scirs2_series/advanced_fusion_intelligence/

temporal.rs

//! Temporal and Causal Analysis Components for Advanced Fusion Intelligence
//!
//! This module contains all temporal processing, causal analysis, and spacetime-related
//! structures and implementations for the advanced fusion intelligence system, including
//! multi-timeline processing, causal discovery, paradox resolution, and dimensional analysis.

use scirs2_core::ndarray::Array1;
use scirs2_core::numeric::{Float, FromPrimitive};
use std::collections::HashMap;
use std::fmt::Debug;

use crate::error::Result;

/// Multi-timeline processor for temporal analysis
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct MultiTimelineProcessor<F: Float + Debug> {
    temporal_dimensions: Vec<TemporalDimension<F>>,
    timeline_synchronizer: TimelineSynchronizer<F>,
    causal_structure_analyzer: CausalStructureAnalyzer<F>,
}

/// Individual temporal dimension
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct TemporalDimension<F: Float + Debug> {
    dimension_id: usize,
    time_resolution: F,
    causal_direction: CausalDirection,
    branching_factor: F,
}

/// Direction of causal relationships
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum CausalDirection {
    /// Forward causation
    Forward,
    /// Backward causation
    Backward,
    /// Bidirectional causation
    Bidirectional,
    /// Non-causal relationship
    NonCausal,
}

/// Timeline synchronizer for multi-dimensional time
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct TimelineSynchronizer<F: Float + Debug> {
    synchronization_protocol: SynchronizationProtocol,
    temporal_alignment: F,
    causality_preservation: F,
}

/// Protocols for timeline synchronization
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum SynchronizationProtocol {
    /// Global clock synchronization
    GlobalClock,
    /// Local causal synchronization
    LocalCausal,
    /// Quantum entangled synchronization
    QuantumEntangled,
    /// Consciousness-guided synchronization
    ConsciousnessGuided,
}

/// Analyzer for causal structures
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CausalStructureAnalyzer<F: Float + Debug> {
    causal_graph: CausalGraph<F>,
    intervention_effects: Vec<InterventionEffect<F>>,
    counterfactual_reasoning: CounterfactualReasoning<F>,
}

/// Graph representation of causal relationships
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CausalGraph<F: Float + Debug> {
    nodes: Vec<CausalNode<F>>,
    edges: Vec<CausalEdge<F>>,
    confounders: Vec<Confounder<F>>,
}

/// Node in the causal graph
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CausalNode<F: Float + Debug> {
    node_id: usize,
    variable_name: String,
    node_type: NodeType,
    value: F,
}

/// Types of nodes in causal graphs
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum NodeType {
    /// Observable variable
    Observable,
    /// Hidden variable
    Hidden,
    /// Intervention variable
    Intervention,
    /// Outcome variable
    Outcome,
}

/// Edge in the causal graph
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CausalEdge<F: Float + Debug> {
    source: usize,
    target: usize,
    strength: F,
    edge_type: EdgeType,
}

/// Types of causal edges
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum EdgeType {
    /// Direct causal relationship
    Direct,
    /// Mediated causal relationship
    Mediated,
    /// Confounded relationship
    Confounded,
    /// Collider relationship
    Collider,
}

/// Confounder in causal relationships
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct Confounder<F: Float + Debug> {
    confounder_id: usize,
    affected_variables: Vec<usize>,
    confounding_strength: F,
}

/// Effect of interventions on the causal system
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct InterventionEffect<F: Float + Debug> {
    intervention_target: usize,
    intervention_value: F,
    causal_effect: F,
    confidence_interval: (F, F),
}

/// System for counterfactual reasoning
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CounterfactualReasoning<F: Float + Debug> {
    counterfactual_queries: Vec<CounterfactualQuery<F>>,
    reasoning_engine: ReasoningEngine<F>,
}

/// Query for counterfactual analysis
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CounterfactualQuery<F: Float + Debug> {
    query_id: usize,
    intervention: String,
    outcome: String,
    counterfactual_probability: F,
}

/// Engine for reasoning operations
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ReasoningEngine<F: Float + Debug> {
    reasoning_type: ReasoningType,
    inference_strength: F,
    uncertainty_handling: UncertaintyHandling,
}

/// Types of reasoning
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum ReasoningType {
    /// Deductive reasoning
    Deductive,
    /// Inductive reasoning
    Inductive,
    /// Abductive reasoning
    Abductive,
    /// Counterfactual reasoning
    Counterfactual,
}

/// Methods for handling uncertainty
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum UncertaintyHandling {
    /// Bayesian approach
    Bayesian,
    /// Fuzzy logic approach
    Fuzzy,
    /// Possibilistic approach
    Possibilistic,
    /// Quantum approach
    Quantum,
}

/// Engine for causal analysis
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CausalAnalysisEngine<F: Float + Debug> {
    causal_discovery: CausalDiscovery<F>,
    causal_inference: CausalInference<F>,
    effect_estimation: EffectEstimation<F>,
}

/// System for discovering causal relationships
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CausalDiscovery<F: Float + Debug> {
    discovery_algorithm: DiscoveryAlgorithm,
    constraint_tests: Vec<ConstraintTest<F>>,
    structure_learning: StructureLearning<F>,
}

/// Algorithms for causal discovery
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum DiscoveryAlgorithm {
    /// PC algorithm
    PC,
    /// Greedy Equivalence Search
    GES,
    /// Greedy Interventional Equivalence Search
    GIES,
    /// Direct Linear Non-Gaussian Acyclic Model
    DirectLiNGAM,
    /// Quantum causal discovery
    QuantumCausal,
}

/// Test for causal constraints
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ConstraintTest<F: Float + Debug> {
    test_type: TestType,
    significance_level: F,
    test_statistic: F,
}

/// Types of statistical tests
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum TestType {
    /// Independence test
    Independence,
    /// Conditional independence test
    ConditionalIndependence,
    /// Instrumental variable test
    InstrumentalVariable,
    /// Randomization test
    Randomization,
}

/// System for learning causal structure
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct StructureLearning<F: Float + Debug> {
    learning_method: LearningMethod,
    regularization: F,
    model_selection: ModelSelection,
}

/// Methods for structure learning
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum LearningMethod {
    /// Score-based learning
    ScoreBased,
    /// Constraint-based learning
    ConstraintBased,
    /// Hybrid approach
    Hybrid,
    /// Deep learning approach
    DeepLearning,
}

/// Methods for model selection
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum ModelSelection {
    /// Bayesian Information Criterion
    BIC,
    /// Akaike Information Criterion
    AIC,
    /// Cross-validation
    CrossValidation,
    /// Bayesian model selection
    Bayesian,
}

/// System for causal inference
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CausalInference<F: Float + Debug> {
    inference_framework: InferenceFramework,
    identification_strategy: IdentificationStrategy<F>,
    sensitivity_analysis: SensitivityAnalysis<F>,
}

/// Frameworks for causal inference
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum InferenceFramework {
    /// Potential outcomes framework
    PotentialOutcomes,
    /// Structural equation models
    StructuralEquations,
    /// Graphical models
    GraphicalModels,
    /// Quantum causal models
    QuantumCausal,
}

/// Strategy for causal identification
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct IdentificationStrategy<F: Float + Debug> {
    strategy_type: StrategyType,
    assumptions: Vec<CausalAssumption>,
    validity_checks: Vec<ValidityCheck<F>>,
}

/// Types of identification strategies
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum StrategyType {
    /// Resource allocation strategy
    ResourceAllocation,
    /// Attention control strategy
    AttentionControl,
    /// Learning adjustment strategy
    LearningAdjustment,
    /// Consciousness modulation strategy
    ConsciousnessModulation,
}

/// Assumptions for causal inference
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum CausalAssumption {
    /// Exchangeability assumption
    Exchangeability,
    /// Positivity and consistency
    PositivityConsistency,
    /// No interference assumption
    NoInterference,
    /// Monotonicity and stability
    MonotonicityStable,
}

/// Check for validity of causal assumptions
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ValidityCheck<F: Float + Debug> {
    check_type: CheckType,
    validity_score: F,
    diagnostic_statistics: Vec<F>,
}

/// Types of validity checks
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum CheckType {
    /// Placebo test
    PlaceboTest,
    /// Falsification test
    FalsificationTest,
    /// Robustness check
    RobustnessCheck,
    /// Sensitivity analysis
    SensitivityAnalysis,
}

/// Analysis of sensitivity to assumptions
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct SensitivityAnalysis<F: Float + Debug> {
    sensitivity_parameters: Vec<SensitivityParameter<F>>,
    robustness_bounds: RobustnessBounds<F>,
}

/// Parameter for sensitivity analysis
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct SensitivityParameter<F: Float + Debug> {
    parameter_name: String,
    parameter_range: (F, F),
    effect_sensitivity: F,
}

/// Bounds for robustness analysis
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct RobustnessBounds<F: Float + Debug> {
    lower_bound: F,
    upper_bound: F,
    confidence_level: F,
}

/// System for estimating causal effects
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct EffectEstimation<F: Float + Debug> {
    estimation_method: EstimationMethod,
    effect_measures: Vec<EffectMeasure<F>>,
    variance_estimation: VarianceEstimation<F>,
}

/// Methods for effect estimation
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum EstimationMethod {
    /// Doubly robust estimation
    DoublyRobust,
    /// Instrumental variable estimation
    InstrumentalVariable,
    /// Regression discontinuity
    RegressionDiscontinuity,
    /// Quantum matching
    MatchingQuantum,
}

/// Measure of causal effect
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct EffectMeasure<F: Float + Debug> {
    measure_type: MeasureType,
    point_estimate: F,
    confidence_interval: (F, F),
    p_value: F,
}

/// Types of effect measures
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum MeasureType {
    /// Average treatment effect
    AverageTreatmentEffect,
    /// Conditional average treatment effect
    ConditionalAverageTreatmentEffect,
    /// Local average treatment effect
    LocalAverageTreatmentEffect,
    /// Quantile treatment effect
    QuantileEffectTreatment,
}

/// Estimation of variance
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct VarianceEstimation<F: Float + Debug> {
    estimation_type: VarianceEstimationType,
    bootstrap_samples: usize,
    variance_estimate: F,
}

/// Types of variance estimation
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum VarianceEstimationType {
    /// Analytical variance estimation
    Analytical,
    /// Bootstrap variance estimation
    Bootstrap,
    /// Jackknife variance estimation
    Jackknife,
    /// Bayesian variance estimation
    Bayesian,
}

/// Resolver for temporal paradoxes
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct TemporalParadoxResolver<F: Float + Debug> {
    paradox_detection: ParadoxDetection<F>,
    resolution_strategies: Vec<ResolutionStrategy<F>>,
    consistency_maintenance: ConsistencyMaintenance<F>,
}

/// System for detecting temporal paradoxes
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ParadoxDetection<F: Float + Debug> {
    paradox_types: Vec<ParadoxType>,
    detection_algorithms: Vec<DetectionAlgorithm<F>>,
    severity_assessment: SeverityAssessment<F>,
}

/// Types of temporal paradoxes
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum ParadoxType {
    /// Grandfather paradox
    Grandfather,
    /// Bootstrap paradox
    Bootstrap,
    /// Information paradox
    Information,
    /// Causal paradox
    Causal,
}

/// Algorithm for paradox detection
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct DetectionAlgorithm<F: Float + Debug> {
    algorithm_name: String,
    detection_sensitivity: F,
    false_positive_rate: F,
}

/// Assessment of paradox severity
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct SeverityAssessment<F: Float + Debug> {
    severity_metrics: Vec<SeverityMetric<F>>,
    impact_analysis: ImpactAnalysis<F>,
}

/// Metric for assessing severity
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct SeverityMetric<F: Float + Debug> {
    metric_name: String,
    severity_score: F,
    confidence: F,
}

/// Analysis of paradox impact
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ImpactAnalysis<F: Float + Debug> {
    temporal_impact: F,
    causal_impact: F,
    information_impact: F,
}

/// Strategy for resolving paradoxes
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ResolutionStrategy<F: Float + Debug> {
    strategy_name: String,
    resolution_method: ResolutionMethod,
    success_probability: F,
    computational_cost: F,
}

/// Methods for paradox resolution
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum ResolutionMethod {
    /// Novikov self-consistency principle
    NovikOffPrinciple,
    /// Many-worlds interpretation
    ManyWorlds,
    /// Self-consistency approach
    SelfConsistency,
    /// Quantum superposition approach
    QuantumSuperposition,
}

/// System for maintaining consistency
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ConsistencyMaintenance<F: Float + Debug> {
    consistency_checks: Vec<ConsistencyCheck<F>>,
    repair_mechanisms: Vec<RepairMechanism<F>>,
}

/// Check for temporal consistency
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ConsistencyCheck<F: Float + Debug> {
    check_name: String,
    consistency_level: F,
    violation_tolerance: F,
}

/// Mechanism for repairing inconsistencies
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct RepairMechanism<F: Float + Debug> {
    mechanism_name: String,
    repair_strength: F,
    side_effects: F,
}

/// Mapper for spacetime analysis
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct SpacetimeMapper<F: Float + Debug> {
    spacetime_model: SpacetimeModel<F>,
    dimensional_analysis: DimensionalAnalysis<F>,
    metric_tensor: MetricTensor<F>,
}

/// Model of spacetime structure
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct SpacetimeModel<F: Float + Debug> {
    dimensions: usize,
    curvature: F,
    topology: TopologyType,
    metric_signature: Vec<i8>,
}

/// Types of spacetime topology
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum TopologyType {
    /// Euclidean topology
    Euclidean,
    /// Minkowski spacetime
    Minkowski,
    /// Riemannian manifold
    Riemannian,
    /// Quantum Lorentzian spacetime
    LorentzianQuantum,
}

/// Analysis of dimensional structure
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct DimensionalAnalysis<F: Float + Debug> {
    spatial_dimensions: usize,
    temporal_dimensions: usize,
    compactified_dimensions: usize,
    extra_dimensions: Vec<ExtraDimension<F>>,
}

/// Extra dimension beyond standard spacetime
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ExtraDimension<F: Float + Debug> {
    dimension_type: DimensionType,
    compactification_scale: F,
    accessibility: F,
}

/// Types of dimensions
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum DimensionType {
    /// Spatial dimension
    Spatial,
    /// Temporal dimension
    Temporal,
    /// Quantum dimension
    Quantum,
    /// Information dimension
    Information,
}

/// Metric tensor for spacetime geometry
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct MetricTensor<F: Float + Debug> {
    tensor_components: Vec<Vec<F>>,
    determinant: F,
    signature: Vec<i8>,
    curvature_scalar: F,
}

impl<F: Float + Debug + Clone + FromPrimitive> MultiTimelineProcessor<F> {
    /// Create new multi-timeline processor
    pub fn new(num_dimensions: usize) -> Self {
        let mut temporal_dimensions = Vec::new();

        for i in 0..num_dimensions {
            let dimension = TemporalDimension {
                dimension_id: i,
                time_resolution: F::from_f64(0.001).unwrap(), // 1ms resolution
                causal_direction: CausalDirection::Forward,
                branching_factor: F::from_f64(1.0).unwrap(),
            };
            temporal_dimensions.push(dimension);
        }

        MultiTimelineProcessor {
            temporal_dimensions,
            timeline_synchronizer: TimelineSynchronizer::new(),
            causal_structure_analyzer: CausalStructureAnalyzer::new(),
        }
    }

    /// Process temporal data across multiple timelines
    pub fn process_temporal_data(&mut self, temporal_data: &[Array1<F>]) -> Result<Array1<F>> {
        if temporal_data.is_empty() {
            return Ok(Array1::zeros(0));
        }

        // Synchronize timelines
        let synchronized_data = self
            .timeline_synchronizer
            .synchronize_timelines(temporal_data)?;

        // Analyze causal structure
        let causal_analysis = self
            .causal_structure_analyzer
            .analyze_causality(&synchronized_data)?;

        // Integrate temporal dimensions
        let integrated_result = self.integrate_temporal_dimensions(&causal_analysis)?;

        Ok(integrated_result)
    }

    /// Integrate data across temporal dimensions
    fn integrate_temporal_dimensions(&self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut integrated = data.clone();

        // Apply temporal dimension processing
        for dimension in &self.temporal_dimensions {
            integrated = dimension.process_temporal_data(&integrated)?;
        }

        Ok(integrated)
    }

    /// Detect temporal anomalies
    pub fn detect_temporal_anomalies(&self, data: &Array1<F>) -> Result<Vec<F>> {
        let mut anomalies = Vec::new();

        for (i, &value) in data.iter().enumerate() {
            // Simple anomaly detection based on statistical deviation
            let expected_value = F::from_f64(0.5).unwrap(); // Placeholder
            let deviation = (value - expected_value).abs();
            let threshold = F::from_f64(2.0).unwrap();

            if deviation > threshold {
                anomalies.push(F::from_usize(i).unwrap());
            }
        }

        Ok(anomalies)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> TemporalDimension<F> {
    /// Process data through this temporal dimension
    pub fn process_temporal_data(&self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut processed = data.clone();

        // Apply causal direction filtering
        match self.causal_direction {
            CausalDirection::Forward => {
                // Forward temporal processing
                for i in 1..processed.len() {
                    processed[i] = processed[i] + processed[i - 1] * F::from_f64(0.1).unwrap();
                }
            }
            CausalDirection::Backward => {
                // Backward temporal processing
                for i in (0..processed.len() - 1).rev() {
                    processed[i] = processed[i] + processed[i + 1] * F::from_f64(0.1).unwrap();
                }
            }
            CausalDirection::Bidirectional => {
                // Bidirectional processing
                let forward = self.process_forward(&processed)?;
                let backward = self.process_backward(&processed)?;
                for i in 0..processed.len() {
                    processed[i] = (forward[i] + backward[i]) / F::from_f64(2.0).unwrap();
                }
            }
            CausalDirection::NonCausal => {
                // No temporal coupling
            }
        }

        Ok(processed)
    }

    /// Process data in forward direction
    fn process_forward(&self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut forward = data.clone();
        for i in 1..forward.len() {
            forward[i] = forward[i] + forward[i - 1] * F::from_f64(0.05).unwrap();
        }
        Ok(forward)
    }

    /// Process data in backward direction
    fn process_backward(&self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut backward = data.clone();
        for i in (0..backward.len() - 1).rev() {
            backward[i] = backward[i] + backward[i + 1] * F::from_f64(0.05).unwrap();
        }
        Ok(backward)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for TimelineSynchronizer<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> TimelineSynchronizer<F> {
    /// Create new timeline synchronizer
    pub fn new() -> Self {
        TimelineSynchronizer {
            synchronization_protocol: SynchronizationProtocol::GlobalClock,
            temporal_alignment: F::from_f64(0.95).unwrap(),
            causality_preservation: F::from_f64(0.9).unwrap(),
        }
    }

    /// Synchronize multiple timelines
    pub fn synchronize_timelines(&mut self, timelines: &[Array1<F>]) -> Result<Array1<F>> {
        if timelines.is_empty() {
            return Ok(Array1::zeros(0));
        }

        match self.synchronization_protocol {
            SynchronizationProtocol::GlobalClock => self.global_clock_sync(timelines),
            SynchronizationProtocol::LocalCausal => self.local_causal_sync(timelines),
            SynchronizationProtocol::QuantumEntangled => self.quantum_entangled_sync(timelines),
            SynchronizationProtocol::ConsciousnessGuided => {
                self.consciousness_guided_sync(timelines)
            }
        }
    }

    /// Global clock synchronization
    fn global_clock_sync(&self, timelines: &[Array1<F>]) -> Result<Array1<F>> {
        // Find minimum length across all timelines
        let min_len = timelines.iter().map(|t| t.len()).min().unwrap_or(0);
        let mut synchronized = Array1::zeros(min_len);

        // Average across timelines
        for i in 0..min_len {
            let mut sum = F::zero();
            for timeline in timelines {
                if i < timeline.len() {
                    sum = sum + timeline[i];
                }
            }
            synchronized[i] = sum / F::from_usize(timelines.len()).unwrap();
        }

        Ok(synchronized)
    }

    /// Local causal synchronization
    fn local_causal_sync(&self, timelines: &[Array1<F>]) -> Result<Array1<F>> {
        // Apply causal ordering constraints
        let min_len = timelines.iter().map(|t| t.len()).min().unwrap_or(0);
        let mut synchronized = Array1::zeros(min_len);

        for i in 0..min_len {
            let mut weighted_sum = F::zero();
            let mut total_weight = F::zero();

            for (j, timeline) in timelines.iter().enumerate() {
                if i < timeline.len() {
                    // Weight by causal relevance (simplified)
                    let causal_weight = F::from_f64(1.0).unwrap() / (F::from_usize(j + 1).unwrap());
                    weighted_sum = weighted_sum + timeline[i] * causal_weight;
                    total_weight = total_weight + causal_weight;
                }
            }

            if total_weight > F::zero() {
                synchronized[i] = weighted_sum / total_weight;
            }
        }

        Ok(synchronized)
    }

    /// Quantum entangled synchronization
    fn quantum_entangled_sync(&self, timelines: &[Array1<F>]) -> Result<Array1<F>> {
        // Apply quantum entanglement principles
        let min_len = timelines.iter().map(|t| t.len()).min().unwrap_or(0);
        let mut synchronized = Array1::zeros(min_len);

        for i in 0..min_len {
            // Quantum superposition of timeline states
            let mut entangled_state = F::zero();
            for timeline in timelines {
                if i < timeline.len() {
                    // Apply quantum phase factors
                    let phase_factor =
                        F::from_f64((i as f64 * std::f64::consts::PI / 4.0).cos()).unwrap();
                    entangled_state = entangled_state + timeline[i] * phase_factor;
                }
            }

            // Normalize by square root of number of timelines (quantum normalization)
            let normalization = F::from_usize(timelines.len()).unwrap().sqrt();
            synchronized[i] = entangled_state / normalization;
        }

        Ok(synchronized)
    }

    /// Consciousness-guided synchronization
    fn consciousness_guided_sync(&self, timelines: &[Array1<F>]) -> Result<Array1<F>> {
        // Apply consciousness principles for synchronization
        let min_len = timelines.iter().map(|t| t.len()).min().unwrap_or(0);
        let mut synchronized = Array1::zeros(min_len);

        for i in 0..min_len {
            // Consciousness-weighted integration
            let mut consciousness_sum = F::zero();
            let mut consciousness_weight_total = F::zero();

            for timeline in timelines {
                if i < timeline.len() {
                    // Consciousness weight based on timeline coherence
                    let coherence = self.calculate_timeline_coherence(timeline)?;
                    consciousness_sum = consciousness_sum + timeline[i] * coherence;
                    consciousness_weight_total = consciousness_weight_total + coherence;
                }
            }

            if consciousness_weight_total > F::zero() {
                synchronized[i] = consciousness_sum / consciousness_weight_total;
            }
        }

        Ok(synchronized)
    }

    /// Calculate coherence of a timeline
    fn calculate_timeline_coherence(&self, timeline: &Array1<F>) -> Result<F> {
        if timeline.len() < 2 {
            return Ok(F::from_f64(1.0).unwrap());
        }

        // Calculate coherence as inverse of variance
        let mean = timeline.iter().fold(F::zero(), |acc, &x| acc + x)
            / F::from_usize(timeline.len()).unwrap();
        let variance = timeline
            .iter()
            .fold(F::zero(), |acc, &x| acc + (x - mean) * (x - mean))
            / F::from_usize(timeline.len()).unwrap();

        let coherence = F::from_f64(1.0).unwrap() / (F::from_f64(1.0).unwrap() + variance);
        Ok(coherence)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for CausalStructureAnalyzer<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> CausalStructureAnalyzer<F> {
    /// Create new causal structure analyzer
    pub fn new() -> Self {
        CausalStructureAnalyzer {
            causal_graph: CausalGraph::new(),
            intervention_effects: Vec::new(),
            counterfactual_reasoning: CounterfactualReasoning::new(),
        }
    }

    /// Analyze causality in temporal data
    pub fn analyze_causality(&mut self, data: &Array1<F>) -> Result<Array1<F>> {
        // Build causal graph from data
        self.causal_graph.build_from_data(data)?;

        // Compute intervention effects
        self.compute_intervention_effects(data)?;

        // Apply counterfactual reasoning
        let counterfactual_result = self.counterfactual_reasoning.reason_about_data(data)?;

        Ok(counterfactual_result)
    }

    /// Compute effects of hypothetical interventions
    fn compute_intervention_effects(&mut self, data: &Array1<F>) -> Result<()> {
        self.intervention_effects.clear();

        // Compute intervention effects for each node
        for (i, _) in data.iter().enumerate() {
            let intervention_effect = InterventionEffect {
                intervention_target: i,
                intervention_value: F::from_f64(1.0).unwrap(),
                causal_effect: F::from_f64(0.5).unwrap(), // Simplified calculation
                confidence_interval: (F::from_f64(0.3).unwrap(), F::from_f64(0.7).unwrap()),
            };
            self.intervention_effects.push(intervention_effect);
        }

        Ok(())
    }

    /// Get causal strength between variables
    pub fn get_causal_strength(&self, source: usize, target: usize) -> Result<F> {
        for edge in &self.causal_graph.edges {
            if edge.source == source && edge.target == target {
                return Ok(edge.strength);
            }
        }
        Ok(F::zero())
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for CausalGraph<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> CausalGraph<F> {
    /// Create new causal graph
    pub fn new() -> Self {
        CausalGraph {
            nodes: Vec::new(),
            edges: Vec::new(),
            confounders: Vec::new(),
        }
    }

    /// Build causal graph from data
    pub fn build_from_data(&mut self, data: &Array1<F>) -> Result<()> {
        // Create nodes for each data point
        self.nodes.clear();
        for (i, &value) in data.iter().enumerate() {
            let node = CausalNode {
                node_id: i,
                variable_name: format!("var_{}", i),
                node_type: NodeType::Observable,
                value,
            };
            self.nodes.push(node);
        }

        // Create edges based on temporal ordering and correlation
        self.edges.clear();
        for i in 0..data.len().saturating_sub(1) {
            let correlation = self.calculate_correlation(data[i], data[i + 1])?;
            let edge = CausalEdge {
                source: i,
                target: i + 1,
                strength: correlation,
                edge_type: EdgeType::Direct,
            };
            self.edges.push(edge);
        }

        Ok(())
    }

    /// Calculate correlation between two values
    fn calculate_correlation(&self, value1: F, value2: F) -> Result<F> {
        // Simplified correlation calculation
        let diff = (value1 - value2).abs();
        let max_val = value1.max(value2);

        if max_val > F::zero() {
            Ok(F::from_f64(1.0).unwrap() - diff / max_val)
        } else {
            Ok(F::from_f64(1.0).unwrap())
        }
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for CounterfactualReasoning<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> CounterfactualReasoning<F> {
    /// Create new counterfactual reasoning system
    pub fn new() -> Self {
        CounterfactualReasoning {
            counterfactual_queries: Vec::new(),
            reasoning_engine: ReasoningEngine::new(),
        }
    }

    /// Reason about counterfactual scenarios
    pub fn reason_about_data(&mut self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut counterfactual_result = data.clone();

        // Apply counterfactual transformations
        for (i, value) in counterfactual_result.iter_mut().enumerate() {
            // Generate counterfactual query
            let query = CounterfactualQuery {
                query_id: i,
                intervention: format!("set_var_{}_to_zero", i),
                outcome: format!("observe_var_{}", i),
                counterfactual_probability: F::from_f64(0.5).unwrap(),
            };
            self.counterfactual_queries.push(query);

            // Apply counterfactual reasoning
            let counterfactual_adjustment = self.reasoning_engine.compute_counterfactual(*value)?;
            *value = *value + counterfactual_adjustment;
        }

        Ok(counterfactual_result)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for ReasoningEngine<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> ReasoningEngine<F> {
    /// Create new reasoning engine
    pub fn new() -> Self {
        ReasoningEngine {
            reasoning_type: ReasoningType::Counterfactual,
            inference_strength: F::from_f64(0.8).unwrap(),
            uncertainty_handling: UncertaintyHandling::Bayesian,
        }
    }

    /// Compute counterfactual adjustment
    pub fn compute_counterfactual(&self, observed_value: F) -> Result<F> {
        match self.reasoning_type {
            ReasoningType::Counterfactual => {
                // Simple counterfactual adjustment
                let adjustment =
                    observed_value * F::from_f64(0.1).unwrap() * self.inference_strength;
                Ok(adjustment)
            }
            _ => Ok(F::zero()),
        }
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for TemporalParadoxResolver<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> TemporalParadoxResolver<F> {
    /// Create new temporal paradox resolver
    pub fn new() -> Self {
        TemporalParadoxResolver {
            paradox_detection: ParadoxDetection::new(),
            resolution_strategies: vec![
                ResolutionStrategy::new(
                    "self_consistency".to_string(),
                    ResolutionMethod::SelfConsistency,
                ),
                ResolutionStrategy::new("many_worlds".to_string(), ResolutionMethod::ManyWorlds),
            ],
            consistency_maintenance: ConsistencyMaintenance::new(),
        }
    }

    /// Resolve temporal paradoxes in data
    pub fn resolve_paradoxes(&mut self, temporal_data: &Array1<F>) -> Result<Array1<F>> {
        // Detect paradoxes
        let paradoxes = self.paradox_detection.detect_paradoxes(temporal_data)?;

        if paradoxes.is_empty() {
            return Ok(temporal_data.clone());
        }

        // Apply resolution strategies
        let mut resolved_data = temporal_data.clone();
        for strategy in &self.resolution_strategies {
            resolved_data = strategy.apply_resolution(&resolved_data)?;
        }

        // Maintain consistency
        resolved_data = self
            .consistency_maintenance
            .maintain_consistency(&resolved_data)?;

        Ok(resolved_data)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for ParadoxDetection<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> ParadoxDetection<F> {
    /// Create new paradox detection system
    pub fn new() -> Self {
        ParadoxDetection {
            paradox_types: vec![
                ParadoxType::Grandfather,
                ParadoxType::Bootstrap,
                ParadoxType::Information,
                ParadoxType::Causal,
            ],
            detection_algorithms: vec![DetectionAlgorithm {
                algorithm_name: "causal_loop_detector".to_string(),
                detection_sensitivity: F::from_f64(0.9).unwrap(),
                false_positive_rate: F::from_f64(0.05).unwrap(),
            }],
            severity_assessment: SeverityAssessment::new(),
        }
    }

    /// Detect paradoxes in temporal data
    pub fn detect_paradoxes(&mut self, data: &Array1<F>) -> Result<Vec<usize>> {
        let mut detected_paradoxes = Vec::new();

        // Simple paradox detection based on causal violations
        for i in 1..data.len() {
            // Check for causal violations (effect before cause)
            if data[i] > data[i - 1] * F::from_f64(2.0).unwrap() {
                detected_paradoxes.push(i);
            }
        }

        Ok(detected_paradoxes)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for SeverityAssessment<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> SeverityAssessment<F> {
    /// Create new severity assessment system
    pub fn new() -> Self {
        SeverityAssessment {
            severity_metrics: vec![SeverityMetric {
                metric_name: "temporal_disruption".to_string(),
                severity_score: F::from_f64(0.5).unwrap(),
                confidence: F::from_f64(0.8).unwrap(),
            }],
            impact_analysis: ImpactAnalysis {
                temporal_impact: F::from_f64(0.3).unwrap(),
                causal_impact: F::from_f64(0.4).unwrap(),
                information_impact: F::from_f64(0.2).unwrap(),
            },
        }
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> ResolutionStrategy<F> {
    /// Create new resolution strategy
    pub fn new(name: String, method: ResolutionMethod) -> Self {
        ResolutionStrategy {
            strategy_name: name,
            resolution_method: method,
            success_probability: F::from_f64(0.8).unwrap(),
            computational_cost: F::from_f64(0.5).unwrap(),
        }
    }

    /// Apply resolution strategy to data
    pub fn apply_resolution(&self, data: &Array1<F>) -> Result<Array1<F>> {
        match self.resolution_method {
            ResolutionMethod::SelfConsistency => self.apply_self_consistency(data),
            ResolutionMethod::ManyWorlds => self.apply_many_worlds(data),
            ResolutionMethod::QuantumSuperposition => self.apply_quantum_superposition(data),
            ResolutionMethod::NovikOffPrinciple => self.apply_novikov_principle(data),
        }
    }

    /// Apply self-consistency principle
    fn apply_self_consistency(&self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut consistent_data = data.clone();

        // Enforce self-consistency through iterative adjustment
        for iteration in 0..10 {
            let mut adjusted = false;

            for i in 1..consistent_data.len() {
                // Check consistency constraint
                if consistent_data[i] < consistent_data[i - 1] {
                    // Adjust to maintain consistency
                    consistent_data[i] = consistent_data[i - 1] * F::from_f64(1.01).unwrap();
                    adjusted = true;
                }
            }

            if !adjusted {
                break;
            }
        }

        Ok(consistent_data)
    }

    /// Apply many-worlds interpretation
    fn apply_many_worlds(&self, data: &Array1<F>) -> Result<Array1<F>> {
        // Create superposition of possible worlds
        let mut many_worlds_data = data.clone();

        for value in many_worlds_data.iter_mut() {
            // Superposition of multiple world states
            let world_1 = *value;
            let world_2 = *value * F::from_f64(1.1).unwrap();
            let world_3 = *value * F::from_f64(0.9).unwrap();

            // Probabilistic combination
            *value = (world_1 + world_2 + world_3) / F::from_f64(3.0).unwrap();
        }

        Ok(many_worlds_data)
    }

    /// Apply quantum superposition
    fn apply_quantum_superposition(&self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut superposition_data = data.clone();

        for (i, value) in superposition_data.iter_mut().enumerate() {
            // Quantum phase modulation
            let phase = F::from_f64(i as f64 * std::f64::consts::PI / 4.0).unwrap();
            let amplitude = F::from_f64(0.8).unwrap();

            *value = *value * amplitude * phase.cos();
        }

        Ok(superposition_data)
    }

    /// Apply Novikov self-consistency principle
    fn apply_novikov_principle(&self, data: &Array1<F>) -> Result<Array1<F>> {
        // Ensure causal consistency through the Novikov principle
        let mut novikov_data = data.clone();

        // Iteratively adjust to prevent paradoxes
        for _ in 0..5 {
            for i in 1..novikov_data.len() {
                // Ensure causal ordering
                if novikov_data[i] > novikov_data[i - 1] * F::from_f64(1.5).unwrap() {
                    // Reduce to maintain causal consistency
                    novikov_data[i] = novikov_data[i - 1] * F::from_f64(1.2).unwrap();
                }
            }
        }

        Ok(novikov_data)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for ConsistencyMaintenance<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> ConsistencyMaintenance<F> {
    /// Create new consistency maintenance system
    pub fn new() -> Self {
        ConsistencyMaintenance {
            consistency_checks: vec![ConsistencyCheck {
                check_name: "causal_ordering".to_string(),
                consistency_level: F::from_f64(0.9).unwrap(),
                violation_tolerance: F::from_f64(0.1).unwrap(),
            }],
            repair_mechanisms: vec![RepairMechanism {
                mechanism_name: "gradient_smoothing".to_string(),
                repair_strength: F::from_f64(0.8).unwrap(),
                side_effects: F::from_f64(0.1).unwrap(),
            }],
        }
    }

    /// Maintain consistency in temporal data
    pub fn maintain_consistency(&mut self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut consistent_data = data.clone();

        // Apply consistency checks
        for check in &self.consistency_checks {
            if !self.check_consistency(&consistent_data, check)? {
                // Apply repair mechanisms
                for mechanism in &self.repair_mechanisms {
                    consistent_data = mechanism.apply_repair(&consistent_data)?;
                }
            }
        }

        Ok(consistent_data)
    }

    /// Check if data satisfies consistency requirements
    fn check_consistency(&self, data: &Array1<F>, check: &ConsistencyCheck<F>) -> Result<bool> {
        match check.check_name.as_str() {
            "causal_ordering" => {
                // Check causal ordering consistency
                for i in 1..data.len() {
                    let ratio = data[i] / data[i - 1];
                    if ratio > F::from_f64(2.0).unwrap() {
                        // Arbitrary threshold
                        return Ok(false);
                    }
                }
                Ok(true)
            }
            _ => Ok(true),
        }
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> RepairMechanism<F> {
    /// Apply repair mechanism to data
    pub fn apply_repair(&self, data: &Array1<F>) -> Result<Array1<F>> {
        match self.mechanism_name.as_str() {
            "gradient_smoothing" => {
                let mut repaired_data = data.clone();

                // Apply gradient smoothing
                for i in 1..repaired_data.len() - 1 {
                    let gradient_left = repaired_data[i] - repaired_data[i - 1];
                    let gradient_right = repaired_data[i + 1] - repaired_data[i];

                    // Smooth large gradient changes
                    if (gradient_right - gradient_left).abs() > F::from_f64(1.0).unwrap() {
                        let smoothed_value = (repaired_data[i - 1] + repaired_data[i + 1])
                            / F::from_f64(2.0).unwrap();
                        repaired_data[i] = repaired_data[i]
                            * (F::from_f64(1.0).unwrap() - self.repair_strength)
                            + smoothed_value * self.repair_strength;
                    }
                }

                Ok(repaired_data)
            }
            _ => Ok(data.clone()),
        }
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for SpacetimeMapper<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> SpacetimeMapper<F> {
    /// Create new spacetime mapper
    pub fn new() -> Self {
        SpacetimeMapper {
            spacetime_model: SpacetimeModel::new(),
            dimensional_analysis: DimensionalAnalysis::new(),
            metric_tensor: MetricTensor::new(),
        }
    }

    /// Map data onto spacetime structure
    pub fn map_to_spacetime(&self, data: &Array1<F>) -> Result<Array1<F>> {
        // Apply spacetime transformation
        let mut spacetime_data = data.clone();

        // Apply metric tensor transformation
        spacetime_data = self.metric_tensor.transform(&spacetime_data)?;

        // Apply dimensional analysis
        spacetime_data = self
            .dimensional_analysis
            .analyze_dimensions(&spacetime_data)?;

        Ok(spacetime_data)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for SpacetimeModel<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> SpacetimeModel<F> {
    /// Create new spacetime model
    pub fn new() -> Self {
        SpacetimeModel {
            dimensions: 4, // 3 spatial + 1 temporal
            curvature: F::from_f64(0.01).unwrap(),
            topology: TopologyType::Minkowski,
            metric_signature: vec![1, -1, -1, -1], // Minkowski signature
        }
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for DimensionalAnalysis<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> DimensionalAnalysis<F> {
    /// Create new dimensional analysis
    pub fn new() -> Self {
        DimensionalAnalysis {
            spatial_dimensions: 3,
            temporal_dimensions: 1,
            compactified_dimensions: 0,
            extra_dimensions: Vec::new(),
        }
    }

    /// Analyze dimensional structure of data
    pub fn analyze_dimensions(&self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut dimensional_data = data.clone();

        // Apply dimensional scaling
        let dimension_factor =
            F::from_usize(self.spatial_dimensions + self.temporal_dimensions).unwrap();
        dimensional_data.mapv_inplace(|x| x / dimension_factor.sqrt());

        Ok(dimensional_data)
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> Default for MetricTensor<F> {
    fn default() -> Self {
        Self::new()
    }
}

impl<F: Float + Debug + Clone + FromPrimitive> MetricTensor<F> {
    /// Create new metric tensor
    pub fn new() -> Self {
        // 4x4 Minkowski metric tensor
        let mut tensor_components = vec![vec![F::zero(); 4]; 4];
        tensor_components[0][0] = F::from_f64(1.0).unwrap(); // time-time
        tensor_components[1][1] = F::from_f64(-1.0).unwrap(); // x-x
        tensor_components[2][2] = F::from_f64(-1.0).unwrap(); // y-y
        tensor_components[3][3] = F::from_f64(-1.0).unwrap(); // z-z

        MetricTensor {
            tensor_components,
            determinant: F::from_f64(-1.0).unwrap(),
            signature: vec![1, -1, -1, -1],
            curvature_scalar: F::zero(),
        }
    }

    /// Transform data using metric tensor
    pub fn transform(&self, data: &Array1<F>) -> Result<Array1<F>> {
        let mut transformed_data = data.clone();

        // Apply metric transformation (simplified)
        for (i, value) in transformed_data.iter_mut().enumerate() {
            let metric_component = if i < self.tensor_components.len() {
                self.tensor_components[i % 4][i % 4]
            } else {
                F::from_f64(1.0).unwrap()
            };

            *value = *value * metric_component;
        }

        Ok(transformed_data)
    }
}