return {
            'mean_violation': np.mean(balance_violations),
            'std_violation': np.std(balance_violations),
            'max_violation': np.max(np.abs(balance_violations)),
            'conservation_quality': 1.0 / (1.0 + np.std(balance_violations))
        }
    else:
        return {
            'mean_violation': 0.0,
            'std_violation': 0.0, 
            'max_violation': 0.0,
            'conservation_quality': 1.0
        }


# ============================================================================
# COMPREHENSIVE UNIFIED ANALYSIS
# ============================================================================

def compute_unified_field_suite(G: Any) -> Dict[str, Dict[Any, float]]:
    """Compute complete unified field analysis.
    
    Returns all unified fields, tensor invariants, and conservation measures
    in a single comprehensive analysis.
    
    Returns
    -------
    Dict[str, Dict[Any, float]]
        Complete field analysis with categories:
        - 'complex_fields': Ψ magnitude and phase
        - 'emergent_fields': χ, 𝒮, 𝒞 
        - 'tensor_invariants': ℰ, 𝒜, 𝒬
        - 'conservation': ρ, 𝐉 components
        - 'diagnostics': Conservation quality metrics
    """
    results = {}
    
    # Complex geometric field
    psi = compute_complex_geometric_field(G)
    results['psi_magnitude'] = compute_field_magnitude(psi)
    results['psi_phase'] = compute_field_phase(psi) 
    
    # Emergent fields
    results['chirality'] = compute_chirality_field(G)
    results['symmetry_breaking'] = compute_symmetry_breaking_field(G)
    results['coherence_coupling'] = compute_coherence_coupling_field(G)
    
    # Tensor invariants
    results['energy_density'] = compute_energy_density(G)
    results['action_density'] = compute_action_density(G)
    results['topological_charge'] = compute_topological_charge(G)
    
    # Conservation quantities
    results['charge_density'] = compute_charge_density(G)
    current_vector = compute_current_vector(G)
    results['current_j_phi'] = {n: cv[0] for n, cv in current_vector.items()}
    results['current_j_dnfr'] = {n: cv[1] for n, cv in current_vector.items()}
    
    # Conservation diagnostics  
    conservation_metrics = test_conservation_balance(G)
    results['conservation_metrics'] = conservation_metrics
    
    return results


# ============================================================================
# ANALYSIS AND VISUALIZATION UTILITIES  
# ============================================================================

def analyze_field_correlations(results: Dict[str, Dict[Any, float]]) -> Dict[str, float]:
    """Analyze correlations between unified fields.
    
    Returns correlation matrix for key field relationships to verify
    theoretical predictions (e.g., K_φ ↔ J_φ anticorrelation).
    """
    # Extract field arrays (assuming consistent node ordering)
    fields = {}
    sample_nodes = list(next(iter(results.values())).keys())
    
    for field_name, field_data in results.items():
        if isinstance(field_data, dict) and sample_nodes[0] in field_data:
            fields[field_name] = np.array([field_data[n] for n in sample_nodes])
    
    # Compute correlation matrix for key relationships
    correlations = {}
    field_names = list(fields.keys())
    
    for i, name1 in enumerate(field_names):
        for j, name2 in enumerate(field_names):
            if i < j:  # Upper triangular
                corr = np.corrcoef(fields[name1], fields[name2])[0, 1]
                correlations[f'{name1}_vs_{name2}'] = corr
                
    return correlations


def summary_statistics(results: Dict[str, Dict[Any, float]]) -> Dict[str, Dict[str, float]]:
    """Compute summary statistics for all unified fields."""
    stats = {}
    
    for field_name, field_data in results.items():
        if isinstance(field_data, dict):
            values = list(field_data.values())
            if values and all(isinstance(v, (int, float)) for v in values):
                stats[field_name] = {
                    'mean': np.mean(values),
                    'std': np.std(values),
                    'min': np.min(values),
                    'max': np.max(values),
                    'range': np.max(values) - np.min(values)
                }
        elif isinstance(field_data, dict) and 'mean_violation' in field_data:
            # Conservation metrics case
            stats[field_name] = field_data
            
    return stats


# ============================================================================
# PROTOTYPE TESTING
# ============================================================================

def demo_unified_fields():
    """Demonstration of unified field calculations."""
    if nx is None:
        print("NetworkX not available - cannot run demo")
        return
        
    print("🧮 TNFR Unified Fields Prototype Demo")
    print("=" * 50)
    
    # Create test network
    G = nx.watts_strogatz_graph(12, k=3, p=0.3, seed=42)
    
    # Initialize with non-trivial patterns  
    for i, node in enumerate(G.nodes()):
        G.nodes[node]['theta'] = 2*np.pi*i/12 + 0.3*np.sin(4*np.pi*i/12)
        G.nodes[node]['delta_nfr'] = 0.2 * (1 + np.cos(6*np.pi*i/12))
        
    # Compute unified analysis
    results = compute_unified_field_suite(G)
    stats = summary_statistics(results)
    correlations = analyze_field_correlations(results)
    
    print("\n📊 Field Statistics Summary:")
    for field_name, field_stats in stats.items():
        if isinstance(field_stats, dict) and 'mean' in field_stats:
            print(f"  {field_name}: μ={field_stats['mean']:.4f}, σ={field_stats['std']:.4f}")
            
    print("\n🔍 Key Correlations:")
    for corr_name, corr_value in correlations.items():
        print(f"  {corr_name}: r={corr_value:+.3f}")
        
    print(f"\n⚖️ Conservation Quality: {results['conservation_metrics']['conservation_quality']:.3f}")
    print(f"   Balance violation: μ={results['conservation_metrics']['mean_violation']:.6f}")
    
    print("\n✅ Unified field prototype demonstration complete!")


if __name__ == "__main__":
    demo_unified_fields()