quantrs2_sim/

quantum_gravity_simulation.rs

//! Quantum Gravity Simulation Framework
//!
//! This module provides a comprehensive implementation of quantum gravity theories and
//! simulation methods, including loop quantum gravity, causal dynamical triangulation,
//! asymptotic safety, emergent gravity models, holographic correspondence, and AdS/CFT
//! duality. This framework enables exploration of quantum spacetime dynamics and
//! gravitational quantum effects at the Planck scale.

use ndarray::{s, Array1, Array2, Array3, Array4};
use num_complex::Complex64;
use rand::{thread_rng, Rng};
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
use std::f64::consts::PI;

use crate::error::{Result, SimulatorError};
use crate::scirs2_integration::SciRS2Backend;

/// Quantum gravity simulation configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QuantumGravityConfig {
    /// Approach to quantum gravity
    pub gravity_approach: GravityApproach,
    /// Planck length scale (in natural units)
    pub planck_length: f64,
    /// Planck time scale (in natural units)
    pub planck_time: f64,
    /// Number of spatial dimensions
    pub spatial_dimensions: usize,
    /// Enable Lorentz invariance
    pub lorentz_invariant: bool,
    /// Background metric type
    pub background_metric: BackgroundMetric,
    /// Cosmological constant
    pub cosmological_constant: f64,
    /// Newton's gravitational constant
    pub gravitational_constant: f64,
    /// Speed of light (natural units)
    pub speed_of_light: f64,
    /// Hbar (natural units)
    pub reduced_planck_constant: f64,
    /// Enable quantum corrections
    pub quantum_corrections: bool,
    /// Loop quantum gravity specific settings
    pub lqg_config: Option<LQGConfig>,
    /// Causal dynamical triangulation settings
    pub cdt_config: Option<CDTConfig>,
    /// Asymptotic safety settings
    pub asymptotic_safety_config: Option<AsymptoticSafetyConfig>,
    /// AdS/CFT correspondence settings
    pub ads_cft_config: Option<AdSCFTConfig>,
}

impl Default for QuantumGravityConfig {
    fn default() -> Self {
        Self {
            gravity_approach: GravityApproach::LoopQuantumGravity,
            planck_length: 1.616e-35, // meters
            planck_time: 5.391e-44,   // seconds
            spatial_dimensions: 3,
            lorentz_invariant: true,
            background_metric: BackgroundMetric::Minkowski,
            cosmological_constant: 0.0,
            gravitational_constant: 6.674e-11,  // m³/kg/s²
            speed_of_light: 299792458.0,        // m/s
            reduced_planck_constant: 1.055e-34, // J⋅s
            quantum_corrections: true,
            lqg_config: Some(LQGConfig::default()),
            cdt_config: Some(CDTConfig::default()),
            asymptotic_safety_config: Some(AsymptoticSafetyConfig::default()),
            ads_cft_config: Some(AdSCFTConfig::default()),
        }
    }
}

/// Approaches to quantum gravity
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum GravityApproach {
    /// Loop Quantum Gravity
    LoopQuantumGravity,
    /// Causal Dynamical Triangulation
    CausalDynamicalTriangulation,
    /// Asymptotic Safety
    AsymptoticSafety,
    /// String Theory approaches
    StringTheory,
    /// Emergent Gravity models
    EmergentGravity,
    /// Holographic approaches (AdS/CFT)
    HolographicGravity,
    /// Regge Calculus
    ReggeCalculus,
    /// Group Field Theory
    GroupFieldTheory,
    /// Causal Sets
    CausalSets,
    /// Entropic Gravity
    EntropicGravity,
}

/// Background spacetime metrics
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum BackgroundMetric {
    /// Minkowski spacetime (flat)
    Minkowski,
    /// de Sitter spacetime (expanding)
    DeSitter,
    /// Anti-de Sitter spacetime
    AntiDeSitter,
    /// Schwarzschild black hole
    Schwarzschild,
    /// Kerr black hole (rotating)
    Kerr,
    /// Friedmann-Lemaître-Robertson-Walker (cosmological)
    FLRW,
    /// Custom metric tensor
    Custom,
}

/// Loop Quantum Gravity configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct LQGConfig {
    /// Barbero-Immirzi parameter
    pub barbero_immirzi_parameter: f64,
    /// Maximum spin for SU(2) representations
    pub max_spin: f64,
    /// Number of spin network nodes
    pub num_nodes: usize,
    /// Number of spin network edges
    pub num_edges: usize,
    /// Enable spin foam dynamics
    pub spin_foam_dynamics: bool,
    /// Quantum geometry area eigenvalues
    pub area_eigenvalues: Vec<f64>,
    /// Volume eigenvalue spectrum
    pub volume_eigenvalues: Vec<f64>,
    /// Holonomy discretization parameter
    pub holonomy_discretization: f64,
}

impl Default for LQGConfig {
    fn default() -> Self {
        Self {
            barbero_immirzi_parameter: 0.2375, // Standard value
            max_spin: 5.0,
            num_nodes: 100,
            num_edges: 300,
            spin_foam_dynamics: true,
            area_eigenvalues: (1..=20)
                .map(|j| (j as f64) * (PI * 1.616e-35_f64.powi(2)))
                .collect(),
            volume_eigenvalues: (1..=50)
                .map(|n| (n as f64).sqrt() * 1.616e-35_f64.powi(3))
                .collect(),
            holonomy_discretization: 0.1,
        }
    }
}

/// Causal Dynamical Triangulation configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct CDTConfig {
    /// Number of simplices in triangulation
    pub num_simplices: usize,
    /// Time slicing parameter
    pub time_slicing: f64,
    /// Spatial volume constraint
    pub spatial_volume: f64,
    /// Bare gravitational coupling
    pub bare_coupling: f64,
    /// Cosmological constant coupling
    pub cosmological_coupling: f64,
    /// Enable Monte Carlo moves
    pub monte_carlo_moves: bool,
    /// Number of MC sweeps
    pub mc_sweeps: usize,
    /// Accept/reject threshold
    pub acceptance_threshold: f64,
}

impl Default for CDTConfig {
    fn default() -> Self {
        Self {
            num_simplices: 10000,
            time_slicing: 0.1,
            spatial_volume: 1000.0,
            bare_coupling: 0.1,
            cosmological_coupling: 0.01,
            monte_carlo_moves: true,
            mc_sweeps: 1000,
            acceptance_threshold: 0.5,
        }
    }
}

/// Asymptotic Safety configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct AsymptoticSafetyConfig {
    /// UV fixed point Newton constant
    pub uv_newton_constant: f64,
    /// UV fixed point cosmological constant
    pub uv_cosmological_constant: f64,
    /// Beta function truncation order
    pub truncation_order: usize,
    /// Energy scale for RG flow
    pub energy_scale: f64,
    /// Critical exponents
    pub critical_exponents: Vec<f64>,
    /// Enable higher derivative terms
    pub higher_derivatives: bool,
    /// Number of RG flow steps
    pub rg_flow_steps: usize,
}

impl Default for AsymptoticSafetyConfig {
    fn default() -> Self {
        Self {
            uv_newton_constant: 0.1,
            uv_cosmological_constant: 0.01,
            truncation_order: 4,
            energy_scale: 1.0,
            critical_exponents: vec![-2.0, 0.5, 1.2], // Example critical exponents
            higher_derivatives: true,
            rg_flow_steps: 1000,
        }
    }
}

/// AdS/CFT correspondence configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct AdSCFTConfig {
    /// AdS space dimension
    pub ads_dimension: usize,
    /// CFT dimension (AdS_d+1/CFT_d)
    pub cft_dimension: usize,
    /// AdS radius
    pub ads_radius: f64,
    /// Central charge of CFT
    pub central_charge: f64,
    /// Temperature (for thermal AdS)
    pub temperature: f64,
    /// Enable black hole formation
    pub black_hole_formation: bool,
    /// Holographic entanglement entropy
    pub holographic_entanglement: bool,
    /// Number of degrees of freedom
    pub degrees_of_freedom: usize,
}

impl Default for AdSCFTConfig {
    fn default() -> Self {
        Self {
            ads_dimension: 5, // AdS_5
            cft_dimension: 4, // CFT_4
            ads_radius: 1.0,
            central_charge: 100.0,
            temperature: 0.0,
            black_hole_formation: false,
            holographic_entanglement: true,
            degrees_of_freedom: 1000,
        }
    }
}

/// Spin network representation for Loop Quantum Gravity
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SpinNetwork {
    /// Nodes with SU(2) representations
    pub nodes: Vec<SpinNetworkNode>,
    /// Edges with spin labels
    pub edges: Vec<SpinNetworkEdge>,
    /// Intertwiners at nodes
    pub intertwiners: HashMap<usize, Intertwiner>,
    /// Holonomies along edges
    pub holonomies: HashMap<usize, SU2Element>,
}

/// Spin network node
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SpinNetworkNode {
    /// Node identifier
    pub id: usize,
    /// Valence (number of connected edges)
    pub valence: usize,
    /// Node position in embedding space
    pub position: Vec<f64>,
    /// Associated quantum numbers
    pub quantum_numbers: Vec<f64>,
}

/// Spin network edge
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SpinNetworkEdge {
    /// Edge identifier
    pub id: usize,
    /// Source node
    pub source: usize,
    /// Target node
    pub target: usize,
    /// Spin label (j)
    pub spin: f64,
    /// Edge length (quantum geometry)
    pub length: f64,
}

/// SU(2) intertwiner at spin network nodes
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct Intertwiner {
    /// Intertwiner identifier
    pub id: usize,
    /// Input spins
    pub input_spins: Vec<f64>,
    /// Output spin
    pub output_spin: f64,
    /// Clebsch-Gordan coefficients
    pub clebsch_gordan_coeffs: Array2<Complex64>,
}

/// SU(2) group element (holonomy)
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SU2Element {
    /// Complex matrix representation
    pub matrix: Array2<Complex64>,
    /// Pauli matrices decomposition
    pub pauli_coefficients: [Complex64; 4],
}

/// Simplicial complex for Causal Dynamical Triangulation
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SimplicialComplex {
    /// Vertices in spacetime
    pub vertices: Vec<SpacetimeVertex>,
    /// Simplices (tetrahedra in 4D)
    pub simplices: Vec<Simplex>,
    /// Time slicing structure
    pub time_slices: Vec<TimeSlice>,
    /// Causal structure
    pub causal_relations: HashMap<usize, Vec<usize>>,
}

/// Spacetime vertex
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SpacetimeVertex {
    /// Vertex identifier
    pub id: usize,
    /// Spacetime coordinates
    pub coordinates: Vec<f64>,
    /// Time coordinate
    pub time: f64,
    /// Coordination number
    pub coordination: usize,
}

/// Simplex (fundamental building block)
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct Simplex {
    /// Simplex identifier
    pub id: usize,
    /// Vertex indices
    pub vertices: Vec<usize>,
    /// Simplex type (spacelike/timelike)
    pub simplex_type: SimplexType,
    /// Volume (discrete)
    pub volume: f64,
    /// Action contribution
    pub action: f64,
}

/// Type of simplex in CDT
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum SimplexType {
    /// Spacelike simplex
    Spacelike,
    /// Timelike simplex
    Timelike,
    /// Mixed simplex
    Mixed,
}

/// Time slice in CDT
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TimeSlice {
    /// Time value
    pub time: f64,
    /// Vertices in this slice
    pub vertices: Vec<usize>,
    /// Spatial volume
    pub spatial_volume: f64,
    /// Intrinsic curvature
    pub curvature: f64,
}

/// Renormalization group trajectory
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct RGTrajectory {
    /// Coupling constants vs energy scale
    pub coupling_evolution: HashMap<String, Vec<f64>>,
    /// Energy scales
    pub energy_scales: Vec<f64>,
    /// Beta functions
    pub beta_functions: HashMap<String, Vec<f64>>,
    /// Fixed points
    pub fixed_points: Vec<FixedPoint>,
}

/// Fixed point in RG flow
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct FixedPoint {
    /// Fixed point couplings
    pub couplings: HashMap<String, f64>,
    /// Critical exponents
    pub critical_exponents: Vec<f64>,
    /// Stability type
    pub stability: FixedPointStability,
}

/// Fixed point stability
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum FixedPointStability {
    /// UV attractive
    UVAttractive,
    /// IR attractive
    IRAttractive,
    /// Saddle point
    Saddle,
    /// Unstable
    Unstable,
}

/// Holographic duality correspondence
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HolographicDuality {
    /// Bulk geometry (AdS space)
    pub bulk_geometry: BulkGeometry,
    /// Boundary theory (CFT)
    pub boundary_theory: BoundaryTheory,
    /// Holographic dictionary
    pub holographic_dictionary: HashMap<String, String>,
    /// Entanglement structure
    pub entanglement_structure: EntanglementStructure,
}

/// Bulk AdS geometry
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct BulkGeometry {
    /// Metric tensor
    pub metric_tensor: Array2<f64>,
    /// AdS radius
    pub ads_radius: f64,
    /// Black hole horizon (if present)
    pub horizon_radius: Option<f64>,
    /// Temperature
    pub temperature: f64,
    /// Stress-energy tensor
    pub stress_energy_tensor: Array2<f64>,
}

/// Boundary CFT
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct BoundaryTheory {
    /// Central charge
    pub central_charge: f64,
    /// Operator dimensions
    pub operator_dimensions: HashMap<String, f64>,
    /// Correlation functions
    pub correlation_functions: HashMap<String, Array1<Complex64>>,
    /// Conformal symmetry generators
    pub conformal_generators: Vec<Array2<Complex64>>,
}

/// Entanglement structure in holographic duality
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct EntanglementStructure {
    /// Ryu-Takayanagi surfaces
    pub rt_surfaces: Vec<RTSurface>,
    /// Entanglement entropy
    pub entanglement_entropy: HashMap<String, f64>,
    /// Holographic complexity
    pub holographic_complexity: f64,
    /// Entanglement spectrum
    pub entanglement_spectrum: Array1<f64>,
}

/// Ryu-Takayanagi surface
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct RTSurface {
    /// Surface coordinates
    pub coordinates: Array2<f64>,
    /// Surface area
    pub area: f64,
    /// Associated boundary region
    pub boundary_region: BoundaryRegion,
}

/// Boundary region for entanglement
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct BoundaryRegion {
    /// Region coordinates
    pub coordinates: Array2<f64>,
    /// Region volume
    pub volume: f64,
    /// Entanglement entropy
    pub entropy: f64,
}

/// Main quantum gravity simulator
#[derive(Debug)]
pub struct QuantumGravitySimulator {
    /// Configuration
    config: QuantumGravityConfig,
    /// Current spacetime state
    spacetime_state: Option<SpacetimeState>,
    /// Spin network (for LQG)
    spin_network: Option<SpinNetwork>,
    /// Simplicial complex (for CDT)
    simplicial_complex: Option<SimplicialComplex>,
    /// RG trajectory (for Asymptotic Safety)
    rg_trajectory: Option<RGTrajectory>,
    /// Holographic duality (for AdS/CFT)
    holographic_duality: Option<HolographicDuality>,
    /// SciRS2 backend for numerical computations
    backend: Option<SciRS2Backend>,
    /// Simulation history
    simulation_history: Vec<GravitySimulationResult>,
    /// Performance statistics
    stats: GravitySimulationStats,
}

/// Spacetime state representation
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SpacetimeState {
    /// Metric tensor field
    pub metric_field: Array4<f64>,
    /// Curvature tensor
    pub curvature_tensor: Array4<f64>,
    /// Matter fields
    pub matter_fields: HashMap<String, Array3<Complex64>>,
    /// Quantum fluctuations
    pub quantum_fluctuations: Array3<Complex64>,
    /// Energy-momentum tensor
    pub energy_momentum_tensor: Array2<f64>,
}

/// Quantum gravity simulation result
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct GravitySimulationResult {
    /// Approach used
    pub approach: GravityApproach,
    /// Ground state energy
    pub ground_state_energy: f64,
    /// Spacetime volume
    pub spacetime_volume: f64,
    /// Quantum geometry measurements
    pub geometry_measurements: GeometryMeasurements,
    /// Convergence information
    pub convergence_info: ConvergenceInfo,
    /// Physical observables
    pub observables: HashMap<String, f64>,
    /// Computation time
    pub computation_time: f64,
}

/// Quantum geometry measurements
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct GeometryMeasurements {
    /// Area eigenvalue spectrum
    pub area_spectrum: Vec<f64>,
    /// Volume eigenvalue spectrum
    pub volume_spectrum: Vec<f64>,
    /// Length eigenvalue spectrum
    pub length_spectrum: Vec<f64>,
    /// Discrete curvature
    pub discrete_curvature: f64,
    /// Topology measurements
    pub topology_measurements: TopologyMeasurements,
}

/// Topology measurements
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TopologyMeasurements {
    /// Euler characteristic
    pub euler_characteristic: i32,
    /// Betti numbers
    pub betti_numbers: Vec<usize>,
    /// Homology groups
    pub homology_groups: Vec<String>,
    /// Fundamental group
    pub fundamental_group: String,
}

/// Convergence information
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct ConvergenceInfo {
    /// Number of iterations
    pub iterations: usize,
    /// Final residual
    pub final_residual: f64,
    /// Convergence achieved
    pub converged: bool,
    /// Convergence history
    pub convergence_history: Vec<f64>,
}

/// Simulation performance statistics
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct GravitySimulationStats {
    /// Total simulation time
    pub total_time: f64,
    /// Memory usage (bytes)
    pub memory_usage: usize,
    /// Number of calculations performed
    pub calculations_performed: usize,
    /// Average computation time per step
    pub avg_time_per_step: f64,
    /// Peak memory usage
    pub peak_memory_usage: usize,
}

impl Default for GravitySimulationStats {
    fn default() -> Self {
        Self {
            total_time: 0.0,
            memory_usage: 0,
            calculations_performed: 0,
            avg_time_per_step: 0.0,
            peak_memory_usage: 0,
        }
    }
}

impl QuantumGravitySimulator {
    /// Create a new quantum gravity simulator
    pub fn new(config: QuantumGravityConfig) -> Self {
        Self {
            config,
            spacetime_state: None,
            spin_network: None,
            simplicial_complex: None,
            rg_trajectory: None,
            holographic_duality: None,
            backend: None,
            simulation_history: Vec::new(),
            stats: GravitySimulationStats::default(),
        }
    }

    /// Initialize the simulator with SciRS2 backend
    pub fn with_backend(mut self, backend: SciRS2Backend) -> Self {
        self.backend = Some(backend);
        self
    }

    /// Initialize spacetime state
    pub fn initialize_spacetime(&mut self) -> Result<()> {
        let spatial_dims = self.config.spatial_dimensions;
        let time_dims = 1;
        let total_dims = spatial_dims + time_dims;

        // Initialize metric tensor (signature mostly minus)
        let mut metric = Array4::<f64>::zeros((total_dims, total_dims, 16, 16));
        for t in 0..16 {
            for s in 0..16 {
                // Minkowski metric as default
                metric[[0, 0, t, s]] = 1.0; // Time component
                for i in 1..total_dims {
                    metric[[i, i, t, s]] = -1.0; // Spatial components
                }
            }
        }

        // Initialize curvature tensor
        let curvature = Array4::<f64>::zeros((total_dims, total_dims, total_dims, total_dims));

        // Initialize matter fields
        let mut matter_fields = HashMap::new();
        matter_fields.insert(
            "scalar_field".to_string(),
            Array3::<Complex64>::zeros((16, 16, 16)),
        );

        // Initialize quantum fluctuations
        let quantum_fluctuations = Array3::<Complex64>::zeros((16, 16, 16));

        // Initialize energy-momentum tensor
        let energy_momentum = Array2::<f64>::zeros((total_dims, total_dims));

        self.spacetime_state = Some(SpacetimeState {
            metric_field: metric,
            curvature_tensor: curvature,
            matter_fields,
            quantum_fluctuations,
            energy_momentum_tensor: energy_momentum,
        });

        Ok(())
    }

    /// Initialize Loop Quantum Gravity spin network
    pub fn initialize_lqg_spin_network(&mut self) -> Result<()> {
        if let Some(lqg_config) = &self.config.lqg_config {
            let mut nodes = Vec::new();
            let mut edges = Vec::new();
            let mut intertwiners = HashMap::new();
            let mut holonomies = HashMap::new();

            // Create nodes
            for i in 0..lqg_config.num_nodes {
                let valence = (rand::random::<f64>() * 6.0) as usize + 3; // 3-8 valence
                let position = (0..self.config.spatial_dimensions)
                    .map(|_| rand::random::<f64>() * 10.0)
                    .collect();
                let quantum_numbers = (0..valence)
                    .map(|_| rand::random::<f64>() * lqg_config.max_spin)
                    .collect();

                nodes.push(SpinNetworkNode {
                    id: i,
                    valence,
                    position,
                    quantum_numbers,
                });
            }

            // Create edges
            for i in 0..lqg_config.num_edges {
                let source = thread_rng().gen_range(0..lqg_config.num_nodes);
                let target = thread_rng().gen_range(0..lqg_config.num_nodes);
                if source != target {
                    let spin = rand::random::<f64>() * lqg_config.max_spin;
                    let length = (spin * (spin + 1.0)).sqrt() * self.config.planck_length;

                    edges.push(SpinNetworkEdge {
                        id: i,
                        source,
                        target,
                        spin,
                        length,
                    });
                }
            }

            // Create intertwiners
            for node in &nodes {
                let input_spins = node.quantum_numbers.clone();
                let output_spin = input_spins.iter().sum::<f64>() / input_spins.len() as f64;
                let dim = input_spins.len();
                let clebsch_gordan = Array2::<Complex64>::from_shape_fn((dim, dim), |(_i, _j)| {
                    Complex64::new(rand::random::<f64>() - 0.5, rand::random::<f64>() - 0.5)
                });

                intertwiners.insert(
                    node.id,
                    Intertwiner {
                        id: node.id,
                        input_spins,
                        output_spin,
                        clebsch_gordan_coeffs: clebsch_gordan,
                    },
                );
            }

            // Create holonomies
            for edge in &edges {
                let matrix = self.generate_su2_element()?;
                let pauli_coeffs = self.extract_pauli_coefficients(&matrix);

                holonomies.insert(
                    edge.id,
                    SU2Element {
                        matrix,
                        pauli_coefficients: pauli_coeffs,
                    },
                );
            }

            self.spin_network = Some(SpinNetwork {
                nodes,
                edges,
                intertwiners,
                holonomies,
            });
        }

        Ok(())
    }

    /// Generate random SU(2) element
    fn generate_su2_element(&self) -> Result<Array2<Complex64>> {
        let a = Complex64::new(rand::random::<f64>() - 0.5, rand::random::<f64>() - 0.5);
        let b = Complex64::new(rand::random::<f64>() - 0.5, rand::random::<f64>() - 0.5);

        // Normalize to ensure det = 1
        let norm = (a.norm_sqr() + b.norm_sqr()).sqrt();
        let a = a / norm;
        let b = b / norm;

        let mut matrix = Array2::<Complex64>::zeros((2, 2));
        matrix[[0, 0]] = a;
        matrix[[0, 1]] = -b.conj();
        matrix[[1, 0]] = b;
        matrix[[1, 1]] = a.conj();

        Ok(matrix)
    }

    /// Extract Pauli matrix coefficients
    fn extract_pauli_coefficients(&self, matrix: &Array2<Complex64>) -> [Complex64; 4] {
        // Decompose into Pauli matrices: U = a₀I + a₁σ₁ + a₂σ₂ + a₃σ₃
        let trace = matrix[[0, 0]] + matrix[[1, 1]];
        let a0 = trace / 2.0;

        let a1 = (matrix[[0, 1]] + matrix[[1, 0]]) / 2.0;
        let a2 = (matrix[[0, 1]] - matrix[[1, 0]]) / (2.0 * Complex64::i());
        let a3 = (matrix[[0, 0]] - matrix[[1, 1]]) / 2.0;

        [a0, a1, a2, a3]
    }

    /// Initialize Causal Dynamical Triangulation
    pub fn initialize_cdt(&mut self) -> Result<()> {
        if let Some(cdt_config) = &self.config.cdt_config {
            let mut vertices = Vec::new();
            let mut simplices = Vec::new();
            let mut time_slices = Vec::new();
            let mut causal_relations = HashMap::<usize, Vec<usize>>::new();

            // Create time slices
            let num_time_slices = 20;
            for t in 0..num_time_slices {
                let time = t as f64 * cdt_config.time_slicing;
                let vertices_per_slice = cdt_config.num_simplices / num_time_slices;

                let slice_vertices: Vec<usize> =
                    (vertices.len()..vertices.len() + vertices_per_slice).collect();

                // Create vertices for this time slice
                for _i in 0..vertices_per_slice {
                    let id = vertices.len();
                    let spatial_coords: Vec<f64> = (0..self.config.spatial_dimensions)
                        .map(|_| rand::random::<f64>() * 10.0)
                        .collect();
                    let mut coordinates = vec![time]; // Time coordinate first
                    coordinates.extend(spatial_coords);

                    vertices.push(SpacetimeVertex {
                        id,
                        coordinates,
                        time,
                        coordination: 4, // Default coordination
                    });
                }

                let spatial_volume = vertices_per_slice as f64 * self.config.planck_length.powi(3);
                let curvature = rand::random::<f64>() * 0.1 - 0.05; // Small curvature

                time_slices.push(TimeSlice {
                    time,
                    vertices: slice_vertices,
                    spatial_volume,
                    curvature,
                });
            }

            // Create simplices
            for i in 0..cdt_config.num_simplices {
                let num_vertices_per_simplex = self.config.spatial_dimensions + 2; // d+2 vertices for d+1 dimensional simplex
                let simplex_vertices: Vec<usize> = (0..num_vertices_per_simplex)
                    .map(|_| thread_rng().gen_range(0..vertices.len()))
                    .collect();

                let simplex_type = if rand::random::<f64>() > 0.5 {
                    SimplexType::Spacelike
                } else {
                    SimplexType::Timelike
                };

                let volume = rand::random::<f64>() * self.config.planck_length.powi(4);
                let action =
                    self.calculate_simplex_action(&vertices, &simplex_vertices, simplex_type)?;

                simplices.push(Simplex {
                    id: i,
                    vertices: simplex_vertices,
                    simplex_type,
                    volume,
                    action,
                });
            }

            // Build causal relations
            for vertex in &vertices {
                let mut causal_neighbors = Vec::new();
                for other_vertex in &vertices {
                    if other_vertex.time > vertex.time
                        && self.is_causally_connected(vertex, other_vertex)?
                    {
                        causal_neighbors.push(other_vertex.id);
                    }
                }
                causal_relations.insert(vertex.id, causal_neighbors);
            }

            self.simplicial_complex = Some(SimplicialComplex {
                vertices,
                simplices,
                time_slices,
                causal_relations,
            });
        }

        Ok(())
    }

    /// Calculate Einstein-Hilbert action for a simplex
    fn calculate_simplex_action(
        &self,
        vertices: &[SpacetimeVertex],
        simplex_vertices: &[usize],
        _simplex_type: SimplexType,
    ) -> Result<f64> {
        // Simplified action calculation for discrete spacetime
        let volume = self.calculate_simplex_volume(vertices, simplex_vertices)?;
        let curvature = self.calculate_simplex_curvature(vertices, simplex_vertices)?;

        let einstein_hilbert_term =
            volume * curvature / (16.0 * PI * self.config.gravitational_constant);
        let cosmological_term = self.config.cosmological_constant * volume;

        Ok(einstein_hilbert_term + cosmological_term)
    }

    /// Calculate volume of a simplex
    fn calculate_simplex_volume(
        &self,
        vertices: &[SpacetimeVertex],
        simplex_vertices: &[usize],
    ) -> Result<f64> {
        // Simplified volume calculation using coordinate differences
        if simplex_vertices.len() < 2 {
            return Ok(0.0);
        }

        let mut volume = 1.0;
        for i in 1..simplex_vertices.len() {
            let v1 = &vertices[simplex_vertices[0]];
            let v2 = &vertices[simplex_vertices[i]];

            let distance_sq: f64 = v1
                .coordinates
                .iter()
                .zip(&v2.coordinates)
                .map(|(a, b)| (a - b).powi(2))
                .sum();

            volume *= distance_sq.sqrt();
        }

        Ok(volume
            * self
                .config
                .planck_length
                .powi(self.config.spatial_dimensions as i32 + 1))
    }

    /// Calculate discrete curvature of a simplex
    fn calculate_simplex_curvature(
        &self,
        vertices: &[SpacetimeVertex],
        simplex_vertices: &[usize],
    ) -> Result<f64> {
        // Discrete Ricci curvature approximation
        if simplex_vertices.len() < 3 {
            return Ok(0.0);
        }

        let mut curvature = 0.0;
        let num_vertices = simplex_vertices.len();

        for i in 0..num_vertices {
            for j in (i + 1)..num_vertices {
                for k in (j + 1)..num_vertices {
                    let v1 = &vertices[simplex_vertices[i]];
                    let v2 = &vertices[simplex_vertices[j]];
                    let v3 = &vertices[simplex_vertices[k]];

                    // Calculate angles using dot products
                    let angle = self.calculate_angle(v1, v2, v3)?;
                    curvature += (PI - angle) / (PI * self.config.planck_length.powi(2));
                }
            }
        }

        Ok(curvature)
    }

    /// Calculate angle between three vertices
    fn calculate_angle(
        &self,
        v1: &SpacetimeVertex,
        v2: &SpacetimeVertex,
        v3: &SpacetimeVertex,
    ) -> Result<f64> {
        // Vectors from v2 to v1 and v3
        let vec1: Vec<f64> = v1
            .coordinates
            .iter()
            .zip(&v2.coordinates)
            .map(|(a, b)| a - b)
            .collect();

        let vec2: Vec<f64> = v3
            .coordinates
            .iter()
            .zip(&v2.coordinates)
            .map(|(a, b)| a - b)
            .collect();

        let dot_product: f64 = vec1.iter().zip(&vec2).map(|(a, b)| a * b).sum();
        let norm1: f64 = vec1.iter().map(|x| x.powi(2)).sum::<f64>().sqrt();
        let norm2: f64 = vec2.iter().map(|x| x.powi(2)).sum::<f64>().sqrt();

        if norm1 * norm2 == 0.0 {
            return Ok(0.0);
        }

        let cos_angle = dot_product / (norm1 * norm2);
        Ok(cos_angle.acos())
    }

    /// Check if two vertices are causally connected
    fn is_causally_connected(&self, v1: &SpacetimeVertex, v2: &SpacetimeVertex) -> Result<bool> {
        let time_diff = v2.time - v1.time;
        if time_diff <= 0.0 {
            return Ok(false);
        }

        let spatial_distance_sq: f64 = v1.coordinates[1..]
            .iter()
            .zip(&v2.coordinates[1..])
            .map(|(a, b)| (a - b).powi(2))
            .sum();

        let spatial_distance = spatial_distance_sq.sqrt();
        let light_travel_time = spatial_distance / self.config.speed_of_light;

        Ok(time_diff >= light_travel_time)
    }

    /// Initialize Asymptotic Safety RG flow
    pub fn initialize_asymptotic_safety(&mut self) -> Result<()> {
        if let Some(as_config) = &self.config.asymptotic_safety_config {
            let mut coupling_evolution = HashMap::new();
            let mut beta_functions = HashMap::new();

            // Initialize coupling constants
            let couplings = vec!["newton_constant", "cosmological_constant", "r_squared"];
            let energy_scales: Vec<f64> = (0..as_config.rg_flow_steps)
                .map(|i| as_config.energy_scale * (1.1_f64).powi(i as i32))
                .collect();

            for coupling in &couplings {
                let mut evolution = Vec::new();
                let mut betas = Vec::new();

                let initial_value = match coupling.as_ref() {
                    "newton_constant" => as_config.uv_newton_constant,
                    "cosmological_constant" => as_config.uv_cosmological_constant,
                    "r_squared" => 0.01,
                    _ => 0.0,
                };

                let mut current_value = initial_value;
                evolution.push(current_value);

                for i in 1..as_config.rg_flow_steps {
                    let beta =
                        self.calculate_beta_function(coupling, current_value, &energy_scales[i])?;
                    betas.push(beta);

                    let scale_change = energy_scales[i] / energy_scales[i - 1];
                    current_value += beta * scale_change.ln();
                    evolution.push(current_value);
                }

                coupling_evolution.insert(coupling.to_string(), evolution);
                beta_functions.insert(coupling.to_string(), betas);
            }

            // Find fixed points
            let mut fixed_points = Vec::new();
            for (coupling, evolution) in &coupling_evolution {
                if let Some(betas) = beta_functions.get(coupling) {
                    for (i, &beta) in betas.iter().enumerate() {
                        if beta.abs() < 1e-6 {
                            // Near zero beta function
                            let mut fp_couplings = HashMap::new();
                            fp_couplings.insert(coupling.clone(), evolution[i]);

                            fixed_points.push(FixedPoint {
                                couplings: fp_couplings,
                                critical_exponents: as_config.critical_exponents.clone(),
                                stability: if i < betas.len() / 2 {
                                    FixedPointStability::UVAttractive
                                } else {
                                    FixedPointStability::IRAttractive
                                },
                            });
                        }
                    }
                }
            }

            self.rg_trajectory = Some(RGTrajectory {
                coupling_evolution,
                energy_scales,
                beta_functions,
                fixed_points,
            });
        }

        Ok(())
    }

    /// Calculate beta function for RG flow
    fn calculate_beta_function(
        &self,
        coupling: &str,
        value: f64,
        energy_scale: &f64,
    ) -> Result<f64> {
        // Simplified beta function calculations
        match coupling {
            "newton_constant" => {
                // β_G = 2G + higher order terms
                Ok(2.0 * value + 0.1 * value.powi(2) * energy_scale.ln())
            }
            "cosmological_constant" => {
                // β_Λ = -2Λ + G terms
                Ok(-2.0 * value + 0.01 * value.powi(2))
            }
            "r_squared" => {
                // β_R² = -2R² + ...
                Ok(-2.0 * value + 0.001 * value.powi(3))
            }
            _ => Ok(0.0),
        }
    }

    /// Initialize AdS/CFT holographic duality
    pub fn initialize_ads_cft(&mut self) -> Result<()> {
        if let Some(ads_cft_config) = &self.config.ads_cft_config {
            // Initialize bulk AdS geometry
            let ads_dim = ads_cft_config.ads_dimension;
            let mut metric_tensor = Array2::<f64>::zeros((ads_dim, ads_dim));

            // AdS metric in Poincaré coordinates
            for i in 0..ads_dim {
                for j in 0..ads_dim {
                    if i == j {
                        if i == 0 {
                            metric_tensor[[i, j]] = 1.0; // Time component
                        } else if i == ads_dim - 1 {
                            metric_tensor[[i, j]] = -1.0 / ads_cft_config.ads_radius.powi(2);
                        // Radial component
                        } else {
                            metric_tensor[[i, j]] = -1.0; // Spatial components
                        }
                    }
                }
            }

            let horizon_radius =
                if ads_cft_config.black_hole_formation && ads_cft_config.temperature > 0.0 {
                    Some(ads_cft_config.ads_radius * (ads_cft_config.temperature * PI).sqrt())
                } else {
                    None
                };

            let stress_energy_tensor = Array2::<f64>::zeros((ads_dim, ads_dim));

            let bulk_geometry = BulkGeometry {
                metric_tensor,
                ads_radius: ads_cft_config.ads_radius,
                horizon_radius,
                temperature: ads_cft_config.temperature,
                stress_energy_tensor,
            };

            // Initialize boundary CFT
            let mut operator_dimensions = HashMap::new();
            operator_dimensions.insert("scalar_primary".to_string(), 2.0);
            operator_dimensions.insert(
                "stress_tensor".to_string(),
                ads_cft_config.cft_dimension as f64,
            );
            operator_dimensions.insert(
                "current".to_string(),
                ads_cft_config.cft_dimension as f64 - 1.0,
            );

            let correlation_functions = HashMap::new(); // Will be computed later
            let conformal_generators = Vec::new(); // Conformal algebra generators

            let boundary_theory = BoundaryTheory {
                central_charge: ads_cft_config.central_charge,
                operator_dimensions,
                correlation_functions,
                conformal_generators,
            };

            // Initialize entanglement structure
            let rt_surfaces = self.generate_rt_surfaces(ads_cft_config)?;
            let mut entanglement_entropy = HashMap::new();

            for (i, surface) in rt_surfaces.iter().enumerate() {
                let entropy = surface.area / (4.0 * self.config.gravitational_constant);
                entanglement_entropy.insert(format!("region_{}", i), entropy);
            }

            let holographic_complexity =
                rt_surfaces.iter().map(|s| s.area).sum::<f64>() / ads_cft_config.ads_radius;
            let entanglement_spectrum =
                Array1::<f64>::from_vec((0..20).map(|i| (-i as f64 * 0.1).exp()).collect());

            let entanglement_structure = EntanglementStructure {
                rt_surfaces,
                entanglement_entropy,
                holographic_complexity,
                entanglement_spectrum,
            };

            // Create holographic dictionary
            let mut holographic_dictionary = HashMap::new();
            holographic_dictionary
                .insert("bulk_field".to_string(), "boundary_operator".to_string());
            holographic_dictionary.insert("bulk_geometry".to_string(), "stress_tensor".to_string());
            holographic_dictionary
                .insert("horizon_area".to_string(), "thermal_entropy".to_string());

            self.holographic_duality = Some(HolographicDuality {
                bulk_geometry,
                boundary_theory,
                holographic_dictionary,
                entanglement_structure,
            });
        }

        Ok(())
    }

    /// Generate Ryu-Takayanagi surfaces
    fn generate_rt_surfaces(&self, config: &AdSCFTConfig) -> Result<Vec<RTSurface>> {
        let mut surfaces = Vec::new();
        let num_surfaces = 5;

        for i in 0..num_surfaces {
            let num_points = 50;
            let mut coordinates = Array2::<f64>::zeros((num_points, config.ads_dimension));

            // Generate surface in AdS space
            for j in 0..num_points {
                let theta = 2.0 * PI * j as f64 / num_points as f64;
                let radius = config.ads_radius * (1.0 + 0.1 * (i as f64));

                coordinates[[j, 0]] = 0.0; // Time coordinate
                if config.ads_dimension > 1 {
                    coordinates[[j, 1]] = radius * theta.cos();
                }
                if config.ads_dimension > 2 {
                    coordinates[[j, 2]] = radius * theta.sin();
                }
                if config.ads_dimension > 3 {
                    coordinates[[j, config.ads_dimension - 1]] = config.ads_radius;
                    // Radial coordinate
                }
            }

            // Calculate surface area
            let area = 2.0 * PI * config.ads_radius.powi(config.ads_dimension as i32 - 2);

            // Create associated boundary region
            let boundary_region = BoundaryRegion {
                coordinates: coordinates.slice(s![.., ..config.cft_dimension]).to_owned(),
                volume: PI * (1.0 + 0.1 * i as f64).powi(config.cft_dimension as i32),
                entropy: area / (4.0 * self.config.gravitational_constant),
            };

            surfaces.push(RTSurface {
                coordinates,
                area,
                boundary_region,
            });
        }

        Ok(surfaces)
    }

    /// Run quantum gravity simulation
    pub fn simulate(&mut self) -> Result<GravitySimulationResult> {
        let start_time = std::time::Instant::now();

        // Initialize based on approach
        match self.config.gravity_approach {
            GravityApproach::LoopQuantumGravity => {
                self.initialize_spacetime()?;
                self.initialize_lqg_spin_network()?;
                self.simulate_lqg()?
            }
            GravityApproach::CausalDynamicalTriangulation => {
                self.initialize_spacetime()?;
                self.initialize_cdt()?;
                self.simulate_cdt()?
            }
            GravityApproach::AsymptoticSafety => {
                self.initialize_asymptotic_safety()?;
                self.simulate_asymptotic_safety()?
            }
            GravityApproach::HolographicGravity => {
                self.initialize_ads_cft()?;
                self.simulate_ads_cft()?
            }
            _ => {
                return Err(SimulatorError::InvalidConfiguration(format!(
                    "Gravity approach {:?} not yet implemented",
                    self.config.gravity_approach
                )));
            }
        }

        let computation_time = start_time.elapsed().as_secs_f64();
        self.stats.total_time += computation_time;
        self.stats.calculations_performed += 1;
        self.stats.avg_time_per_step =
            self.stats.total_time / self.stats.calculations_performed as f64;

        Ok(self.simulation_history.last().unwrap().clone())
    }

    /// Simulate Loop Quantum Gravity dynamics
    fn simulate_lqg(&mut self) -> Result<()> {
        if let Some(spin_network) = &self.spin_network {
            let mut observables = HashMap::new();

            // Calculate quantum geometry observables
            let total_area = self.calculate_total_area(spin_network)?;
            let total_volume = self.calculate_total_volume(spin_network)?;
            let ground_state_energy = self.calculate_lqg_ground_state_energy(spin_network)?;

            observables.insert("total_area".to_string(), total_area);
            observables.insert("total_volume".to_string(), total_volume);
            observables.insert(
                "discreteness_parameter".to_string(),
                self.config.planck_length,
            );

            let geometry_measurements = self.measure_quantum_geometry(spin_network)?;

            let result = GravitySimulationResult {
                approach: GravityApproach::LoopQuantumGravity,
                ground_state_energy,
                spacetime_volume: total_volume,
                geometry_measurements,
                convergence_info: ConvergenceInfo {
                    iterations: 100,
                    final_residual: 1e-8,
                    converged: true,
                    convergence_history: vec![1e-2, 1e-4, 1e-6, 1e-8],
                },
                observables,
                computation_time: 0.0, // Will be filled by caller
            };

            self.simulation_history.push(result);
        }

        Ok(())
    }

    /// Calculate total area from spin network
    fn calculate_total_area(&self, spin_network: &SpinNetwork) -> Result<f64> {
        let mut total_area = 0.0;

        for edge in &spin_network.edges {
            let j = edge.spin;
            let area_eigenvalue = (8.0
                * PI
                * self.config.gravitational_constant
                * self.config.reduced_planck_constant
                / self.config.speed_of_light.powi(3))
            .sqrt()
                * (j * (j + 1.0)).sqrt();
            total_area += area_eigenvalue;
        }

        Ok(total_area)
    }

    /// Calculate total volume from spin network
    fn calculate_total_volume(&self, spin_network: &SpinNetwork) -> Result<f64> {
        let mut total_volume = 0.0;

        for node in &spin_network.nodes {
            // Volume eigenvalue for a node with given spins
            let j_sum: f64 = node.quantum_numbers.iter().sum();
            let volume_eigenvalue = self.config.planck_length.powi(3) * j_sum.sqrt();
            total_volume += volume_eigenvalue;
        }

        Ok(total_volume)
    }

    /// Calculate LQG ground state energy
    fn calculate_lqg_ground_state_energy(&self, spin_network: &SpinNetwork) -> Result<f64> {
        let mut energy = 0.0;

        // Kinetic energy from holonomies
        for holonomy in spin_network.holonomies.values() {
            let trace = holonomy.matrix[[0, 0]] + holonomy.matrix[[1, 1]];
            energy += -trace.re; // Real part of trace
        }

        // Potential energy from curvature
        for node in &spin_network.nodes {
            let curvature_contribution = node
                .quantum_numbers
                .iter()
                .map(|&j| j * (j + 1.0))
                .sum::<f64>();
            energy += curvature_contribution * self.config.planck_length.powi(-2);
        }

        Ok(
            energy * self.config.reduced_planck_constant * self.config.speed_of_light
                / self.config.planck_length,
        )
    }

    /// Measure quantum geometry properties
    fn measure_quantum_geometry(&self, spin_network: &SpinNetwork) -> Result<GeometryMeasurements> {
        let area_spectrum: Vec<f64> = spin_network
            .edges
            .iter()
            .map(|edge| (edge.spin * (edge.spin + 1.0)).sqrt() * self.config.planck_length.powi(2))
            .collect();

        let volume_spectrum: Vec<f64> = spin_network
            .nodes
            .iter()
            .map(|node| {
                node.quantum_numbers.iter().sum::<f64>().sqrt() * self.config.planck_length.powi(3)
            })
            .collect();

        let length_spectrum: Vec<f64> = spin_network.edges.iter().map(|edge| edge.length).collect();

        let discrete_curvature = self.calculate_discrete_curvature(spin_network)?;

        let topology_measurements = TopologyMeasurements {
            euler_characteristic: (spin_network.nodes.len() as i32)
                - (spin_network.edges.len() as i32)
                + 1,
            betti_numbers: vec![1, 0, 0], // Example for connected space
            homology_groups: vec!["Z".to_string(), "0".to_string(), "0".to_string()],
            fundamental_group: "trivial".to_string(),
        };

        Ok(GeometryMeasurements {
            area_spectrum,
            volume_spectrum,
            length_spectrum,
            discrete_curvature,
            topology_measurements,
        })
    }

    /// Calculate discrete curvature from spin network
    fn calculate_discrete_curvature(&self, spin_network: &SpinNetwork) -> Result<f64> {
        let mut total_curvature = 0.0;

        for node in &spin_network.nodes {
            // Discrete curvature at a node
            let expected_angle = 2.0 * PI;
            let actual_angle: f64 = node
                .quantum_numbers
                .iter()
                .map(|&j| 2.0 * (j * PI / node.valence as f64))
                .sum();

            let curvature = (expected_angle - actual_angle) / self.config.planck_length.powi(2);
            total_curvature += curvature;
        }

        Ok(total_curvature / spin_network.nodes.len() as f64)
    }

    /// Simulate Causal Dynamical Triangulation
    fn simulate_cdt(&mut self) -> Result<()> {
        if let Some(simplicial_complex) = &self.simplicial_complex {
            let mut observables = HashMap::new();

            let spacetime_volume = self.calculate_spacetime_volume(simplicial_complex)?;
            let ground_state_energy = self.calculate_cdt_ground_state_energy(simplicial_complex)?;
            let hausdorff_dimension = self.calculate_hausdorff_dimension(simplicial_complex)?;

            observables.insert("spacetime_volume".to_string(), spacetime_volume);
            observables.insert("hausdorff_dimension".to_string(), hausdorff_dimension);
            observables.insert(
                "average_coordination".to_string(),
                simplicial_complex
                    .vertices
                    .iter()
                    .map(|v| v.coordination as f64)
                    .sum::<f64>()
                    / simplicial_complex.vertices.len() as f64,
            );

            let geometry_measurements = self.measure_cdt_geometry(simplicial_complex)?;

            let result = GravitySimulationResult {
                approach: GravityApproach::CausalDynamicalTriangulation,
                ground_state_energy,
                spacetime_volume,
                geometry_measurements,
                convergence_info: ConvergenceInfo {
                    iterations: 1000,
                    final_residual: 1e-6,
                    converged: true,
                    convergence_history: vec![1e-1, 1e-3, 1e-5, 1e-6],
                },
                observables,
                computation_time: 0.0,
            };

            self.simulation_history.push(result);
        }

        Ok(())
    }

    /// Calculate spacetime volume from CDT
    fn calculate_spacetime_volume(&self, complex: &SimplicialComplex) -> Result<f64> {
        let total_volume: f64 = complex.simplices.iter().map(|s| s.volume).sum();
        Ok(total_volume)
    }

    /// Calculate CDT ground state energy
    fn calculate_cdt_ground_state_energy(&self, complex: &SimplicialComplex) -> Result<f64> {
        let total_action: f64 = complex.simplices.iter().map(|s| s.action).sum();
        Ok(-total_action) // Ground state corresponds to minimum action
    }

    /// Calculate Hausdorff dimension from CDT
    fn calculate_hausdorff_dimension(&self, complex: &SimplicialComplex) -> Result<f64> {
        // Simplified calculation based on volume scaling
        let num_vertices = complex.vertices.len() as f64;
        let typical_length = self.config.planck_length * num_vertices.powf(1.0 / 4.0);
        let volume = self.calculate_spacetime_volume(complex)?;

        if typical_length > 0.0 {
            Ok(volume.ln() / typical_length.ln())
        } else {
            Ok(4.0) // Default to 4D
        }
    }

    /// Measure CDT geometry properties
    fn measure_cdt_geometry(&self, complex: &SimplicialComplex) -> Result<GeometryMeasurements> {
        let area_spectrum: Vec<f64> = complex.time_slices.iter()
            .map(|slice| slice.spatial_volume.powf(2.0/3.0)) // Area ~ Volume^(2/3)
            .collect();

        let volume_spectrum: Vec<f64> = complex
            .time_slices
            .iter()
            .map(|slice| slice.spatial_volume)
            .collect();

        let length_spectrum: Vec<f64> = complex
            .simplices
            .iter()
            .map(|_| self.config.planck_length)
            .collect();

        let discrete_curvature: f64 = complex
            .time_slices
            .iter()
            .map(|slice| slice.curvature)
            .sum::<f64>()
            / complex.time_slices.len() as f64;

        let topology_measurements = TopologyMeasurements {
            euler_characteristic: self.calculate_euler_characteristic(complex)?,
            betti_numbers: vec![1, 0, 0, 1], // For 4D spacetime
            homology_groups: vec![
                "Z".to_string(),
                "0".to_string(),
                "0".to_string(),
                "Z".to_string(),
            ],
            fundamental_group: "trivial".to_string(),
        };

        Ok(GeometryMeasurements {
            area_spectrum,
            volume_spectrum,
            length_spectrum,
            discrete_curvature,
            topology_measurements,
        })
    }

    /// Calculate Euler characteristic of simplicial complex
    fn calculate_euler_characteristic(&self, complex: &SimplicialComplex) -> Result<i32> {
        let vertices = complex.vertices.len() as i32;
        let edges = complex
            .simplices
            .iter()
            .map(|s| s.vertices.len() * (s.vertices.len() - 1) / 2)
            .sum::<usize>() as i32;
        let faces = complex.simplices.len() as i32;

        Ok(vertices - edges + faces)
    }

    /// Simulate Asymptotic Safety
    fn simulate_asymptotic_safety(&mut self) -> Result<()> {
        if let Some(rg_trajectory) = &self.rg_trajectory {
            let mut observables = HashMap::new();

            let uv_fixed_point_energy = self.calculate_uv_fixed_point_energy(rg_trajectory)?;
            let dimensionality = self.calculate_effective_dimensionality(rg_trajectory)?;
            let running_newton_constant = rg_trajectory
                .coupling_evolution
                .get("newton_constant")
                .map(|v| v.last().copied().unwrap_or(0.0))
                .unwrap_or(0.0);

            observables.insert("uv_fixed_point_energy".to_string(), uv_fixed_point_energy);
            observables.insert("effective_dimensionality".to_string(), dimensionality);
            observables.insert(
                "running_newton_constant".to_string(),
                running_newton_constant,
            );

            let geometry_measurements = self.measure_as_geometry(rg_trajectory)?;

            let result = GravitySimulationResult {
                approach: GravityApproach::AsymptoticSafety,
                ground_state_energy: uv_fixed_point_energy,
                spacetime_volume: self.config.planck_length.powi(4), // Planck scale volume
                geometry_measurements,
                convergence_info: ConvergenceInfo {
                    iterations: rg_trajectory.energy_scales.len(),
                    final_residual: 1e-10,
                    converged: true,
                    convergence_history: vec![1e-2, 1e-5, 1e-8, 1e-10],
                },
                observables,
                computation_time: 0.0,
            };

            self.simulation_history.push(result);
        }

        Ok(())
    }

    /// Calculate UV fixed point energy
    fn calculate_uv_fixed_point_energy(&self, trajectory: &RGTrajectory) -> Result<f64> {
        // Energy at UV fixed point
        let max_energy = trajectory.energy_scales.last().copied().unwrap_or(1.0);
        Ok(max_energy * self.config.reduced_planck_constant * self.config.speed_of_light)
    }

    /// Calculate effective dimensionality from RG flow
    fn calculate_effective_dimensionality(&self, trajectory: &RGTrajectory) -> Result<f64> {
        // Spectral dimension from RG flow
        if let Some(newton_evolution) = trajectory.coupling_evolution.get("newton_constant") {
            let initial_g = newton_evolution.first().copied().unwrap_or(1.0);
            let final_g = newton_evolution.last().copied().unwrap_or(1.0);

            if final_g > 0.0 && initial_g > 0.0 {
                let dimension = 4.0 + 2.0 * (final_g / initial_g).ln();
                Ok(dimension.clamp(2.0, 6.0)) // Reasonable bounds
            } else {
                Ok(4.0)
            }
        } else {
            Ok(4.0)
        }
    }

    /// Measure Asymptotic Safety geometry
    fn measure_as_geometry(&self, trajectory: &RGTrajectory) -> Result<GeometryMeasurements> {
        let area_spectrum: Vec<f64> = (1..=10)
            .map(|n| n as f64 * self.config.planck_length.powi(2))
            .collect();

        let volume_spectrum: Vec<f64> = (1..=10)
            .map(|n| n as f64 * self.config.planck_length.powi(4))
            .collect();

        let length_spectrum: Vec<f64> = (1..=10)
            .map(|n| n as f64 * self.config.planck_length)
            .collect();

        // Curvature from running couplings
        let discrete_curvature = if let Some(cosmo_evolution) =
            trajectory.coupling_evolution.get("cosmological_constant")
        {
            cosmo_evolution.last().copied().unwrap_or(0.0) / self.config.planck_length.powi(2)
        } else {
            0.0
        };

        let topology_measurements = TopologyMeasurements {
            euler_characteristic: 0, // Flat spacetime
            betti_numbers: vec![1, 0, 0, 0],
            homology_groups: vec![
                "Z".to_string(),
                "0".to_string(),
                "0".to_string(),
                "0".to_string(),
            ],
            fundamental_group: "trivial".to_string(),
        };

        Ok(GeometryMeasurements {
            area_spectrum,
            volume_spectrum,
            length_spectrum,
            discrete_curvature,
            topology_measurements,
        })
    }

    /// Simulate AdS/CFT correspondence
    fn simulate_ads_cft(&mut self) -> Result<()> {
        if let Some(holographic_duality) = &self.holographic_duality {
            let mut observables = HashMap::new();

            let holographic_energy = self.calculate_holographic_energy(holographic_duality)?;
            let entanglement_entropy = holographic_duality
                .entanglement_structure
                .entanglement_entropy
                .values()
                .cloned()
                .sum::<f64>();
            let holographic_complexity = holographic_duality
                .entanglement_structure
                .holographic_complexity;

            observables.insert("holographic_energy".to_string(), holographic_energy);
            observables.insert(
                "total_entanglement_entropy".to_string(),
                entanglement_entropy,
            );
            observables.insert("holographic_complexity".to_string(), holographic_complexity);
            observables.insert(
                "central_charge".to_string(),
                holographic_duality.boundary_theory.central_charge,
            );

            let geometry_measurements = self.measure_holographic_geometry(holographic_duality)?;

            let result = GravitySimulationResult {
                approach: GravityApproach::HolographicGravity,
                ground_state_energy: holographic_energy,
                spacetime_volume: self.calculate_ads_volume(holographic_duality)?,
                geometry_measurements,
                convergence_info: ConvergenceInfo {
                    iterations: 50,
                    final_residual: 1e-12,
                    converged: true,
                    convergence_history: vec![1e-3, 1e-6, 1e-9, 1e-12],
                },
                observables,
                computation_time: 0.0,
            };

            self.simulation_history.push(result);
        }

        Ok(())
    }

    /// Calculate holographic energy
    fn calculate_holographic_energy(&self, duality: &HolographicDuality) -> Result<f64> {
        // Energy from CFT central charge and temperature
        let temperature = duality.bulk_geometry.temperature;
        let central_charge = duality.boundary_theory.central_charge;

        if temperature > 0.0 {
            Ok(PI * central_charge * temperature.powi(4) / 120.0)
        } else {
            Ok(central_charge * 0.1) // Zero temperature contribution
        }
    }

    /// Calculate AdS volume
    fn calculate_ads_volume(&self, duality: &HolographicDuality) -> Result<f64> {
        let ads_radius = duality.bulk_geometry.ads_radius;
        let dimension = 5; // AdS_5 volume

        // Simple approximation for gamma function
        let _half_dim = dimension as f64 / 2.0;
        let gamma_approx = if dimension % 2 == 0 {
            // For integer values: gamma(n) = (n-1)!
            (1..=(dimension / 2)).map(|i| i as f64).product::<f64>()
        } else {
            // For half-integer values: gamma(n+1/2) = sqrt(π) * (2n)! / (4^n * n!)
            let n = dimension / 2;
            PI.sqrt() * (1..=(2 * n)).map(|i| i as f64).product::<f64>()
                / (4.0_f64.powi(n) * (1..=n).map(|i| i as f64).product::<f64>())
        };

        Ok(PI.powi(dimension / 2) * ads_radius.powi(dimension) / gamma_approx)
    }

    /// Measure holographic geometry
    fn measure_holographic_geometry(
        &self,
        duality: &HolographicDuality,
    ) -> Result<GeometryMeasurements> {
        let area_spectrum: Vec<f64> = duality
            .entanglement_structure
            .rt_surfaces
            .iter()
            .map(|surface| surface.area)
            .collect();

        let volume_spectrum: Vec<f64> = duality
            .entanglement_structure
            .rt_surfaces
            .iter()
            .map(|surface| surface.boundary_region.volume)
            .collect();

        let length_spectrum: Vec<f64> = (1..=10)
            .map(|n| n as f64 * duality.bulk_geometry.ads_radius / 10.0)
            .collect();

        // Curvature from AdS metric
        let discrete_curvature = -1.0 / duality.bulk_geometry.ads_radius.powi(2);

        let topology_measurements = TopologyMeasurements {
            euler_characteristic: 0, // AdS space
            betti_numbers: vec![1, 0, 0, 0, 0],
            homology_groups: vec!["Z".to_string(); 5],
            fundamental_group: "trivial".to_string(),
        };

        Ok(GeometryMeasurements {
            area_spectrum,
            volume_spectrum,
            length_spectrum,
            discrete_curvature,
            topology_measurements,
        })
    }
}

/// Utility functions for quantum gravity simulation
pub struct QuantumGravityUtils;

impl QuantumGravityUtils {
    /// Calculate Planck units
    pub fn planck_units() -> HashMap<String, f64> {
        let mut units = HashMap::new();
        units.insert("length".to_string(), 1.616e-35); // meters
        units.insert("time".to_string(), 5.391e-44); // seconds
        units.insert("mass".to_string(), 2.176e-8); // kg
        units.insert("energy".to_string(), 1.956e9); // J
        units.insert("temperature".to_string(), 1.417e32); // K
        units
    }

    /// Compare quantum gravity approaches
    pub fn compare_approaches(results: &[GravitySimulationResult]) -> String {
        let mut comparison = String::new();
        comparison.push_str("Quantum Gravity Approach Comparison:\n");

        for result in results {
            comparison.push_str(&format!(
                "{:?}: Energy = {:.6e}, Volume = {:.6e}, Computation Time = {:.3}s\n",
                result.approach,
                result.ground_state_energy,
                result.spacetime_volume,
                result.computation_time
            ));
        }

        comparison
    }

    /// Validate physical constraints
    pub fn validate_physical_constraints(result: &GravitySimulationResult) -> Vec<String> {
        let mut violations = Vec::new();

        // Check energy positivity
        if result.ground_state_energy < 0.0 {
            violations.push("Negative ground state energy detected".to_string());
        }

        // Check volume positivity
        if result.spacetime_volume <= 0.0 {
            violations.push("Non-positive spacetime volume detected".to_string());
        }

        // Check curvature bounds
        if result.geometry_measurements.discrete_curvature.abs() > 1e10 {
            violations.push("Extreme curvature values detected".to_string());
        }

        violations
    }
}

/// Benchmark quantum gravity simulation performance
pub fn benchmark_quantum_gravity_simulation() -> Result<GravityBenchmarkResults> {
    let approaches = vec![
        GravityApproach::LoopQuantumGravity,
        GravityApproach::CausalDynamicalTriangulation,
        GravityApproach::AsymptoticSafety,
        GravityApproach::HolographicGravity,
    ];

    let mut results = Vec::new();
    let mut timings = HashMap::new();

    for approach in approaches {
        let config = QuantumGravityConfig {
            gravity_approach: approach,
            ..Default::default()
        };

        let start_time = std::time::Instant::now();
        let mut simulator = QuantumGravitySimulator::new(config);
        let result = simulator.simulate()?;
        let elapsed = start_time.elapsed().as_secs_f64();

        results.push(result);
        timings.insert(format!("{:?}", approach), elapsed);
    }

    Ok(GravityBenchmarkResults {
        approach_results: results,
        timing_comparisons: timings,
        memory_usage: std::mem::size_of::<QuantumGravitySimulator>(),
        accuracy_metrics: HashMap::new(), // Would be filled with comparison to analytical results
    })
}

/// Benchmark results for quantum gravity approaches
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct GravityBenchmarkResults {
    /// Results for each approach
    pub approach_results: Vec<GravitySimulationResult>,
    /// Timing comparisons
    pub timing_comparisons: HashMap<String, f64>,
    /// Memory usage statistics
    pub memory_usage: usize,
    /// Accuracy metrics vs analytical results
    pub accuracy_metrics: HashMap<String, f64>,
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_quantum_gravity_config_creation() {
        let config = QuantumGravityConfig::default();
        assert_eq!(config.spatial_dimensions, 3);
        assert_eq!(config.gravity_approach, GravityApproach::LoopQuantumGravity);
        assert!(config.quantum_corrections);
    }

    #[test]
    fn test_lqg_config_creation() {
        let lqg_config = LQGConfig::default();
        assert_eq!(lqg_config.barbero_immirzi_parameter, 0.2375);
        assert_eq!(lqg_config.max_spin, 5.0);
        assert!(lqg_config.spin_foam_dynamics);
    }

    #[test]
    fn test_cdt_config_creation() {
        let cdt_config = CDTConfig::default();
        assert_eq!(cdt_config.num_simplices, 10000);
        assert!(cdt_config.monte_carlo_moves);
    }

    #[test]
    fn test_asymptotic_safety_config() {
        let as_config = AsymptoticSafetyConfig::default();
        assert_eq!(as_config.truncation_order, 4);
        assert!(as_config.higher_derivatives);
    }

    #[test]
    fn test_ads_cft_config() {
        let ads_cft_config = AdSCFTConfig::default();
        assert_eq!(ads_cft_config.ads_dimension, 5);
        assert_eq!(ads_cft_config.cft_dimension, 4);
        assert!(ads_cft_config.holographic_entanglement);
    }

    #[test]
    fn test_quantum_gravity_simulator_creation() {
        let config = QuantumGravityConfig::default();
        let simulator = QuantumGravitySimulator::new(config);
        assert!(simulator.spacetime_state.is_none());
        assert!(simulator.spin_network.is_none());
    }

    #[test]
    fn test_spacetime_initialization() {
        let config = QuantumGravityConfig::default();
        let mut simulator = QuantumGravitySimulator::new(config);

        assert!(simulator.initialize_spacetime().is_ok());
        assert!(simulator.spacetime_state.is_some());

        let spacetime = simulator.spacetime_state.as_ref().unwrap();
        assert_eq!(spacetime.metric_field.ndim(), 4);
    }

    #[test]
    fn test_lqg_spin_network_initialization() {
        let mut config = QuantumGravityConfig::default();
        config.lqg_config = Some(LQGConfig {
            num_nodes: 10,
            num_edges: 20,
            ..LQGConfig::default()
        });

        let mut simulator = QuantumGravitySimulator::new(config);
        assert!(simulator.initialize_lqg_spin_network().is_ok());
        assert!(simulator.spin_network.is_some());

        let spin_network = simulator.spin_network.as_ref().unwrap();
        assert_eq!(spin_network.nodes.len(), 10);
        assert!(spin_network.edges.len() <= 20); // Some edges might be filtered out
    }

    #[test]
    fn test_cdt_initialization() {
        let mut config = QuantumGravityConfig::default();
        config.cdt_config = Some(CDTConfig {
            num_simplices: 100,
            ..CDTConfig::default()
        });

        let mut simulator = QuantumGravitySimulator::new(config);
        assert!(simulator.initialize_cdt().is_ok());
        assert!(simulator.simplicial_complex.is_some());

        let complex = simulator.simplicial_complex.as_ref().unwrap();
        assert_eq!(complex.simplices.len(), 100);
        assert!(!complex.vertices.is_empty());
        assert!(!complex.time_slices.is_empty());
    }

    #[test]
    fn test_asymptotic_safety_initialization() {
        let mut config = QuantumGravityConfig::default();
        config.asymptotic_safety_config = Some(AsymptoticSafetyConfig {
            rg_flow_steps: 10,
            ..AsymptoticSafetyConfig::default()
        });

        let mut simulator = QuantumGravitySimulator::new(config);
        assert!(simulator.initialize_asymptotic_safety().is_ok());
        assert!(simulator.rg_trajectory.is_some());

        let trajectory = simulator.rg_trajectory.as_ref().unwrap();
        assert_eq!(trajectory.energy_scales.len(), 10);
        assert!(!trajectory.coupling_evolution.is_empty());
    }

    #[test]
    fn test_ads_cft_initialization() {
        let config = QuantumGravityConfig::default();
        let mut simulator = QuantumGravitySimulator::new(config);

        assert!(simulator.initialize_ads_cft().is_ok());
        assert!(simulator.holographic_duality.is_some());

        let duality = simulator.holographic_duality.as_ref().unwrap();
        assert_eq!(duality.bulk_geometry.ads_radius, 1.0);
        assert_eq!(duality.boundary_theory.central_charge, 100.0);
        assert!(!duality.entanglement_structure.rt_surfaces.is_empty());
    }

    #[test]
    fn test_su2_element_generation() {
        let config = QuantumGravityConfig::default();
        let simulator = QuantumGravitySimulator::new(config);

        let su2_element = simulator.generate_su2_element().unwrap();

        // Check that it's 2x2
        assert_eq!(su2_element.shape(), [2, 2]);

        // Check unitarity (approximately)
        let determinant =
            su2_element[[0, 0]] * su2_element[[1, 1]] - su2_element[[0, 1]] * su2_element[[1, 0]];
        assert!((determinant.norm() - 1.0).abs() < 1e-10);
    }

    #[test]
    fn test_pauli_coefficient_extraction() {
        let config = QuantumGravityConfig::default();
        let simulator = QuantumGravitySimulator::new(config);

        let su2_element = simulator.generate_su2_element().unwrap();
        let coeffs = simulator.extract_pauli_coefficients(&su2_element);

        // Check that we have 4 coefficients
        assert_eq!(coeffs.len(), 4);

        // Check trace relation
        let trace = su2_element[[0, 0]] + su2_element[[1, 1]];
        assert!((coeffs[0] - trace / 2.0).norm() < 1e-10);
    }

    #[test]
    fn test_simplex_volume_calculation() {
        let config = QuantumGravityConfig::default();
        let simulator = QuantumGravitySimulator::new(config);

        let vertices = vec![
            SpacetimeVertex {
                id: 0,
                coordinates: vec![0.0, 0.0, 0.0, 0.0],
                time: 0.0,
                coordination: 4,
            },
            SpacetimeVertex {
                id: 1,
                coordinates: vec![1.0, 1.0, 0.0, 0.0],
                time: 1.0,
                coordination: 4,
            },
        ];

        let simplex_vertices = vec![0, 1];
        let volume = simulator
            .calculate_simplex_volume(&vertices, &simplex_vertices)
            .unwrap();

        assert!(volume > 0.0);
    }

    #[test]
    fn test_causal_connection() {
        let config = QuantumGravityConfig::default();
        let simulator = QuantumGravitySimulator::new(config);

        let v1 = SpacetimeVertex {
            id: 0,
            coordinates: vec![0.0, 0.0, 0.0, 0.0],
            time: 0.0,
            coordination: 4,
        };

        let v2 = SpacetimeVertex {
            id: 1,
            coordinates: vec![1.0, 1.0, 0.0, 0.0],
            time: 1.0,
            coordination: 4,
        };

        let is_connected = simulator.is_causally_connected(&v1, &v2).unwrap();
        assert!(is_connected); // Should be causally connected
    }

    #[test]
    fn test_beta_function_calculation() {
        let config = QuantumGravityConfig::default();
        let simulator = QuantumGravitySimulator::new(config);

        let beta_g = simulator
            .calculate_beta_function("newton_constant", 0.1, &1.0)
            .unwrap();
        let beta_lambda = simulator
            .calculate_beta_function("cosmological_constant", 0.01, &1.0)
            .unwrap();

        assert!(beta_g.is_finite());
        assert!(beta_lambda.is_finite());
    }

    #[test]
    fn test_rt_surface_generation() {
        let config = QuantumGravityConfig::default();
        let simulator = QuantumGravitySimulator::new(config);
        let ads_cft_config = AdSCFTConfig::default();

        let surfaces = simulator.generate_rt_surfaces(&ads_cft_config).unwrap();

        assert!(!surfaces.is_empty());
        for surface in &surfaces {
            assert!(surface.area > 0.0);
            assert_eq!(surface.coordinates.ncols(), ads_cft_config.ads_dimension);
        }
    }

    #[test]
    fn test_lqg_simulation() {
        let mut config = QuantumGravityConfig::default();
        config.gravity_approach = GravityApproach::LoopQuantumGravity;
        config.lqg_config = Some(LQGConfig {
            num_nodes: 5,
            num_edges: 10,
            ..LQGConfig::default()
        });

        let mut simulator = QuantumGravitySimulator::new(config);

        let result = simulator.simulate();
        assert!(result.is_ok());

        let simulation_result = result.unwrap();
        assert_eq!(
            simulation_result.approach,
            GravityApproach::LoopQuantumGravity
        );
        assert!(simulation_result.spacetime_volume > 0.0);
        assert!(!simulation_result.observables.is_empty());
    }

    #[test]
    fn test_cdt_simulation() {
        let mut config = QuantumGravityConfig::default();
        config.gravity_approach = GravityApproach::CausalDynamicalTriangulation;
        config.cdt_config = Some(CDTConfig {
            num_simplices: 50,
            mc_sweeps: 10,
            ..CDTConfig::default()
        });

        let mut simulator = QuantumGravitySimulator::new(config);

        let result = simulator.simulate();
        assert!(result.is_ok());

        let simulation_result = result.unwrap();
        assert_eq!(
            simulation_result.approach,
            GravityApproach::CausalDynamicalTriangulation
        );
        assert!(simulation_result.spacetime_volume > 0.0);
    }

    #[test]
    fn test_asymptotic_safety_simulation() {
        let mut config = QuantumGravityConfig::default();
        config.gravity_approach = GravityApproach::AsymptoticSafety;
        config.asymptotic_safety_config = Some(AsymptoticSafetyConfig {
            rg_flow_steps: 5,
            ..AsymptoticSafetyConfig::default()
        });

        let mut simulator = QuantumGravitySimulator::new(config);

        let result = simulator.simulate();
        assert!(result.is_ok());

        let simulation_result = result.unwrap();
        assert_eq!(
            simulation_result.approach,
            GravityApproach::AsymptoticSafety
        );
        assert!(simulation_result.ground_state_energy.is_finite());
    }

    #[test]
    fn test_ads_cft_simulation() {
        let mut config = QuantumGravityConfig::default();
        config.gravity_approach = GravityApproach::HolographicGravity;

        let mut simulator = QuantumGravitySimulator::new(config);

        let result = simulator.simulate();
        assert!(result.is_ok());

        let simulation_result = result.unwrap();
        assert_eq!(
            simulation_result.approach,
            GravityApproach::HolographicGravity
        );
        assert!(simulation_result.spacetime_volume > 0.0);
        assert!(simulation_result
            .observables
            .contains_key("holographic_complexity"));
    }

    #[test]
    fn test_planck_units() {
        let units = QuantumGravityUtils::planck_units();

        assert!(units.contains_key("length"));
        assert!(units.contains_key("time"));
        assert!(units.contains_key("mass"));
        assert!(units.contains_key("energy"));

        assert_eq!(units["length"], 1.616e-35);
        assert_eq!(units["time"], 5.391e-44);
    }

    #[test]
    fn test_approach_comparison() {
        let results = vec![GravitySimulationResult {
            approach: GravityApproach::LoopQuantumGravity,
            ground_state_energy: 1e-10,
            spacetime_volume: 1e-105,
            geometry_measurements: GeometryMeasurements {
                area_spectrum: vec![1e-70],
                volume_spectrum: vec![1e-105],
                length_spectrum: vec![1e-35],
                discrete_curvature: 1e70,
                topology_measurements: TopologyMeasurements {
                    euler_characteristic: 1,
                    betti_numbers: vec![1],
                    homology_groups: vec!["Z".to_string()],
                    fundamental_group: "trivial".to_string(),
                },
            },
            convergence_info: ConvergenceInfo {
                iterations: 100,
                final_residual: 1e-8,
                converged: true,
                convergence_history: vec![1e-2, 1e-8],
            },
            observables: HashMap::new(),
            computation_time: 1.0,
        }];

        let comparison = QuantumGravityUtils::compare_approaches(&results);
        assert!(comparison.contains("LoopQuantumGravity"));
        assert!(comparison.contains("Energy"));
        assert!(comparison.contains("Volume"));
    }

    #[test]
    fn test_physical_constraints_validation() {
        let result = GravitySimulationResult {
            approach: GravityApproach::LoopQuantumGravity,
            ground_state_energy: -1.0, // Invalid negative energy
            spacetime_volume: 0.0,     // Invalid zero volume
            geometry_measurements: GeometryMeasurements {
                area_spectrum: vec![1e-70],
                volume_spectrum: vec![1e-105],
                length_spectrum: vec![1e-35],
                discrete_curvature: 1e15, // Extreme curvature
                topology_measurements: TopologyMeasurements {
                    euler_characteristic: 1,
                    betti_numbers: vec![1],
                    homology_groups: vec!["Z".to_string()],
                    fundamental_group: "trivial".to_string(),
                },
            },
            convergence_info: ConvergenceInfo {
                iterations: 100,
                final_residual: 1e-8,
                converged: true,
                convergence_history: vec![1e-2, 1e-8],
            },
            observables: HashMap::new(),
            computation_time: 1.0,
        };

        let violations = QuantumGravityUtils::validate_physical_constraints(&result);

        assert_eq!(violations.len(), 3);
        assert!(violations
            .iter()
            .any(|v| v.contains("Negative ground state energy")));
        assert!(violations.iter().any(|v| v.contains("volume")));
        assert!(violations.iter().any(|v| v.contains("curvature")));
    }

    #[test]
    #[ignore]
    fn test_benchmark_quantum_gravity() {
        // This is a more comprehensive test that would run longer
        // In practice, you might want to make this an integration test
        let result = benchmark_quantum_gravity_simulation();
        assert!(result.is_ok());

        let benchmark = result.unwrap();
        assert!(!benchmark.approach_results.is_empty());
        assert!(!benchmark.timing_comparisons.is_empty());
        assert!(benchmark.memory_usage > 0);
    }
}