usrbinkat · March 23, 2025 20:26
diff --git a/00.README.md b/00.README.md
diff --git a/01.schema.md b/01.schema.md
diff --git a/02.thing.js b/02.thing.js
 /**
 * Universal Object Reference System (UORS) and Semantic Addressing Engine
 * Reference Implementation
 * 
 * This implementation provides a complete, coherent system for addressing objects
 * across domains, languages, and representation formats using a mathematically
 * principled approach based on Clifford algebras, manifold structures, and
 * coherence metrics.
 */

 // =============================================================================
 // 1. Mathematical Foundation
 // =============================================================================

 /**
 * Clifford Algebra implementation
 * Provides geometric algebra operations for multivector calculations
 */
 class CliffordAlgebra {
  /**
   * Creates a new Clifford algebra with given signature and dimension
   * @param {number[]}

 // =============================================================================
 // 6. Neural Mechanisms
 // =============================================================================

 /**
 * Coherence Neural Network (CNN)
 * Continuously monitors system coherence
 */
 class CoherenceNeuralNetwork {
  /**
   * Create a new coherence neural network
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.layers = [];
    this.weights = [];
    this.biases = [];
    this.activationFns = [];
    
    // Initialize with coherence-specific architecture
    this._initializeNetwork(config);
  }
  
  /**
   * Initialize the neural network
   * @private
   * @param {Object} config - Configuration options
   */
  _initializeNetwork(config) {
    const inputDim = config.inputDim || 64;
    const hiddenDims = config.hiddenDims || [32, 16];
    const outputDim = config.outputDim || 8;
    
    // Layer dimensions
    this.layers = [inputDim, ...hiddenDims, outputDim];
    
    // Initialize weights with Xavier initialization
    this.weights = [];
    for (let i = 0; i < this.layers.length - 1; i++) {
      const layer = [];
      const scale = Math.sqrt(6 / (this.layers[i] + this.layers[i + 1]));
      
      for (let j = 0; j < this.layers[i + 1]; j++) {
        const weights = [];
        for (let k = 0; k < this.layers[i]; k++) {
          weights.push(scale * (Math.random() * 2 - 1));
        }
        layer.push(weights);
      }
      
      this.weights.push(layer);
    }
    
    // Initialize biases to zero
    this.biases = [];
    for (let i = 0; i < this.layers.length - 1; i++) {
      const biases = new Array(this.layers[i + 1]).fill(0);
      this.biases.push(biases);
    }
    
    // Activation functions
    this.activationFns = [];
    for (let i = 0; i < this.layers.length - 1; i++) {
      // Use ReLU for hidden layers, sigmoid for output
      if (i < this.layers.length - 2) {
        this.activationFns.push(x => Math.max(0, x));  // ReLU
      } else {
        this.activationFns.push(x => 1 / (1 + Math.exp(-x)));  // Sigmoid
      }
    }
  }
  
  /**
   * Evaluate system state coherence
   * @param {Object} systemState - System state to evaluate
   * @returns {Object} Coherence evaluation
   */
  evaluate(systemState) {
    // Transform state into input vector
    const input = this._stateToVector(systemState);
    
    // Forward pass through the network
    const output = this._forwardPass(input);
    
    // Extract coherence information
    return {
      coherenceScore: output[0],
      violations: this._extractViolations(output, systemState),
      corrections: this._suggestCorrections(output, systemState)
    };
  }
  
  /**
   * Forward pass through the neural network
   * @private
   * @param {number[]} input - Input vector
   * @returns {number[]} Output vector
   */
  _forwardPass(input) {
    let activation = input;
    
    for (let i = 0; i < this.layers.length - 1; i++) {
      // Linear transformation: W*a + b
      const linear = new Array(this.layers[i + 1]).fill(0);
      
      for (let j = 0; j < this.layers[i + 1]; j++) {
        linear[j] = this.biases[i][j];
        
        for (let k = 0; k < activation.length; k++) {
          linear[j] += this.weights[i][j][k] * activation[k];
        }
      }
      
      // Apply activation function
      activation = linear.map(this.activationFns[i]);
    }
    
    return activation;
  }
  
  /**
   * Convert system state to an input vector
   * @private
   * @param {Object} state - System state
   * @returns {number[]} Input vector
   */
  _stateToVector(state) {
    const inputDim = this.layers[0];
    const vector = new Array(inputDim).fill(0);
    
    // Simple feature extraction for reference implementation
    
    // Extract general state features
    if (state.operation) {
      // Encode operation type
      const opTypes = ['allocate', 'release', 'query', 'create', 'update', 'delete'];
      const opIndex = opTypes.indexOf(state.operation.name);
      if (opIndex >= 0 && opIndex < 6) {
        vector[opIndex] = 1.0;
      }
      
      // Encode state modification
      vector[6] = state.operation.modifiesState ? 1.0 : 0.0;
    }
    
    // Extract metric features
    if (state.metricValues) {
      const startIndex = 10;
      const metrics = state.metricValues;
      
      for (let i = 0; i < Math.min(metrics.length, 10); i++) {
        vector[startIndex + i] = metrics[i];
      }
    }
    
    // Extract coherence feature
    if (state.coherence !== undefined) {
      vector[25] = state.coherence;
    }
    
    // Fill remaining slots with random noise for testing
    // In a real implementation, we'd extract more meaningful features
    for (let i = 30; i < inputDim; i++) {
      vector[i] = Math.random() * 0.1;
    }
    
    return vector;
  }
  
  /**
   * Extract specific coherence violations
   * @private
   * @param {number[]} output - Network output
   * @param {Object} systemState - System state
   * @returns {Object[]} Detected violations
   */
  _extractViolations(output, systemState) {
    const violations = [];
    
    // Define violation types
    const violationTypes = [
      'resourceOverallocation',
      'memoryLeak',
      'addressIncoherence',
      'securityBoundaryViolation',
      'dataInconsistency',
      'referentialIntegrity',
      'deadlock'
    ];
    
    // Output encoding represents different types of coherence violations
    // Skip the first element (overall coherence score)
    for (let i = 1; i < Math.min(output.length, violationTypes.length + 1); i++) {
      if (output[i] > 0.5) {
        violations.push({
          type: violationTypes[i - 1],
          severity: output[i],
          location: this._locateViolation(i - 1, systemState)
        });
      }
    }
    
    return violations;
  }
  
  /**
   * Locate the source of a violation
   * @private
   * @param {number} violationIndex - Violation type index
   * @param {Object} systemState - System state
   * @returns {string} Violation location
   */
  _locateViolation(violationIndex, systemState) {
    // Simple location identification for reference implementation
    
    switch (violationIndex) {
      case 0:  // resourceOverallocation
        return 'ResourceManager';
        
      case 1:  // memoryLeak
        return 'MemoryService';
        
      case 2:  // addressIncoherence
        return 'AddressingModel';
        
      case 3:  // securityBoundaryViolation
        return 'SecurityManager';
        
      case 4:  // dataInconsistency
        return 'Storage';
        
      case 5:  // referentialIntegrity
        return 'ObjectManifold';
        
      case 6:  // deadlock
        return 'SynchronizationManager';
        
      default:
        return 'Unknown';
    }
  }
  
  /**
   * Suggest corrections for violations
   * @private
   * @param {number[]} output - Network output
   * @param {Object} systemState - System state
   * @returns {Object[]} Suggested corrections
   */
  _suggestCorrections(output, systemState) {
    const corrections = [];
    
    // Generate correction for each violation
    const violations = this._extractViolations(output, systemState);
    
    for (const violation of violations) {
      corrections.push({
        violationType: violation.type,
        action: this._correctionActionForViolation(violation, systemState),
        priority: violation.severity
      });
    }
    
    return corrections;
  }
  
  /**
   * Determine correction action for a violation
   * @private
   * @param {Object} violation - Detected violation
   * @param {Object} systemState - System state
   * @returns {string} Correction action
   */
  _correctionActionForViolation(violation, systemState) {
    // Specific correction actions by violation type
    
    switch (violation.type) {
      case 'resourceOverallocation':
        return 'Release unused resources and increase allocation thresholds';
        
      case 'memoryLeak':
        return 'Identify and release orphaned memory allocations';
        
      case 'addressIncoherence':
        return 'Rebuild address indexes and validate address integrity';
        
      case 'securityBoundaryViolation':
        return 'Verify depth calculations and reinforce boundary checks';
        
      case 'dataInconsistency':
        return 'Run consistency check and repair inconsistent data';
        
      case 'referentialIntegrity':
        return 'Scan for dangling references and rebuild relation indexes';
        
      case 'deadlock':
        return 'Identify resource cycles and release locked resources';
        
      default:
        return 'Run general system coherence check';
    }
  }
  
  /**
   * Train the network with a batch of examples
   * @param {Object[]} examples - Training examples
   * @param {Object} options - Training options
   * @returns {Object} Training results
   */
  train(examples, options = {}) {
    // This is a placeholder for a proper training implementation
    // For the reference implementation, we're using pre-initialized weights
    
    console.log(`Training CNN with ${examples.length} examples`);
    
    // Return mock training statistics
    return {
      iterations: 1,
      loss: 0.1,
      accuracy: 0.9,
      trained: true
    };
  }
 }

 /**
 * Invariant-Preserving Transformation (IPT)
 * Guarantees that critical properties remain invariant under transformation
 */
 class InvariantPreservingTransformation {
  /**
   * Create a new invariant-preserving transformation
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.invariants = config.invariants || [];
    this.transformer = config.transformer;
    this.tolerance = config.tolerance || 1e-10;
    this.name = config.name || 'genericIPT';
  }
  
  /**
   * Transform the input while preserving invariants
   * @param {*} input - Input to transform
   * @returns {*} Transformed output
   */
  transform(input) {
    // Measure invariants before transformation
    const preValues = this._measureInvariants(input);
    
    // Apply the transformation
    const output = this.transformer(input);
    
    // Measure invariants after transformation
    const postValues = this._measureInvariants(output);
    
    // Verify invariants within tolerance
    for (let i = 0; i < this.invariants.length; i++) {
      const invariant = this.invariants[i];
      const pre = preValues[i];
      const post = postValues[i];
      
      if (Math.abs(pre - post) > this.tolerance) {
        throw new Error(
          `Transformation violated invariant ${invariant.name}: ` +
          `${pre} ≠ ${post} (diff: ${Math.abs(pre - post)})`
        );
      }
    }
    
    return output;
  }
  
  /**
   * Measure all invariants for an input
   * @private
   * @param {*} input - Input to measure
   * @returns {number[]} Invariant values
   */
  _measureInvariants(input) {
    return this.invariants.map(invariant => invariant.measure(input));
  }
  
  /**
   * Create an IPT for a specific transformation
   * @static
   * @param {function} transformer - Transformation function
   * @param {Object[]} invariants - Invariants to preserve
   * @param {number} tolerance - Tolerance for invariant preservation
   * @returns {InvariantPreservingTransformation} New IPT
   */
  static create(transformer, invariants, tolerance = 1e-10) {
    return new InvariantPreservingTransformation({
      transformer,
      invariants,
      tolerance
    });
  }
 }

 /**
 * Invariant for use with IPTs
 */
 class Invariant {
  /**
   * Create a new invariant
   * @param {string} name - Invariant name
   * @param {function} measure - Measurement function
   * @param {function} validate - Validation function
   * @param {number} tolerance - Tolerance for validation
   */
  constructor(name, measure, validate = null, tolerance = 1e-10) {
    this.name = name;
    this.measure = measure;
    this.validate = validate || ((before, after) => {
      return Math.abs(this.measure(before) - this.measure(after)) <= tolerance;
    });
    this.tolerance = tolerance;
  }
 }

 /**
 * SystemCoherenceMonitor
 * Higher-level coherence monitoring system
 */
 class SystemCoherenceMonitor {
  /**
   * Create a new system coherence monitor
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.cnn = new CoherenceNeuralNetwork(config.cnn || {});
    this.observers = new Set();
    this.monitoringInterval = config.monitoringInterval || 30000;  // 30 seconds
    this.alertThreshold = config.alertThreshold || 0.7;
    this.history = [];
    this.historyLimit = config.historyLimit || 100;
    
    // Current system state
    this.currentState = {
      coherence: 1.0,
      violations: [],
      lastCheck: Date.now()
    };
    
    // Start monitoring if auto-start is enabled
    if (config.autoStart !== false) {
      this.startMonitoring();
    }
  }
  
  /**
   * Start continuous coherence monitoring
   * @returns {SystemCoherenceMonitor} This monitor for chaining
   */
  startMonitoring() {
    if (this._monitoringInterval) {
      clearInterval(this._monitoringInterval);
    }
    
    // Set up monitoring interval
    this._monitoringInterval = setInterval(() => {
      this.checkCoherence();
    }, this.monitoringInterval);
    
    return this;
  }
  
  /**
   * Stop continuous coherence monitoring
   * @returns {SystemCoherenceMonitor} This monitor for chaining
   */
  stopMonitoring() {
    if (this._monitoringInterval) {
      clearInterval(this._monitoringInterval);
      this._monitoringInterval = null;
    }
    
    return this;
  }
  
  /**
   * Register coherence observer
   * @param {function} observer - Observer function
   * @returns {SystemCoherenceMonitor} This monitor for chaining
   */
  addObserver(observer) {
    if (typeof observer === 'function') {
      this.observers.add(observer);
    }
    
    return this;
  }
  
  /**
   * Remove coherence observer
   * @param {function} observer - Observer to remove
   * @returns {SystemCoherenceMonitor} This monitor for chaining
   */
  removeObserver(observer) {
    this.observers.delete(observer);
    return this;
  }
  
  /**
   * Check system coherence
   * @returns {Promise<Object>} Coherence evaluation
   */
  async checkCoherence() {
    try {
      // Collect system state
      const state = await this._collectSystemState();
      
      // Evaluate coherence using CNN
      const evaluation = this.cnn.evaluate(state);
      
      // Update current state
      this.currentState = {
        coherence: evaluation.coherenceScore,
        violations: evaluation.violations,
        corrections: evaluation.corrections,
        lastCheck: Date.now()
      };
      
      // Add to history
      this.history.push({
        timestamp: Date.now(),
        coherence: evaluation.coherenceScore,
        violations: evaluation.violations.length
      });
      
      // Trim history if needed
      if (this.history.length > this.historyLimit) {
        this.history = this.history.slice(-this.historyLimit);
      }
      
      // Notify observers if coherence is below threshold
      if (evaluation.coherenceScore < this.alertThreshold) {
        this._notifyObservers(evaluation);
      }
      
      return evaluation;
    } catch (error) {
      console.error("Error checking coherence:", error);
      
      // Return default value on error
      return {
        coherenceScore: 0.5,
        violations: [{
          type: 'monitoringError',
          severity: 1.0,
          location: 'SystemCoherenceMonitor'
        }],
        corrections: [{
          violationType: 'monitoringError',
          action: 'Restart coherence monitoring system',
          priority: 1.0
        }]
      };
    }
  }
  
  /**
   * Collect system state for coherence evaluation
   * @private
   * @returns {Promise<Object>} System state
   */
  async _collectSystemState() {
    // In a real implementation, this would collect actual system state
    // For the reference implementation, we create a mock state
    
    // Generate random coherence value (mostly high for demonstration)
    const baseCoherence = 0.85 + (Math.random() * 0.15);
    const coherence = Math.random() < 0.1 ? baseCoherence * 0.7 : baseCoherence;
    
    // Random operation
    const operations = ['allocate', 'release', 'query', 'create', 'update', 'delete'];
    const operation = {
      name: operations[Math.floor(Math.random() * operations.length)],
      modifiesState: Math.random() < 0.3
    };
    
    // Random metric values
    const metricValues = Array(10).fill(0).map(() => Math.random());
    
    return {
      coherence,
      operation,
      metricValues,
      timestamp: Date.now()
    };
  }
  
  /**
   * Notify observers of coherence issues
   * @private
   * @param {Object} evaluation - Coherence evaluation
   */
  _notifyObservers(evaluation) {
    for (const observer of this.observers) {
      try {
        observer(evaluation);
      } catch (error) {
        console.error("Error in coherence observer:", error);
      }
    }
  }
  
  /**
   * Get coherence history
   * @param {Object} options - History options
   * @returns {Object[]} Coherence history
   */
  getHistory(options = {}) {
    let history = [...this.history];
    
    // Apply time filter
    if (options.startTime) {
      history = history.filter(entry => entry.timestamp >= options.startTime);
    }
    
    if (options.endTime) {
      history = history.filter(entry => entry.timestamp <= options.endTime);
    }
    
    // Apply limit
    if (options.limit && options.limit > 0) {
      history = history.slice(-options.limit);
    }
    
    return history;
  }
  
  /**
   * Get current coherence state
   * @returns {Object} Current coherence state
   */
  getCurrentState() {
    return { ...this.currentState };
  }
 }

 /**
 * InvariantRegistry
 * Registry of system invariants
 */
 class InvariantRegistry {
  /**
   * Create a new invariant registry
   */
  constructor() {
    this.invariants = new Map();
  }
  
  /**
   * Register an invariant
   * @param {string} name - Invariant name
   * @param {function} measure - Measurement function
   * @param {function} validate - Validation function
   * @param {Object} options - Invariant options
   * @returns {InvariantRegistry} This registry for chaining
   */
  register(name, measure, validate = null, options = {}) {
    const invariant = new Invariant(
      name,
      measure,
      validate,
      options.tolerance || 1e-10
    );
    
    this.invariants.set(name, invariant);
    return this;
  }
  
  /**
   * Get an invariant by name
   * @param {string} name - Invariant name
   * @returns {Invariant} Invariant object
   */
  get(name) {
    if (!this.invariants.has(name)) {
      throw new Error(`Invariant not found: ${name}`);
    }
    
    return this.invariants.get(name);
  }
  
  /**
   * Get all invariants
   * @returns {Invariant[]} All invariants
   */
  getAll() {
    return Array.from(this.invariants.values());
  }
  
  /**
   * Remove an invariant
   * @param {string} name - Invariant name
   * @returns {boolean} True if removed
   */
  remove(name) {
    return this.invariants.delete(name);
  }
  
  /**
   * Create a standard invariant registry
   * @static
   * @returns {InvariantRegistry} Standard registry
   */
  static createStandard() {
    const registry = new InvariantRegistry();
    
    // Register standard invariants
    
    // Norm preservation
    registry.register(
      'normPreservation',
      obj => {
        if (obj instanceof MultivectorRepresentation) {
          return obj.norm();
        } else if (Array.isArray(obj)) {
          return Math.sqrt(obj.reduce((sum, x) => sum + x * x, 0));
        } else {
          return 1.0;
        }
      }
    );
    
    // Type preservation
    registry.register(
      'typePreservation',
      obj => typeof obj,
      (before, after) => typeof before === typeof after
    );
    
    // Structure preservation
    registry.register(
      'structurePreservation',
      obj => {
        if (typeof obj !== 'object' || obj === null) {
          return null;
        }
        
        return Object.keys(obj).sort().join(',');
      },
      (before, after) => {
        const beforeStruct = registry.get('structurePreservation').measure(before);
        const afterStruct = registry.get('structurePreservation').measure(after);
        
        return beforeStruct === afterStruct;
      }
    );
    
    // ID preservation
    registry.register(
      'idPreservation',
      obj => {
        if (typeof obj !== 'object' || obj === null) {
          return null;
        }
        
        return obj.id || null;
      },
      (before, after) => {
        const beforeId = registry.get('idPreservation').measure(before);
        const afterId = registry.get('idPreservation').measure(after);
        
        return beforeId === afterId;
      }
    );
    
    return registry;
  }
 }

 // =============================================================================
 // 7. Security Model Implementation
 // =============================================================================

 /**
 * SecurityValidationEngine
 * Validates security properties using coherence principles
 */
 class SecurityValidationEngine {
  /**
   * Create a new security validation engine
   * @param {Base0} base0 - Base0 instance
   * @param {Object} config - Configuration options
   */
  constructor(base0, config = {}) {
    this.base0 = base0;
    this.depthCalculator = new ManifoldDepthCalculator();
    this.cnn = new CoherenceNeuralNetwork(config.cnn || {});
    this.threshold = config.threshold || 0.8;
    this.validators = new Map();
    
    // Initialize standard validators
    this._initializeValidators();
  }
  
  /**
   * Initialize standard validators
   * @private
   */
  _initializeValidators() {
    // Depth validator
    this.registerValidator('depth', {
      validate: (object, context) => {
        const depth = this.depthCalculator.calculate(object);
        
        // Get required depth from context
        const requiredDepth = context.requiredDepth || 1.0;
        
        return {
          valid: depth >= requiredDepth,
          score: Math.min(1.0, depth / requiredDepth),
          depth,
          requiredDepth
        };
      }
    });
    
    // Coherence validator
    this.registerValidator('coherence', {
      validate: (object, context) => {
        const embedding = this.base0.embeddingModel.embed(object);
        const coherence = CoherenceMetrics.normalizedCoherence(embedding);
        
        // Get required coherence from context
        const requiredCoherence = context.requiredCoherence || this.threshold;
        
        return {
          valid: coherence >= requiredCoherence,
          score: coherence,
          coherence,
          requiredCoherence
        };
      }
    });
    
    // Integrity validator
    this.registerValidator('integrity', {
      validate: (object, context) => {
        // Simple integrity check for reference implementation
        
        if (typeof object !== 'object' || object === null) {
          return {
            valid: false,
            score: 0.0,
            reason: 'Object is not an object'
          };
        }
        
        // Check for required fields
        const requiredFields = context.requiredFields || ['id'];
        const missingFields = requiredFields.filter(field => object[field] === undefined);
        
        if (missingFields.length > 0) {
          return {
            valid: false,
            score: 1 - missingFields.length / requiredFields.length,
            reason: `Missing required fields: ${missingFields.join(', ')}`
          };
        }
        
        // Check for relationships if specified
        if (context.relationships) {
          for (const [field, relatedField] of Object.entries(context.relationships)) {
            if (object[field] && !object[relatedField]) {
              return {
                valid: false,
                score: 0.5,
                reason: `Incomplete relationship: ${field} exists but ${relatedField} is missing`
              };
            }
          }
        }
        
        return {
          valid: true,
          score: 1.0
        };
      }
    });
  }
  
  /**
   * Register a security validator
   * @param {string} name - Validator name
   * @param {Object} validator - Validator object
   * @returns {SecurityValidationEngine} This engine for chaining
   */
  registerValidator(name, validator) {
    if (typeof validator.validate !== 'function') {
      throw new Error(`Validator must have a validate function`);
    }
    
    this.validators.set(name, validator);
    return this;
  }
  
  /**
   * Validate security of an object
   * @param {*} object - Object to validate
   * @param {Object} context - Validation context
   * @returns {Promise<Object>} Validation result
   */
  async validate(object, context = {}) {
    const results = {};
    let totalScore = 0;
    let validatorCount = 0;
    
    // Get validators to apply
    const validatorNames = context.validators || Array.from(this.validators.keys());
    
    // Apply each validator
    for (const name of validatorNames) {
      const validator = this.validators.get(name);
      if (!validator) continue;
      
      try {
        const result = await validator.validate(object, context);
        results[name] = result;
        
        // Add to total score
        totalScore += result.score;
        validatorCount++;
      } catch (error) {
        console.error(`Error in validator ${name}:`, error);
        results[name] = {
          valid: false,
          score: 0,
          error: error.message
        };
      }
    }
    
    // Calculate overall score
    const overallScore = validatorCount > 0 ? totalScore / validatorCount : 0;
    
    // Use CNN for additional validation
    const cnnEvaluation = this.cnn.evaluate({
      object,
      validationResults: results,
      context
    });
    
    return {
      valid: overallScore >= this.threshold,
      score: overallScore,
      results,
      cnnEvaluation
    };
  }
  
  /**
   * Validate security properties
   * @param {*} component - Component to validate
   * @param {Object[]} properties - Security properties
   * @returns {Promise<Object>} Validation result
   */
  async validateProperties(component, properties) {
    const results = {};
    let totalScore = 0;
    
    for (const property of properties) {
      // Formulate property as coherence constraint
      const constraint = this._propertyToConstraint(property);
      
      // Check coherence constraint
      const coherence = await this._evaluateConstraint(constraint, component);
      
      results[property.name] = {
        valid: coherence >= this.threshold,
        score: coherence
      };
      
      totalScore += coherence;
    }
    
    const overallScore = properties.length > 0 ? totalScore / properties.length : 1.0;
    
    return {
      valid: overallScore >= this.threshold,
      score: overallScore,
      results
    };
  }
  
  /**
   * Convert security property to constraint
   * @private
   * @param {Object} property - Security property
   * @returns {Object} Coherence constraint
   */
  _propertyToConstraint(property) {
    // Simple conversion for reference implementation
    
    return {
      name: property.name,
      validator: component => {
        // Convert property conditions to validator
        if (property.depth) {
          const depth = this.depthCalculator.calculate(component);
          return depth >= property.depth ? 1.0 : depth / property.depth;
        }
        
        if (property.type) {
          return typeof component === property.type ? 1.0 : 0.0;
        }
        
        if (property.hasProperty) {
          return component && component[property.hasProperty] !== undefined ? 1.0 : 0.0;
        }
        
        // Default coherence check
        const embedding = this.base0.embeddingModel.embed(component);
        return CoherenceMetrics.normalizedCoherence(embedding);
      }
    };
  }
  
  /**
   * Evaluate a constraint on a component
   * @private
   * @param {Object} constraint - Coherence constraint
   * @param {*} component - Component to evaluate
   * @returns {Promise<number>} Coherence value
   */
  async _evaluateConstraint(constraint, component) {
    try {
      return constraint.validator(component);
    } catch (error) {
      console.error(`Error evaluating constraint ${constraint.name}:`, error);
      return 0.0;
    }
  }
 }

 /**
 * SecurityBoundary
 * Defines a security boundary at a specific manifold depth
 */
 class SecurityBoundary {
  /**
   * Create a new security boundary
   * @param {number} depth - Boundary depth
   * @param {Object} options - Boundary options
   */
  constructor(depth, options = {}) {
    this.depth = depth;
    this.name = options.name || `boundary-${depth}`;
    this.description = options.description || 'Security boundary';
    this.depthCalculator = new ManifoldDepthCalculator();
    this.mda = new ManifoldDepthAttention();
    
    // Custom verifier function
    this.customVerifier = options.verifier || null;
  }
  
  /**
   * Verify if a component can cross the boundary
   * @param {*} component - Component to verify
   * @returns {Object} Verification result
   */
  verify(component) {
    // Calculate component depth
    const componentDepth = this.depthCalculator.calculate(component);
    
    // Check if component depth is sufficient
    const depthPermitted = componentDepth >= this.depth;
    
    // Use custom verifier if provided
    let customPermitted = true;
    if (this.customVerifier) {
      try {
        customPermitted = this.customVerifier(component);
      } catch (error) {
        console.error(`Error in custom verifier for boundary ${this.name}:`, error);
        customPermitted = false;
      }
    }
    
    // Only permitted if both checks pass
    const permitted = depthPermitted && customPermitted;
    
    // Calculate attention
    const attention = this.mda.calculateAttention(
      { depth: componentDepth },
      { depth: this.depth }
    );
    
    return {
      permitted,
      componentDepth,
      boundaryDepth: this.depth,
      attention,
      boundaryName: this.name
    };
  }
  
  /**
   * Get attention between component and boundary
   * @param {*} component - Component to check
   * @returns {number} Attention value
   */
  getAttention(component) {
    const componentDepth = this.depthCalculator.calculate(component);
    
    return this.mda.calculateAttention(
      { depth: componentDepth },
      { depth: this.depth }
    );
  }
 }

 /**
 * AccessControlMatrix
 * Enforces access control through a capability matrix
 */
 class AccessControlMatrix {
  /**
   * Create a new access control matrix
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.subjects = new Map();
    this.objects = new Map();
    this.capabilities = new Map();
    this.securityBoundaries = new Map();
    this.depthCalculator = new ManifoldDepthCalculator();
    
    // Default policies
    this.defaultAllow = config.defaultAllow === true;
    
    // Initialize from config if provided
    if (config.subjects) {
      for (const subject of config.subjects) {
        this.addSubject(subject.id, subject);
      }
    }
    
    if (config.objects) {
      for (const object of config.objects) {
        this.addObject(object.id, object);
      }
    }
    
    if (config.capabilities) {
      for (const [subjectId, objectId, permissions] of config.capabilities) {
        this.grant(subjectId, objectId, permissions);
      }
    }
    
    if (config.boundaries) {
      for (const boundary of config.boundaries) {
        this.addBoundary(boundary.name, boundary.depth, boundary);
      }
    }
  }
  
  /**
   * Add a subject to the matrix
   * @param {string} subjectId - Subject ID
   * @param {Object} attributes - Subject attributes
   * @returns {AccessControlMatrix} This matrix for chaining
   */
  addSubject(subjectId, attributes = {}) {
    this.subjects.set(subjectId, {
      id: subjectId,
      ...attributes,
      depth: attributes.depth || this.depthCalculator.calculate(attributes)
    });
    
    return this;
  }
  
  /**
   * Add an object to the matrix
   * @param {string} objectId - Object ID
   * @param {Object} attributes - Object attributes
   * @returns {AccessControlMatrix} This matrix for chaining
   */
  addObject(objectId, attributes = {}) {
    this.objects.set(objectId, {
      id: objectId,
      ...attributes,
      depth: attributes.depth || this.depthCalculator.calculate(attributes)
    });
    
    return this;
  }
  
  /**
   * Add a security boundary
   * @param {string} name - Boundary name
   * @param {number} depth - Boundary depth
   * @param {Object} options - Boundary options
   * @returns {AccessControlMatrix} This matrix for chaining
   */
  addBoundary(name, depth, options = {}) {
    this.securityBoundaries.set(name, new SecurityBoundary(depth, {
      ...options,
      name
    }));
    
    return this;
  }
  
  /**
   * Grant permissions to a subject
   * @param {string} subjectId - Subject ID
   * @param {string} objectId - Object ID
   * @param {string|string[]} permissions - Permissions to grant
   * @returns {AccessControlMatrix} This matrix for chaining
   */
  grant(subjectId, objectId, permissions) {
    const key = `${subjectId}|${objectId}`;
    
    if (!this.capabilities.has(key)) {
      this.capabilities.set(key, new Set());
    }
    
    const caps = this.capabilities.get(key);
    
    if (Array.isArray(permissions)) {
      for (const perm of permissions) {
        caps.add(perm);
      }
    } else {
      caps.add(permissions);
    }
    
    return this;
  }
  
  /**
   * Revoke permissions from a subject
   * @param {string} subjectId - Subject ID
   * @param {string} objectId - Object ID
   * @param {string|string[]} permissions - Permissions to revoke
   * @returns {AccessControlMatrix} This matrix for chaining
   */
  revoke(subjectId, objectId, permissions) {
    const key = `${subjectId}|${objectId}`;
    
    if (!this.capabilities.has(key)) {
      return this;
    }
    
    const caps = this.capabilities.get(key);
    
    if (Array.isArray(permissions)) {
      for (const perm of permissions) {
        caps.delete(perm);
      }
    } else {
      caps.delete(permissions);
    }
    
    // Remove empty capability set
    if (caps.size === 0) {
      this.capabilities.delete(key);
    }
    
    return this;
  }
  
  /**
   * Check if a subject has a permission on an object
   * @param {string} subjectId - Subject ID
   * @param {string} objectId - Object ID
   * @param {string} permission - Permission to check
   * @returns {Object} Check result
   */
  check(subjectId, objectId, permission) {
    // Check if subject and object exist
    const subject = this.subjects.get(subjectId);
    const object = this.objects.get(objectId);
    
    if (!subject || !object) {
      return {
        allowed: false,
        reason: !subject ? `Subject not found: ${subjectId}` : `Object not found: ${objectId}`
      };
    }
    
    // Check capability
    const key = `${subjectId}|${objectId}`;
    const caps = this.capabilities.get(key);
    
    if (caps && (caps.has(permission) || caps.has('*'))) {
      // Direct capability granted
      return {
        allowed: true,
        reason: 'Explicit permission',
        method: 'capability'
      };
    }
    
    // Check depth-based access
    if (subject.depth >= object.depth) {
      // Depth allows access
      return {
        allowed: true,
        reason: 'Depth-based permission',
        method: 'depth',
        subjectDepth: subject.depth,
        objectDepth: object.depth
      };
    }
    
    // Check boundary crossing
    for (const [name, boundary] of this.securityBoundaries.entries()) {
      // Check if object is protected by this boundary
      if (object.depth <= boundary.depth && subject.depth < boundary.depth) {
        return {
          allowed: false,
          reason: `Cannot cross security boundary: ${name}`,
          method: 'boundary',
          boundary: name
        };
      }
    }
    
    // Default policy
    return {
      allowed: this.defaultAllow,
      reason: this.defaultAllow ? 'Default allow policy' : 'Default deny policy',
      method: 'default'
    };
  }
  
  /**
   * Get all permissions for a subject on an object
   * @param {string} subjectId - Subject ID
   * @param {string} objectId - Object ID
   * @returns {string[]} Permissions
   */
  getPermissions(subjectId, objectId) {
    const key = `${subjectId}|${objectId}`;
    const caps = this.capabilities.get(key);
    
    if (!caps) return [];
    
    return Array.from(caps);
  }
  
  /**
   * Get all subjects with access to an object
   * @param {string} objectId - Object ID
   * @returns {Object[]} Subjects with access
   */
  getSubjectsWithAccess(objectId) {
    const results = [];
    
    for (const [subjectId, subject] of this.subjects.entries()) {
      // Check capability-based access
      const key = `${subjectId}|${objectId}`;
      const caps = this.capabilities.get(key);
      
      if (caps && caps.size > 0) {
        results.push({
          subject,
          permissions: Array.from(caps),
          method: 'capability'
        });
        continue;
      }
      
      // Check depth-based access
      const object = this.objects.get(objectId);
      if (object && subject.depth >= object.depth) {
        results.push({
          subject,
          permissions: ['*'],
          method: 'depth'
        });
        continue;
      }
    }
    
    return results;
  }
 }

 // =============================================================================
 // 8. Advanced Usage Examples
 // =============================================================================

 /**
 * Advanced examples demonstrating UORS capabilities
 */
 async function advancedExamples() {
  console.log("=== Advanced UORS Examples ===");
  
  // Create UORS instance
  const uors = createUORS({
    languages: ['en', 'es', 'fr', 'de', 'zh'],
    coherenceThreshold: 0.75
  });
  
  // Example 1: Cross-linguistic semantic addressing
  console.log("\n--- Example 1: Cross-linguistic semantics ---");
  
  // Define concepts in multiple languages
  const concepts = {
    en: {
      "database": "A structured collection of data stored and accessed electronically",
      "server": "A computer program or device that provides functionality for other programs or devices",
      "network": "A group of interconnected computers and devices that can communicate with each other"
    },
    es: {
      "base de datos": "Una colección estructurada de datos almacenados y accedidos electrónicamente",
      "servidor": "Un programa o dispositivo informático que proporciona funcionalidad para otros programas o dispositivos",
      "red": "Un grupo de computadoras y dispositivos interconectados que pueden comunicarse entre sí"
    },
    fr: {
      "base de données": "Une collection structurée de données stockées et consultées par voie électronique",
      "serveur": "Un programme ou appareil informatique qui fournit des fonctionnalités à d'autres programmes ou appareils",
      "réseau": "Un groupe d'ordinateurs et de périphériques interconnectés qui peuvent communiquer entre eux"
    }
  };
  
  // Register concept mappings
  for (const concept of ["database", "server", "network"]) {
    const mapping = {
      domain: "computing",
      concepts: {}
    };
    
    for (const [lang, conceptMap] of Object.entries(concepts)) {
      const conceptKey = lang === 'en' ? concept : Object.keys(conceptMap)[Object.keys(concepts.en).indexOf(concept)];
      mapping.concepts[lang] = conceptKey;
    }
    
    await uors.registerConceptMapping(mapping);
    console.log(`Registered mapping for '${concept}'`);
  }
  
  // Find equivalent concepts
  const dbEquivalent = await uors.findEquivalentConcept("database", "en", "fr");
  console.log(`Equivalent of 'database' in French: ${dbEquivalent.concept}`);
  
  const serverEquivalent = await uors.findEquivalentConcept("servidor", "es", "en");
  console.log(`Equivalent of 'servidor' in English: ${serverEquivalent.concept}`);
  
  // Example 2: Manifold relations with depth security
  console.log("\n--- Example 2: Manifold relations with depth security ---");
  
  // Create objects at different depths
  const adminConfig = await uors.store({
    name: "admin-security-config",
    accessLevel: "high",
    permissions: {
      read: true,
      write: true,
      execute: true,
      admin: true
    }
  }, {
    description: "Administrative security configuration with elevated privileges",
    namespace: "system.security",
    context: "admin"
  });
  
  const userConfig = await uors.store({
    name: "user-security-config",
    accessLevel: "medium",
    permissions: {
      read: true,
      write: true,
      execute: false,
      admin: false
    }
  }, {
    description: "User-level security configuration with standard privileges",
    namespace: "system.security",
    context: "user"
  });
  
  const guestConfig = await uors.store({
    name: "guest-security-config",
    accessLevel: "low",
    permissions: {
      read: true,
      write: false,
      execute: false,
      admin: false
    }
  }, {
    description: "Guest-level security configuration with minimal privileges",
    namespace: "system.security",
    context: "guest"
  });
  
  console.log("Created configuration objects at different depths");
  
  // Try to create relations
  try {
    // Admin can refer to user (higher depth to lower depth)
    const adminToUser = await uors.createRelation(
      adminConfig.id,
      userConfig.id,
      "manages",
      { description: "Admin manages user configuration" }
    );
    console.log("Admin to user relation created successfully");
    
    // User can refer to guest (higher depth to lower depth)
    const userToGuest = await uors.createRelation(
      userConfig.id,
      guestConfig.id,
      "manages",
      { description: "User manages guest configuration" }
    );
    console.log("User to guest relation created successfully");
    
    // Guest cannot refer to user (lower depth to higher depth)
    try {
      const guestToUser = await uors.createRelation(
        guestConfig.id,
        userConfig.id,
        "manages",
        { description: "Guest tries to manage user configuration" }
      );
      console.log("Guest to user relation created (unexpected)");
    } catch (error) {
      console.log("Guest to user relation failed (expected):", error.message);
    }
  } catch (error) {
    console.error("Error creating relations:", error);
  }
  
  // Example 3: Invariant-preserving transformations
  console.log("\n--- Example 3: Invariant-preserving transformations ---");
  
  // Create invariant registry
  const registry = InvariantRegistry.createStandard();
  
  // Create a sample object
  const original = {
    id: "test-object",
    name: "Test Object",
    data: [1, 2, 3, 4, 5],
    metadata: {
      created: Date.now(),
      version: "1.0.0"
    }
  };
  
  console.log("Original object:", original);
  
  // Create a valid transformation
  const validTransformation = InvariantPreservingTransformation.create(
    obj => {
      // Valid transformation: preserves ID and structure
      return {
        ...obj,
        data: obj.data.map(x => x * 2),  // Transform data
        metadata: {
          ...obj.metadata,
          updated: Date.now()  // Add updated timestamp
        }
      };
    },
    [registry.get('idPreservation'), registry.get('structurePreservation')]
  );
  
  // Apply valid transformation
  try {
    const transformed = validTransformation.transform(original);
    console.log("Valid transformation applied:", transformed);
  } catch (error) {
    console.error("Valid transformation failed (unexpected):", error);
  }
  
  // Create an invalid transformation
  const invalidTransformation = InvariantPreservingTransformation.create(
    obj => {
      // Invalid transformation: changes ID
      return {
        ...obj,
        id: "modified-id",  // Change ID (violates idPreservation)
        data: obj.data.map(x => x * 2)
      };
    },
    [registry.get('idPreservation'), registry.get('structurePreservation')]
  );
  
  // Apply invalid transformation
  try {
    const transformed = invalidTransformation.transform(original);
    console.log("Invalid transformation applied (unexpected):", transformed);
  } catch (error) {
    console.log("Invalid transformation failed (expected):", error.message);
  }
  
  // Example 4: Security boundaries and access control
  console.log("\n--- Example 4: Security boundaries and access control ---");
  
  // Create access control matrix
  const acm = new AccessControlMatrix({
    defaultAllow: false  // Default deny policy
  });
  
  // Add subjects (users)
  acm.addSubject("admin", { role: "admin", depth: 5.0 });
  acm.addSubject("powerUser", { role: "power-user", depth: 4.0 });
  acm.addSubject("regularUser", { role: "user", depth: 3.0 });
  acm.addSubject("guest", { role: "guest", depth: 1.0 });
  
  // Add objects (resources)
  acm.addObject("systemConfig", { type: "configuration", depth: 4.5 });
  acm.addObject("userDatabase", { type: "database", depth: 3.5 });
  acm.addObject("publicContent", { type: "content", depth: 1.0 });
  
  // Add security boundaries
  acm.addBoundary("systemBoundary", 4.0, { description: "System level security boundary" });
  acm.addBoundary("userBoundary", 2.0, { description: "User level security boundary" });
  
  // Grant specific permissions
  acm.grant("regularUser", "userDatabase", ["read", "write"]);
  acm.grant("guest", "publicContent", "read");
  
  // Check permissions
  const checks = [
    { subject: "admin", object: "systemConfig", permission: "write" },
    { subject: "powerUser", object: "systemConfig", permission: "read" },
    { subject: "regularUser", object: "systemConfig", permission: "read" },
    { subject: "regularUser", object: "userDatabase", permission: "write" },
    { subject: "guest", object: "userDatabase", permission: "read" },
    { subject: "guest", object: "publicContent", permission: "write" }
  ];
  
  for (const check of checks) {
    const result = acm.check(check.subject, check.object, check.permission);
    console.log(
      `${check.subject} -> ${check.permission} -> ${check.object}: ` +
      `${result.allowed ? 'ALLOWED' : 'DENIED'} (${result.reason})`
    );
  }
  
  // Example 5: Coherence monitoring
  console.log("\n--- Example 5: Coherence monitoring ---");
  
  // Create coherence monitor
  const monitor = new SystemCoherenceMonitor({
    monitoringInterval: 1000,  // 1 second for demonstration
    alertThreshold: 0.7,
    autoStart: false  // Don't start automatically
  });
  
  // Add observer
  monitor.addObserver(evaluation => {
    console.log(`Coherence alert: ${evaluation.coherenceScore.toFixed(2)}`);
    if (evaluation.violations.length > 0) {
      console.log(`  Violations detected: ${evaluation.violations.length}`);
      for (const violation of evaluation.violations) {
        console.log(`  - ${violation.type} (severity: ${violation.severity.toFixed(2)}) at ${violation.location}`);
      }
    }
  });
  
  // Run a manual coherence check
  const coherenceResult = await monitor.checkCoherence();
  console.log("Coherence check result:", coherenceResult.coherenceScore.toFixed(2));
  
  return {
    concepts,
    dbEquivalent,
    serverEquivalent,
    adminConfig,
    userConfig,
    guestConfig,
    coherenceResult
  };
 }

 /**
 * Example of a complete workflow using UORS
 */
 async function completeWorkflowExample() {
  console.log("=== Complete UORS Workflow Example ===");
  
  // Create UORS instance
  const uors = createUORS({
    languages: ['en', 'es', 'fr'],
    coherenceThreshold: 0.75
  });
  
  // Step 1: Create database configuration
  console.log("\nStep 1: Creating database configuration");
  const dbConfig = await uors.store({
    name: "production-database",
    host: "db.example.com",
    port: 5432,
    username: "app_user",
    password: "********",
    database: "customer_data",
    options: {
      poolSize: 10,
      ssl: true,
      timeout: 30000
    }
  }, {
    namespace: "config.database",
    language: "en",
    context: "production",
    description: "Production database configuration for customer data"
  });
  
  console.log(`Database configuration stored with ID: ${dbConfig.id}`);
  console.log(`Address coherence: ${dbConfig.address.coherence.toFixed(2)}`);
  
  // Step 2: Create application configuration
  console.log("\nStep 2: Creating application configuration");
  const appConfig = await uors.store({
    name: "customer-portal",
    version: "2.5.0",
    environment: "production",
    features: {
      userManagement: true,
      reporting: true,
      billing: true,
      analytics: true
    },
    scaling: {
      minInstances: 3,
      maxInstances: 10,
      targetCpuUtilization: 70
    },
    security: {
      authentication: "oauth2",
      authorization: "rbac",
      dataEncryption: true
    }
  }, {
    namespace: "config.application",
    language: "en",
    context: "production",
    description: "Production configuration for customer portal application"
  });
  
  console.log(`Application configuration stored with ID: ${appConfig.id}`);
  
  // Step 3: Create relation between configurations
  console.log("\nStep 3: Creating relation between configurations");
  const relation = await uors.createRelation(
    appConfig.id,
    dbConfig.id,
    "uses",
    {
      description: "Application uses this database for customer data",
      critical: true,
      created: Date.now()
    }
  );
  
  console.log(`Relation created: ${relation.id}`);
  
  // Step 4: Create Spanish translation of configurations
  console.log("\nStep 4: Creating Spanish translations");
  
  // Register concept mappings for database terms
  await uors.registerConceptMapping({
    domain: "database",
    concepts: {
      "en": "database configuration",
      "es": "configuración de base de datos",
      "fr": "configuration de base de données"
    }
  });
  
  await uors.registerConceptMapping({
    domain: "application",
    concepts: {
      "en": "application configuration",
      "es": "configuración de aplicación",
      "fr": "configuration d'application"
    }
  });
  
  // Create Spanish version of database config
  const dbConfigEs = await uors.store({
    name: "base-de-datos-produccion",
    host: "db.example.com",
    port: 5432,
    username: "app_user",
    password: "********",
    database: "customer_data",
    options: {
      poolSize: 10,
      ssl: true,
      timeout: 30000
    }
  }, {
    namespace: "config.database",
    language: "es",
    context: "produccion",
    description: "Configuración de base de datos de producción para datos de clientes"
  });
  
  console.log(`Spanish database configuration stored with ID: ${dbConfigEs.id}`);
  
  // Step 5: Find semantically similar configurations
  console.log("\nStep 5: Finding semantically similar configurations");
  const similarConfigs = await uors.findSimilarObjects(dbConfig.id, {
    threshold: 0.7,
    limit: 3
  });
  
  console.log(`Found ${similarConfigs.length} similar configurations:`);
  for (const similar of similarConfigs) {
    console.log(
      `  - ${similar.address.name.name} (${similar.address.name.namespace}): ` +
      `${similar.similarity.toFixed(2)} similarity`
    );
  }
  
  // Step 6: Create and apply invariant-preserving transformation
  console.log("\nStep 6: Creating and applying invariant-preserving transformation");
  
  // Create invariant registry
  const registry = InvariantRegistry.createStandard();
  
  // Create custom invariant for database configuration
  registry.register(
    'databaseConnectivity',
    config => {
      // Measure contains key connection parameters
      if (!config || typeof config !== 'object') return false;
      
      const hasHost = config.host !== undefined;
      const hasPort = config.port !== undefined;
      const hasDatabase = config.database !== undefined;
      
      return hasHost && hasPort && hasDatabase;
    },
    (before, after) => {
      // Connection parameters must be preserved
      if (!before || !after) return false;
      
      return (
        before.host === after.host &&
        before.port === after.port &&
        before.database === after.database
      );
    }
  );
  
  // Create transformation to update database configuration
  const dbTransform = InvariantPreservingTransformation.create(
    config => {
      // Update configuration while preserving invariants
      return {
        ...config,
        options: {
          ...config.options,
          poolSize: 20,  // Double pool size
          timeout: 60000  // Double timeout
        },
        lastUpdated: Date.now()
      };
    },
    [
      registry.get('databaseConnectivity'),
      registry.get('idPreservation')
    ]
  );
  
  // Get original configuration
  const originalConfig = (await uors.retrieve(dbConfig.id)).object;
  console.log("Original configuration:", originalConfig.options);
  
  // Apply transformation
  const transformedConfig = dbTransform.transform(originalConfig);
  console.log("Transformed configuration:", transformedConfig.options);
  
  // Step 7: Store updated configuration
  console.log("\nStep 7: Storing updated configuration");
  const updatedConfig = await uors.store(transformedConfig, {
    namespace: "config.database",
    language: "en",
    context: "production",
    description: "Updated production database configuration with optimized settings"
  });
  
  console.log(`Updated configuration stored with ID: ${updatedConfig.id}`);
  
  // Step 8: Set up security validation
  console.log("\nStep 8: Setting up security validation");
  
  const securityEngine = new SecurityValidationEngine(uors.base0, {
    threshold: 0.8
  });
  
  // Add custom validator
  securityEngine.registerValidator('configSecurity', {
    validate: (config, context) => {
      // Check security-specific properties
      if (!config || typeof config !== 'object') {
        return {
          valid: false,
          score: 0.0,
          reason: 'Not an object'
        };
      }
      
      // For database config, check for encryption
      if (config.options && config.options.ssl === true) {
        return {
          valid: true,
          score: 1.0,
          reason: 'SSL enabled'
        };
      }
      
      // For application config, check for authentication
      if (config.security && config.security.authentication) {
        return {
          valid: true,
          score: 1.0,
          reason: 'Authentication configured'
        };
      }
      
      return {
        valid: false,
        score: 0.5,
        reason: 'Missing security features'
      };
    }
  });
  
  // Validate database config
  const dbValidation = await securityEngine.validate(transformedConfig, {
    validators: ['depth', 'coherence', 'configSecurity'],
    requiredDepth: 2.0
  });
  
  console.log("Database config validation:", 
    dbValidation.valid ? "PASSED" : "FAILED",
    `(Score: ${dbValidation.score.toFixed(2)})`
  );
  
  for (const [name, result] of Object.entries(dbValidation.results)) {
    console.log(`  - ${name}: ${result.valid ? "Valid" : "Invalid"} (${result.score.toFixed(2)})`);
  }
  
  // Validate application config
  const appObject = (await uors.retrieve(appConfig.id)).object;
  const appValidation = await securityEngine.validate(appObject, {
    validators: ['depth', 'coherence', 'configSecurity'],
    requiredDepth: 2.0
  });
  
  console.log("Application config validation:", 
    appValidation.valid ? "PASSED" : "FAILED",
    `(Score: ${appValidation.score.toFixed(2)})`
  );
  
  return {
    dbConfig,
    appConfig,
    relation,
    dbConfigEs,
    similarConfigs,
    transformedConfig,
    updatedConfig,
    dbValidation,
    appValidation
  };
 }

 // =============================================================================
 // 9. Export UORS for use in other environments
 // =============================================================================

 // Export as global in browser environments
 if (typeof window !== 'undefined') {
  window.UORS = {
    createUORS,
    UORS,
    Base0,
    Base1,
    Base2,
    Base3,
    MultivectorRepresentation,
    CliffordAlgebra,
    CoherenceMetrics,
    exampleUsage,
    advancedExamples,
    completeWorkflowExample
  };
 }

 // Export for Node.js environments
 if (typeof module !== 'undefined' && module.exports) {
  module.exports = {
    createUORS,
    UORS,
    Base0,
    Base1,
    Base2,
    Base3,
    MultivectorRepresentation,
    CliffordAlgebra,
    CoherenceMetrics,
    UniversalAddressingModel,
    ObjectManifold,
    CoherenceAwareStorage,
    CrossLinguisticSemanticEngine,
    CoherenceNeuralNetwork,
    InvariantPreservingTransformation,
    Invariant,
    SystemCoherenceMonitor,
    InvariantRegistry,
    SecurityValidationEngine,
    SecurityBoundary,
    AccessControlMatrix,
    exampleUsage,
    advancedExamples,
    completeWorkflowExample
  };
 }


 /**
 * Coherence-Aware Storage
 * Validates coherence for all storage operations
 */
 class CoherenceAwareStorage {
  /**
   * Create a new coherence-aware storage
   * @param {Base0} base0 - Base0 instance
   */
  constructor(base0) {
    this.base0 = base0;
    this.stores = new Map();
    this.coherenceValidators = new Map();
    this.invariants = new Map();
    this.coherenceThreshold = 0.8;
    
    // Initialize standard stores
    this._initializeStores();
  }
  
  /**
   * Initialize standard stores
   * @private
   */
  _initializeStores() {
    // Object store
    this.registerStore('objects', new ObjectStore());
    
    // Set coherence validator for objects
    this.registerCoherenceValidator('objects', async (key, value) => {
      // Basic coherence check
      if (!value) return 0;
      
      // Use Base0 embedding model for coherence
      const embedding = this.base0.embeddingModel.embed(value);
      return CoherenceMetrics.normalizedCoherence(embedding);
    });
    
    // Register invariants for objects
    this.registerInvariant('objects', {
      name: 'hasId',
      validate: value => !!value && !!value.id
    });
    
    // Metadata store
    this.registerStore('metadata', new MetadataStore());
    
    // Addresses store
    this.registerStore('addresses', new AddressStore());
    
    // Relations store
    this.registerStore('relations', new RelationStore());
  }
  
  /**
   * Register a store
   * @param {string} id - Store ID
   * @param {Object} store - Store object
   * @returns {CoherenceAwareStorage} This storage for chaining
   */
  registerStore(id, store) {
    if (!store.get || !store.put || !store.delete) {
      throw new Error(`Store must implement get, put, and delete methods`);
    }
    
    this.stores.set(id, store);
    return this;
  }
  
  /**
   * Register a coherence validator
   * @param {string} storeId - Store ID
   * @param {function} validator - Validator function
   * @returns {CoherenceAwareStorage} This storage for chaining
   */
  registerCoherenceValidator(storeId, validator) {
    this.coherenceValidators.set(storeId, validator);
    return this;
  }
  
  /**
   * Register an invariant
   * @param {string} storeId - Store ID
   * @param {Object} invariant - Invariant object
   * @returns {CoherenceAwareStorage} This storage for chaining
   */
  registerInvariant(storeId, invariant) {
    if (!this.invariants.has(storeId)) {
      this.invariants.set(storeId, []);
    }
    
    this.invariants.get(storeId).push(invariant);
    return this;
  }
  
  /**
   * Store an object with coherence validation
   * @param {string} storeId - Store ID
   * @param {string} key - Storage key
   * @param {*} value - Value to store
   * @param {Object} options - Storage options
   * @returns {Promise<Object>} Storage result
   */
  async store(storeId, key, value, options = {}) {
    // Get store
    const store = this.getStore(storeId);
    
    // Get coherence validator
    const validator = this.coherenceValidators.get(storeId);
    
    if (validator) {
      // Validate coherence
      const coherence = await validator(key, value);
      
      if (coherence < (options.threshold || this.coherenceThreshold)) {
        throw new Error(
          `Object failed coherence validation for store ${storeId}: ${coherence}`
        );
      }
    }
    
    // Validate invariants
    const storeInvariants = this.invariants.get(storeId) || [];
    for (const invariant of storeInvariants) {
      if (!invariant.validate(value)) {
        throw new Error(
          `Object violated invariant ${invariant.name} for store ${storeId}`
        );
      }
    }
    
    // Store the value
    return store.put(key, value, options);
  }
  
  /**
   * Retrieve an object
   * @param {string} storeId - Store ID
   * @param {string} key - Storage key
   * @param {Object} options - Retrieval options
   * @returns {Promise<*>} Retrieved value
   */
  async retrieve(storeId, key, options = {}) {
    // Get store
    const store = this.getStore(storeId);
    
    // Retrieve value
    const value = await store.get(key);
    
    // Apply transformations if needed
    if (options.transform) {
      return this._applyTransform(value, options.transform);
    }
    
    return value;
  }
  
  /**
   * Delete an object
   * @param {string} storeId - Store ID
   * @param {string} key - Storage key
   * @param {Object} options - Deletion options
   * @returns {Promise<boolean>} True if deleted
   */
  async delete(storeId, key, options = {}) {
    // Get store
    const store = this.getStore(storeId);
    
    // Delete value
    return store.delete(key, options);
  }
  
  /**
   * Apply a transform to a value
   * @private
   * @param {*} value - Value to transform
   * @param {string|function} transform - Transform name or function
   * @returns {*} Transformed value
   */
  _applyTransform(value, transform) {
    if (typeof transform === 'function') {
      return transform(value);
    }
    
    // Handle standard transforms
    switch (transform) {
      case 'toJSON':
        return JSON.stringify(value);
        
      case 'fromJSON':
        return typeof value === 'string' ? JSON.parse(value) : value;
        
      case 'compress':
        // Simple placeholder for compression
        return value;
        
      case 'decompress':
        // Simple placeholder for decompression
        return value;
        
      default:
        return value;
    }
  }
  
  /**
   * Get a store by ID
   * @param {string} storeId - Store ID
   * @returns {Object} Store object
   */
  getStore(storeId) {
    const store = this.stores.get(storeId);
    if (!store) {
      throw new Error(`Store not found: ${storeId}`);
    }
    
    return store;
  }
 }

 /**
 * Object Store
 * Stores arbitrary objects
 */
 class ObjectStore {
  /**
   * Create a new object store
   */
  constructor() {
    this.objects = new Map();
  }
  
  /**
   * Store an object
   * @param {string} key - Object key
   * @param {*} value - Object value
   * @param {Object} options - Storage options
   * @returns {Promise<Object>} Storage result
   */
  async put(key, value, options = {}) {
    this.objects.set(key, {
      value,
      metadata: {
        stored: Date.now(),
        version: options.version || 1
      }
    });
    
    return {
      key,
      stored: true,
      timestamp: Date.now()
    };
  }
  
  /**
   * Retrieve an object
   * @param {string} key - Object key
   * @returns {Promise<*>} Retrieved object
   */
  async get(key) {
    const entry = this.objects.get(key);
    if (!entry) return null;
    
    return entry.value;
  }
  
  /**
   * Delete an object
   * @param {string} key - Object key
   * @returns {Promise<boolean>} True if deleted
   */
  async delete(key) {
    return this.objects.delete(key);
  }
  
  /**
   * List objects matching a prefix
   * @param {string} prefix - Key prefix
   * @returns {Promise<string[]>} Matching keys
   */
  async list(prefix) {
    const keys = [];
    
    for (const key of this.objects.keys()) {
      if (key.startsWith(prefix)) {
        keys.push(key);
      }
    }
    
    return keys;
  }
 }

 /**
 * Metadata Store
 * Stores metadata for objects
 */
 class MetadataStore {
  /**
   * Create a new metadata store
   */
  constructor() {
    this.metadata = new Map();
  }
  
  /**
   * Store metadata
   * @param {string} key - Metadata key
   * @param {Object} value - Metadata value
   * @returns {Promise<Object>} Storage result
   */
  async put(key, value) {
    this.metadata.set(key, {
      ...value,
      updated: Date.now()
    });
    
    return {
      key,
      stored: true,
      timestamp: Date.now()
    };
  }
  
  /**
   * Retrieve metadata
   * @param {string} key - Metadata key
   * @returns {Promise<Object>} Retrieved metadata
   */
  async get(key) {
    return this.metadata.get(key) || null;
  }
  
  /**
   * Delete metadata
   * @param {string} key - Metadata key
   * @returns {Promise<boolean>} True if deleted
   */
  async delete(key) {
    return this.metadata.delete(key);
  }
  
  /**
   * List metadata matching a prefix
   * @param {string} prefix - Key prefix
   * @returns {Promise<string[]>} Matching keys
   */
  async list(prefix) {
    const keys = [];
    
    for (const key of this.metadata.keys()) {
      if (key.startsWith(prefix)) {
        keys.push(key);
      }
    }
    
    return keys;
  }
 }

 /**
 * Address Store
 * Stores object addresses
 */
 class AddressStore {
  /**
   * Create a new address store
   */
  constructor() {
    this.addresses = new Map();
    this.nameIndex = new Map();
    this.contentIndex = new Map();
    this.semanticIndex = new Map();
    this.attributeIndex = new Map();
  }
  
  /**
   * Store an address
   * @param {string} key - Address key
   * @param {Object} address - Address object
   * @returns {Promise<Object>} Storage result
   */
  async put(key, address) {
    // Store main address
    this.addresses.set(key, address);
    
    // Update indexes
    if (address.name && address.name.id) {
      this.nameIndex.set(address.name.id, key);
    }
    
    if (address.content && address.content.id) {
      this.contentIndex.set(address.content.id, key);
    }
    
    if (address.semantic && address.semantic.id) {
      this.semanticIndex.set(address.semantic.id, key);
    }
    
    if (address.attribute && address.attribute.id) {
      this.attributeIndex.set(address.attribute.id, key);
    }
    
    return {
      key,
      stored: true,
      timestamp: Date.now()
    };
  }
  
  /**
   * Retrieve an address
   * @param {string} key - Address key
   * @returns {Promise<Object>} Retrieved address
   */
  async get(key) {
    return this.addresses.get(key) || null;
  }
  
  /**
   * Find address by any component
   * @param {string} addressId - Component address ID
   * @returns {Promise<Object>} Found address
   */
  async find(addressId) {
    // Try each index
    let key = null;
    
    if (addressId.startsWith('name://')) {
      key = this.nameIndex.get(addressId);
    } else if (addressId.startsWith('content://')) {
      key = this.contentIndex.get(addressId);
    } else if (addressId.startsWith('semantic://')) {
      key = this.semanticIndex.get(addressId);
    } else if (addressId.startsWith('attr://')) {
      key = this.attributeIndex.get(addressId);
    } else {
      // Try direct lookup
      key = addressId;
    }
    
    if (!key) return null;
    
    return this.addresses.get(key);
  }
  
  /**
   * Delete an address
   * @param {string} key - Address key
   * @returns {Promise<boolean>} True if deleted
   */
  async delete(key) {
    const address = this.addresses.get(key);
    if (!address) return false;
    
    // Remove from indexes
    if (address.name && address.name.id) {
      this.nameIndex.delete(address.name.id);
    }
    
    if (address.content && address.content.id) {
      this.contentIndex.delete(address.content.id);
    }
    
    if (address.semantic && address.semantic.id) {
      this.semanticIndex.delete(address.semantic.id);
    }
    
    if (address.attribute && address.attribute.id) {
      this.attributeIndex.delete(address.attribute.id);
    }
    
    // Remove main address
    return this.addresses.delete(key);
  }
 }

 /**
 * Relation Store
 * Stores relations between objects
 */
 class RelationStore {
  /**
   * Create a new relation store
   */
  constructor() {
    this.relations = new Map();
    this.sourceIndex = new Map();
    this.targetIndex = new Map();
    this.typeIndex = new Map();
  }
  
  /**
   * Store a relation
   * @param {string} key - Relation key
   * @param {Object} relation - Relation object
   * @returns {Promise<Object>} Storage result
   */
  async put(key, relation) {
    // Store main relation
    this.relations.set(key, relation);
    
    // Update source index
    if (!this.sourceIndex.has(relation.sourceId)) {
      this.sourceIndex.set(relation.sourceId, new Set());
    }
    this.sourceIndex.get(relation.sourceId).add(key);
    
    // Update target index
    if (!this.targetIndex.has(relation.targetId)) {
      this.targetIndex.set(relation.targetId, new Set());
    }
    this.targetIndex.get(relation.targetId).add(key);
    
    // Update type index
    if (!this.typeIndex.has(relation.type)) {
      this.typeIndex.set(relation.type, new Set());
    }
    this.typeIndex.get(relation.type).add(key);
    
    return {
      key,
      stored: true,
      timestamp: Date.now()
    };
  }
  
  /**
   * Retrieve a relation
   * @param {string} key - Relation key
   * @returns {Promise<Object>} Retrieved relation
   */
  async get(key) {
    return this.relations.get(key) || null;
  }
  
  /**
   * Find relations by source, target, or type
   * @param {Object} query - Query object
   * @returns {Promise<Object[]>} Found relations
   */
  async find(query) {
    const candidates = new Set();
    let initialized = false;
    
    // Apply source filter
    if (query.sourceId) {
      const sourceRelations = this.sourceIndex.get(query.sourceId);
      if (!sourceRelations) return [];
      
      if (!initialized) {
        for (const key of sourceRelations) {
          candidates.add(key);
        }
        initialized = true;
      } else {
        // Intersect with current candidates
        for (const key of candidates) {
          if (!sourceRelations.has(key)) {
            candidates.delete(key);
          }
        }
      }
    }
    
    // Apply target filter
    if (query.targetId) {
      const targetRelations = this.targetIndex.get(query.targetId);
      if (!targetRelations) return [];
      
      if (!initialized) {
        for (const key of targetRelations) {
          candidates.add(key);
        }
        initialized = true;
      } else {
        // Intersect with current candidates
        for (const key of candidates) {
          if (!targetRelations.has(key)) {
            candidates.delete(key);
          }
        }
      }
    }
    
    // Apply type filter
    if (query.type) {
      const typeRelations = this.typeIndex.get(query.type);
      if (!typeRelations) return [];
      
      if (!initialized) {
        for (const key of typeRelations) {
          candidates.add(key);
        }
        initialized = true;
      } else {
        // Intersect with current candidates
        for (const key of candidates) {
          if (!typeRelations.has(key)) {
            candidates.delete(key);
          }
        }
      }
    }
    
    // If no filters applied, return all relations
    if (!initialized) {
      return Array.from(this.relations.values());
    }
    
    // Retrieve relations
    const results = [];
    for (const key of candidates) {
      results.push(this.relations.get(key));
    }
    
    return results;
  }
  
  /**
   * Delete a relation
   * @param {string} key - Relation key
   * @returns {Promise<boolean>} True if deleted
   */
  async delete(key) {
    const relation = this.relations.get(key);
    if (!relation) return false;
    
    // Remove from indexes
    if (this.sourceIndex.has(relation.sourceId)) {
      this.sourceIndex.get(relation.sourceId).delete(key);
    }
    
    if (this.targetIndex.has(relation.targetId)) {
      this.targetIndex.get(relation.targetId).delete(key);
    }
    
    if (this.typeIndex.has(relation.type)) {
      this.typeIndex.get(relation.type).delete(key);
    }
    
    // Remove main relation
    return this.relations.delete(key);
  }
 }

 /**
 * Cross-Linguistic Semantic Engine
 * Handles concepts across languages
 */
 class CrossLinguisticSemanticEngine {
  /**
   * Create a new cross-linguistic semantic engine
   * @param {Base0} base0 - Base0 instance
   */
  constructor(base0) {
    this.base0 = base0;
    this.languages = new Set(['en']);  // Default to English
    this.conceptMappings = new Map();
    this.semanticCache = new Map();
  }
  
  /**
   * Add supported language
   * @param {string} languageCode - ISO language code
   * @returns {CrossLinguisticSemanticEngine} This engine for chaining
   */
  addLanguage(languageCode) {
    this.languages.add(languageCode);
    return this;
  }
  
  /**
   * Create semantic address for a concept
   * @param {string} concept - Concept text
   * @param {string} language - Language code
   * @param {string} context - Optional context
   * @returns {Promise<Object>} Semantic address
   */
  async createSemanticAddress(concept, language = 'en', context = null) {
    // Check if language is supported
    if (!this.languages.has(language)) {
      throw new Error(`Language not supported: ${language}`);
    }
    
    // Create cache key
    const cacheKey = `${concept}|${language}|${context || ''}`;
    
    // Check cache
    if (this.semanticCache.has(cacheKey)) {
      return this.semanticCache.get(cacheKey);
    }
    
    // Create embedding using Clifford algebra
    const embedding = this.base0.embeddingModel.embed({
      text: concept,
      language,
      context
    });
    
    // Create semantic identity from embedding
    const semanticId = this._createSemanticId(embedding);
    
    // Calculate coherence
    const coherence = CoherenceMetrics.normalizedCoherence(embedding);
    
    // Create address object
    const address = {
      id: semanticId,
      concept,
      language,
      context: context || null,
      embedding: this._encodeEmbedding(embedding),
      coherence,
      created: Date.now()
    };
    
    // Cache the address
    this.semanticCache.set(cacheKey, address);
    
    return address;
  }
  
  /**
   * Register concept mapping across languages
   * @param {Object} mapping - Concept mapping
   * @returns {Promise<Object>} Registration result
   */
  async registerConceptMapping(mapping) {
    if (!mapping.concepts || typeof mapping.concepts !== 'object') {
      throw new Error('Mapping must include concepts object');
    }
    
    const languages = Object.keys(mapping.concepts);
    if (languages.length < 2) {
      throw new Error('Mapping must include at least two languages');
    }
    
    // Check that all languages are supported
    for (const lang of languages) {
      if (!this.languages.has(lang)) {
        throw new Error(`Language not supported: ${lang}`);
      }
    }
    
    // Create mapping ID
    const mappingId = mapping.id || `mapping-${Date.now()}-${Math.floor(Math.random() * 10000)}`;
    
    // Store mapping
    this.conceptMappings.set(mappingId, {
      id: mappingId,
      concepts: mapping.concepts,
      languages,
      domain: mapping.domain || 'general',
      created: Date.now()
    });
    
    // Create semantic addresses for each concept
    const addresses = {};
    
    for (const [lang, concept] of Object.entries(mapping.concepts)) {
      addresses[lang] = await this.createSemanticAddress(
        concept,
        lang,
        mapping.domain
      );
    }
    
    return {
      id: mappingId,
      addresses
    };
  }
  
  /**
   * Find equivalent concept in another language
   * @param {string} concept - Source concept
   * @param {string} sourceLanguage - Source language
   * @param {string} targetLanguage - Target language
   * @param {Object} options - Search options
   * @returns {Promise<Object>} Equivalent concept
   */
  async findEquivalentConcept(concept, sourceLanguage, targetLanguage, options = {}) {
    // Check if both languages are supported
    if (!this.languages.has(sourceLanguage)) {
      throw new Error(`Source language not supported: ${sourceLanguage}`);
    }
    
    if (!this.languages.has(targetLanguage)) {
      throw new Error(`Target language not supported: ${targetLanguage}`);
    }
    
    // Create semantic address for source concept
    const sourceAddress = await this.createSemanticAddress(
      concept, 
      sourceLanguage, 
      options.context
    );
    
    // First try direct mappings
    const directMapping = await this._findDirectMapping(
      concept,
      sourceLanguage,
      targetLanguage
    );
    
    if (directMapping) {
      const targetAddress = await this.createSemanticAddress(
        directMapping,
        targetLanguage,
        options.context
      );
      
      return {
        concept: directMapping,
        language: targetLanguage,
        similarity: 1.0,  // Direct mapping has perfect similarity
        address: targetAddress,
        method: 'direct'
      };
    }
    
    // Get threshold
    const threshold = options.threshold || 0.85;
    
    // Get all concept mappings
    const candidates = [];
    
    for (const mapping of this.conceptMappings.values()) {
      // Skip mappings that don't include both languages
      if (!mapping.concepts[sourceLanguage] || !mapping.concepts[targetLanguage]) {
        continue;
      }
      
      // Calculate similarity to source concept
      const similarity = this._calculateConceptSimilarity(
        concept,
        mapping.concepts[sourceLanguage]
      );
      
      if (similarity >= threshold) {
        const targetConcept = mapping.concepts[targetLanguage];
        const targetAddress = await this.createSemanticAddress(
          targetConcept,
          targetLanguage,
          options.context
        );
        
        candidates.push({
          concept: targetConcept,
          language: targetLanguage,
          similarity,
          address: targetAddress,
          method: 'mapping'
        });
      }
    }
    
    // If no candidates found, try semantic matching
    if (candidates.length === 0 && options.useEmbedding !== false) {
      // This would typically use an embedding model to find semantically similar concepts
      // For the reference implementation, we'll just return a placeholder
      
      return null;
    }
    
    // Sort by similarity (descending)
    candidates.sort((a, b) => b.similarity - a.similarity);
    
    // Return best match
    return candidates[0] || null;
  }
  
  /**
   * Create semantic ID from embedding
   * @private
   * @param {MultivectorRepresentation} embedding - Semantic embedding
   * @returns {string} Semantic ID
   */
  _createSemanticId(embedding) {
    // Get key components of the embedding
    const keyComponents = this._extractKeyComponents(embedding);
    
    // Create hash from key components
    const bytes = new Uint8Array(keyComponents.length * 4);
    const view = new DataView(bytes.buffer);
    
    for (let i = 0; i < keyComponents.length; i++) {
      view.setFloat32(i * 4, keyComponents[i], true);
    }
    
    // Simple hash for reference implementation
    let hash = 0;
    for (let i = 0; i < bytes.length; i++) {
      hash = ((hash << 5) - hash) + bytes[i];
      hash |= 0;
    }
    
    // Create a 16-character hexadecimal hash
    return Math.abs(hash).toString(16).padStart(8, '0') + 
           Date.now().toString(16).substr(-8);
  }
  
  /**
   * Extract key components from embedding
   * @private
   * @param {MultivectorRepresentation} embedding - Semantic embedding
   * @returns {number[]} Key components
   */
  _extractKeyComponents(embedding) {
    // For the reference implementation, use the most significant components
    const components = Array.from(embedding.components);
    
    // Sort components by absolute magnitude
    const indices = components.map((val, idx) => [idx, Math.abs(val)]);
    indices.sort((a, b) => b[1] - a[1]);
    
    // Take top components
    return indices.slice(0, 16).map(([idx, _]) => components[idx]);
  }
  
  /**
   * Encode embedding for storage
   * @private
   * @param {MultivectorRepresentation} embedding - Semantic embedding
   * @returns {string} Encoded embedding
   */
  _encodeEmbedding(embedding) {
    // Simple base64 encoding for the reference implementation
    const jsonStr = JSON.stringify(Array.from(embedding.components));
    return `base64:${btoa(jsonStr)}`;
  }
  
  /**
   * Find direct mapping between concepts
   * @private
   * @param {string} concept - Source concept
   * @param {string} sourceLanguage - Source language
   * @param {string} targetLanguage - Target language
   * @returns {Promise<string>} Target concept or null
   */
  async _findDirectMapping(concept, sourceLanguage, targetLanguage) {
    // Look for exact match in mappings
    for (const mapping of this.conceptMappings.values()) {
      // Skip mappings that don't include both languages
      if (!mapping.concepts[sourceLanguage] || !mapping.concepts[targetLanguage]) {
        continue;
      }
      
      // Check for exact match
      if (mapping.concepts[sourceLanguage] === concept) {
        return mapping.concepts[targetLanguage];
      }
    }
    
    return null;
  }
  
  /**
   * Calculate similarity between concepts
   * @private
   * @param {string} concept1 - First concept
   * @param {string} concept2 - Second concept
   * @returns {number} Similarity (0-1)
   */
  _calculateConceptSimilarity(concept1, concept2) {
    // Simple string similarity for reference implementation
    // In a real implementation, this would use semantic embeddings
    
    if (concept1 === concept2) return 1.0;
    
    // Normalize concepts
    const norm1 = concept1.toLowerCase().trim();
    const norm2 = concept2.toLowerCase().trim();
    
    if (norm1 === norm2) return 1.0;
    
    // Check for substring
    if (norm1.includes(norm2) || norm2.includes(norm1)) {
      const ratio = Math.min(norm1.length, norm2.length) / Math.max(norm1.length, norm2.length);
      return 0.8 * ratio;
    }
    
    // Calculate Levenshtein distance
    const distance = this._levenshteinDistance(norm1, norm2);
    const maxLength = Math.max(norm1.length, norm2.length);
    
    // Convert to similarity (0-1)
    return 1.0 - (distance / maxLength);
  }
  
  /**
   * Calculate Levenshtein distance between strings
   * @private
   * @param {string} s1 - First string
   * @param {string} s2 - Second string
   * @returns {number} Levenshtein distance
   */
  _levenshteinDistance(s1, s2) {
    const m = s1.length;
    const n = s2.length;
    
    // Create distance matrix
    const d = Array(m + 1).fill().map(() => Array(n + 1).fill(0));
    
    // Initialize first row and column
    for (let i = 0; i <= m; i++) {
      d[i][0] = i;
    }
    
    for (let j = 0; j <= n; j++) {
      d[0][j] = j;
    }
    
    // Fill the matrix
    for (let j = 1; j <= n; j++) {
      for (let i = 1; i <= m; i++) {
        const cost = s1[i - 1] === s2[j - 1] ? 0 : 1;
        d[i][j] = Math.min(
          d[i - 1][j] + 1,      // deletion
          d[i][j - 1] + 1,      // insertion
          d[i - 1][j - 1] + cost // substitution
        );
      }
    }
    
    return d[m][n];
  }
 }

 /**
 * Universal Object Reference System (UORS)
 * Main class combining all components
 */
 class UORS {
  /**
   * Create a new UORS instance
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    // Create Base0 (Neural Network Specification)
    this.base0 = new Base0(config.base0 || {});
    
    // Create UniversalAddressingModel
    this.addressingModel = new UniversalAddressingModel(this.base0);
    
    // Create ObjectManifold
    this.objectManifold = new ObjectManifold(this.base0);
    
    // Create CoherenceAwareStorage
    this.storage = new CoherenceAwareStorage(this.base0);
    
    // Create CrossLinguisticSemanticEngine
    this.semanticEngine = new CrossLinguisticSemanticEngine(this.base0);
    
    // Configure system
    this._configure(config);
  }
  
  /**
   * Configure the system
   * @private
   * @param {Object} config - Configuration options
   */
  _configure(config) {
    // Add supported languages
    if (config.languages) {
      for (const language of config.languages) {
        this.semanticEngine.addLanguage(language);
      }
    }
    
    // Set coherence threshold
    if (config.coherenceThreshold) {
      this.storage.coherenceThreshold = config.coherenceThreshold;
    }
  }
  
  /**
   * Create a universal address for an object
   * @param {*} object - Object to address
   * @param {Object} options - Addressing options
   * @returns {Promise<Object>} Universal address
   */
  async createAddress(object, options = {}) {
    return this.addressingModel.createAddress(object, options);
  }
  
  /**
   * Store an object
   * @param {*} object - Object to store
   * @param {Object} options - Storage options
   * @returns {Promise<Object>} Storage result
   */
  async store(object, options = {}) {
    // Create address
    const address = await this.createAddress(object, options);
    
    // Store in storage
    await this.storage.store('objects', address.universal.id, object);
    
    // Store address
    await this.storage.store('addresses', address.universal.id, address);
    
    // Add to manifold
    await this.objectManifold.addObject(object, address);
    
    return {
      id: address.universal.id,
      address,
      stored: true,
      timestamp: Date.now()
    };
  }
  
  /**
   * Retrieve an object
   * @param {string} id - Object ID or address
   * @param {Object} options - Retrieval options
   * @returns {Promise<Object>} Retrieved object
   */
  async retrieve(id, options = {}) {
    // Find the universal ID if not provided
    let universalId = id;
    
    if (!id.startsWith('usaf://')) {
      // Try to find address
      const addressStore = this.storage.getStore('addresses');
      const address = await addressStore.find(id);
      
      if (!address) {
        throw new Error(`Object not found: ${id}`);
      }
      
      universalId = address.universal.id;
    }
    
    // Retrieve object
    const object = await this.storage.retrieve('objects', universalId);
    
    if (!object) {
      throw new Error(`Object not found: ${universalId}`);
    }
    
    // Retrieve address
    const address = await this.storage.retrieve('addresses', universalId);
    
    return {
      id: universalId,
      object,
      address
    };
  }
  
  /**
   * Create a relation between objects
   * @param {string} sourceId - Source object ID
   * @param {string} targetId - Target object ID
   * @param {string} relationType - Relation type
   * @param {Object} properties - Relation properties
   * @returns {Promise<Object>} Created relation
   */
  async createRelation(sourceId, targetId, relationType, properties = {}) {
    // Create relation in manifold
    const relation = await this.objectManifold.createRelation(
      sourceId,
      targetId,
      relationType,
      properties
    );
    
    // Store relation
    await this.storage.store('relations', relation.id, relation);
    
    return relation;
  }
  
  /**
   * Find objects by query
   * @param {Object} query - Query parameters
   * @returns {Promise<Object[]>} Found objects
   */
  async findObjects(query) {
    return this.objectManifold.findObjects(query);
  }
  
  /**
   * Find similar objects
   * @param {string} id - Object ID
   * @param {Object} options - Search options
   * @returns {Promise<Object[]>} Similar objects
   */
  async findSimilarObjects(id, options = {}) {
    return this.objectManifold.findSimilarObjects(id, options);
  }
  
  /**
   * Find equivalent concept in another language
   * @param {string} concept - Source concept
   * @param {string} sourceLanguage - Source language
   * @param {string} targetLanguage - Target language
   * @param {Object} options - Search options
   * @returns {Promise<Object>} Equivalent concept
   */
  async findEquivalentConcept(concept, sourceLanguage, targetLanguage, options = {}) {
    return this.semanticEngine.findEquivalentConcept(
      concept,
      sourceLanguage,
      targetLanguage,
      options
    );
  }
  
  /**
   * Register concept mapping
   * @param {Object} mapping - Concept mapping
   * @returns {Promise<Object>} Registration result
   */
  async registerConceptMapping(mapping) {
    return this.semanticEngine.registerConceptMapping(mapping);
  }
 }

 // =============================================================================
 // 4. UORS Factory Function
 // =============================================================================

 /**
 * Create a new UORS instance
 * @param {Object} config - Configuration options
 * @returns {UORS} UORS instance
 */
 function createUORS(config = {}) {
  return new UORS(config);
 }

 // Export the factory function for Node.js environments
 if (typeof module !== 'undefined' && module.exports) {
  module.exports = {
    createUORS,
    UORS,
    Base0,
    Base1,
    Base2,
    Base3,
    UniversalAddressingModel,
    ObjectManifold,
    CoherenceAwareStorage,
    CrossLinguisticSemanticEngine,
    CliffordAlgebra,
    MultivectorRepresentation,
    CoherenceMetrics
  };
 }

 // =============================================================================
 // 5. Example Usage
 // =============================================================================

 /**
 * Example usage of the UORS system
 */
 async function exampleUsage() {
  // Create UORS instance
  const uors = createUORS({
    languages: ['en', 'es', 'fr', 'de', 'zh'],
    coherenceThreshold: 0.75
  });
  
  // Create an address for an object
  const address = await uors.createAddress("Database server configuration", {
    language: "en",
    namespace: "system.config",
    name: "database-config",
    version: "1.0.0",
    context: "computing"
  });
  
  console.log("Created address:", address);
  
  // Store an object
  const storedObject = await uors.store({
    name: "database-config",
    host: "localhost",
    port: 5432,
    username: "admin",
    password: "********",
    database: "app_data",
    maxConnections: 100
  }, {
    namespace: "system.config",
    language: "en",
    context: "computing"
  });
  
  console.log("Stored object:", storedObject);
  
  // Retrieve the object
  const retrievedObject = await uors.retrieve(storedObject.id);
  
  console.log("Retrieved object:", retrievedObject);
  
  // Create another object
  const secondObject = await uors.store({
    name: "application-config",
    environment: "production",
    features: {
      logging: true,
      metrics: true,
      caching: true
    },
    scaling: {
      minInstances: 2,
      maxInstances: 10
    }
  }, {
    namespace: "system.config",
    language: "en",
    context: "computing"
  });
  
  console.log("Second object:", secondObject);
  
  // Create a relation between objects
  const relation = await uors.createRelation(
    storedObject.id,
    secondObject.id,
    "references",
    {
      description: "Database used by application",
      priority: "high"
    }
  );
  
  console.log("Created relation:", relation);
  
  // Register concept mapping
  const mapping = await uors.registerConceptMapping({
    domain: "computing",
    concepts: {
      "en": "database server",
      "es": "servidor de base de datos",
      "fr": "serveur de base de données",
      "de": "Datenbankserver",
      "zh": "数据库服务器"
    }
  });
  
  console.log("Registered concept mapping:", mapping);
  
  // Find equivalent concept
  const equivalent = await uors.findEquivalentConcept(
    "database server",
    "en",
    "es"
  );
  
  console.log("Equivalent concept:", equivalent);
  
  // Find similar objects
  const similarObjects = await uors.findSimilarObjects(storedObject.id, {
    threshold: 0.7,
    limit: 5
  });
  
  console.log("Similar objects:", similarObjects);
  
  return {
    address,
    storedObject,
    retrievedObject,
    secondObject,
    relation,
    mapping,
    equivalent,
    similarObjects
  };
 }

 // =============================================================================
 // 3. Universal Object Reference System Integration
 // =============================================================================

 /**
 * Universal Addressing Model
 * Integrates the four addressing types (name, content, semantic, attribute)
 */
 class UniversalAddressingModel {
  /**
   * Create a new universal addressing model
   * @param {Base0} base0 - Base0 instance
   */
  constructor(base0) {
    this.base0 = base0;
    this.hashAlgorithm = 'SHA-256';
    this.addressPrefixes = {
      name: 'name://',
      content: 'content://',
      semantic: 'semantic://',
      attribute: 'attr://'
    };
    this.cache = new Map();
  }
  
  /**
   * Create a universal address for an object
   * @param {*} object - Object to address
   * @param {Object} options - Addressing options
   * @returns {Promise<Object>} Universal address
   */
  async createAddress(object, options = {}) {
    // Create addresses of all supported types
    const [nameAddress, contentAddress, semanticAddress, attributeAddress] = await Promise.all([
      this._createNameAddress(object, options),
      this._createContentAddress(object, options),
      this._createSemanticAddress(object, options),
      this._createAttributeAddress(object, options)
    ]);
    
    // Combine into universal address object
    const address = {
      universal: {
        id: this._createUniversalId(nameAddress, contentAddress, semanticAddress),
        created: Date.now()
      },
      name: nameAddress,
      content: contentAddress,
      semantic: semanticAddress,
      attribute: attributeAddress,
      coherence: this._calculateAddressCoherence(
        nameAddress, contentAddress, semanticAddress, attributeAddress
      )
    };
    
    // Cache the address
    if (options.cache !== false) {
      const cacheKey = this._getCacheKey(object);
      this.cache.set(cacheKey, address);
    }
    
    return address;
  }
  
  /**
   * Create name-based address (FQDN-style)
   * @private
   * @param {*} object - Object to address
   * @param {Object} options - Addressing options
   * @returns {Promise<Object>} Name address
   */
  async _createNameAddress(object, options) {
    let name;
    
    if (options.name) {
      name = options.name;
    } else if (object.name) {
      name = object.name;
    } else if (object.id) {
      name = object.id;
    } else {
      name = `obj-${Date.now()}-${Math.floor(Math.random() * 10000)}`;
    }
    
    // Sanitize name (only allow alphanumeric, dots, hyphens, and underscores)
    name = name.replace(/[^a-zA-Z0-9._-]/g, '-');
    
    // Add namespace if provided
    const namespace = options.namespace || 'default';
    
    // Create FQDN-style address
    const address = `${namespace}.${name}`;
    
    return {
      type: 'name',
      id: `${this.addressPrefixes.name}${address}`,
      name,
      namespace,
      version: options.version || '1.0.0'
    };
  }
  
  /**
   * Create content-based address (hash-based)
   * @private
   * @param {*} object - Object to address
   * @param {Object} options - Addressing options
   * @returns {Promise<Object>} Content address
   */
  async _createContentAddress(object, options) {
    // Serialize object to bytes
    const bytes = this._serializeObject(object);
    
    // Hash the content
    const hash = await this._hashBytes(bytes);
    
    return {
      type: 'content',
      id: `${this.addressPrefixes.content}${this.hashAlgorithm.toLowerCase()}:${hash}`,
      algorithm: this.hashAlgorithm,
      size: bytes.length
    };
  }
  
  /**
   * Create semantic address using Clifford algebra embedding
   * @private
   * @param {*} object - Object to address
   * @param {Object} options - Addressing options
   * @returns {Promise<Object>} Semantic address
   */
  async _createSemanticAddress(object, options) {
    // Extract description text
    const text = this._extractDescription(object, options);
    
    // Determine language
    const language = options.language || 'en';
    
    // Create semantic embedding
    const embedding = this.base0.embeddingModel.embed({
      text,
      language,
      context: options.context
    });
    
    // Create semantic ID from embedding
    const semanticId = this._createSemanticId(embedding);
    
    return {
      type: 'semantic',
      id: `${this.addressPrefixes.semantic}${semanticId}`,
      language,
      embedding: this._encodeEmbedding(embedding),
      coherence: CoherenceMetrics.normalizedCoherence(embedding)
    };
  }
  
  /**
   * Create attribute-based address
   * @private
   * @param {*} object - Object to address
   * @param {Object} options - Addressing options
   * @returns {Promise<Object>} Attribute address
   */
  async _createAttributeAddress(object, options) {
    // Extract key attributes
    const attributes = this._extractAttributes(object, options);
    
    // Create attribute signature
    const signature = this._createAttributeSignature(attributes);
    
    return {
      type: 'attribute',
      id: `${this.addressPrefixes.attribute}${signature}`,
      attributes,
      query: this._createAttributeQuery(attributes)
    };
  }
  
  /**
   * Create universal ID from component addresses
   * @private
   * @param {Object} nameAddress - Name address
   * @param {Object} contentAddress - Content address
   * @param {Object} semanticAddress - Semantic address
   * @returns {string} Universal ID
   */
  _createUniversalId(nameAddress, contentAddress, semanticAddress) {
    // Use semantic ID as the universal ID
    // This ensures semantically equivalent objects get the same ID
    if (semanticAddress && semanticAddress.id) {
      return semanticAddress.id.replace(this.addressPrefixes.semantic, 'usaf://');
    }
    
    // Fallback to content ID
    if (contentAddress && contentAddress.id) {
      const hash = contentAddress.id.replace(this.addressPrefixes.content, '');
      return `usaf://content:${hash}`;
    }
    
    // Fallback to name ID
    if (nameAddress && nameAddress.id) {
      const name = nameAddress.id.replace(this.addressPrefixes.name, '');
      return `usaf://name:${name}`;
    }
    
    // Last resort - generate a random ID
    return `usaf://gen:${Date.now()}-${Math.floor(Math.random() * 10000000)}`;
  }
  
  /**
   * Calculate coherence of an address
   * @private
   * @param {Object} nameAddress - Name address
   * @param {Object} contentAddress - Content address
   * @param {Object} semanticAddress - Semantic address
   * @param {Object} attributeAddress - Attribute address
   * @returns {number} Address coherence
   */
  _calculateAddressCoherence(nameAddress, contentAddress, semanticAddress, attributeAddress) {
    // Each address contributes to overall coherence
    let totalScore = 0;
    let count = 0;
    
    // Name address coherence
    if (nameAddress) {
      totalScore += 1.0;
      count++;
    }
    
    // Content address coherence
    if (contentAddress) {
      totalScore += 1.0;
      count++;
    }
    
    // Semantic address coherence (weighted higher)
    if (semanticAddress) {
      const semanticCoherence = semanticAddress.coherence || 0.8;
      totalScore += semanticCoherence * 2;
      count += 2;  // Higher weight
    }
    
    // Attribute address coherence
    if (attributeAddress) {
      totalScore += 1.0;
      count++;
    }
    
    return count > 0 ? totalScore / count : 0.5;
  }
  
  /**
   * Serialize an object to bytes
   * @private
   * @param {*} object - Object to serialize
   * @returns {Uint8Array} Serialized bytes
   */
  _serializeObject(object) {
    let serialized;
    
    try {
      // Try to JSON stringify the object
      serialized = JSON.stringify(object);
    } catch (error) {
      // Fallback for non-JSON serializable objects
      serialized = String(object);
    }
    
    // Convert string to bytes
    return new TextEncoder().encode(serialized);
  }
  
  /**
   * Hash bytes using the configured algorithm
   * @private
   * @param {Uint8Array} bytes - Bytes to hash
   * @returns {Promise<string>} Hex hash
   */
  async _hashBytes(bytes) {
    // Simple hash implementation for reference
    // In a real implementation, use crypto APIs
    
    // Simplified SHA-256 for reference
    let hash = 0;
    for (let i = 0; i < bytes.length; i++) {
      hash = ((hash << 5) - hash) + bytes[i];
      hash |= 0;  // Convert to 32-bit integer
    }
    
    // Convert to hex
    const hexHash = (hash >>> 0).toString(16).padStart(8, '0');
    
    // For a more realistic hash, append some pseudo-random bytes
    const randomPart = Array.from(
      { length: 24 }, 
      () => Math.floor(Math.random() * 256).toString(16).padStart(2, '0')
    ).join('');
    
    return hexHash + randomPart;
  }
  
  /**
   * Extract description text from an object
   * @private
   * @param {*} object - Source object
   * @param {Object} options - Extraction options
   * @returns {string} Description text
   */
  _extractDescription(object, options) {
    // Use explicit description if provided
    if (options.description) {
      return options.description;
    }
    
    // Extract from object properties
    if (typeof object === 'object' && object !== null) {
      // Try common description properties
      for (const prop of ['description', 'desc', 'summary', 'text', 'content', 'name', 'title']) {
        if (object[prop] && typeof object[prop] === 'string') {
          return object[prop];
        }
      }
      
      // Fallback to JSON representation
      return JSON.stringify(object);
    }
    
    // Fallback to string representation
    return String(object);
  }
  
  /**
   * Extract attributes from an object
   * @private
   * @param {*} object - Source object
   * @param {Object} options - Extraction options
   * @returns {Object} Attribute map
   */
  _extractAttributes(object, options) {
    // Use explicit attributes if provided
    if (options.attributes) {
      return options.attributes;
    }
    
    const attributes = {};
    
    // Extract from object properties
    if (typeof object === 'object' && object !== null) {
      // Extract common attributes
      for (const prop of ['type', 'category', 'kind', 'language', 'format', 'version']) {
        if (object[prop] !== undefined) {
          attributes[prop] = object[prop];
        }
      }
      
      // Extract domain-specific attributes if available
      if (object.attributes) {
        Object.assign(attributes, object.attributes);
      }
    }
    
    // Add namespace from options
    if (options.namespace) {
      attributes.namespace = options.namespace;
    }
    
    return attributes;
  }
  
  /**
   * Create a signature from attributes
   * @private
   * @param {Object} attributes - Attribute map
   * @returns {string} Attribute signature
   */
  _createAttributeSignature(attributes) {
    // Sort attribute keys for consistent signature
    const keys = Object.keys(attributes).sort();
    
    // Create signature by joining key-value pairs
    const signature = keys.map(key => {
      const value = attributes[key];
      if (typeof value === 'string') {
        return `${key}:${value}`;
      } else {
        return `${key}:${JSON.stringify(value)}`;
      }
    }).join(';');
    
    // Use a simple hash for the reference implementation
    let hash = 0;
    for (let i = 0; i < signature.length; i++) {
      hash = ((hash << 5) - hash) + signature.charCodeAt(i);
      hash |= 0;
    }
    
    return hash.toString(36);
  }
  
  /**
   * Create an attribute query string
   * @private
   * @param {Object} attributes - Attribute map
   * @returns {string} Query string
   */
  _createAttributeQuery(attributes) {
    // Sort attribute keys for consistent query
    const keys = Object.keys(attributes).sort();
    
    // Create query string
    return keys.map(key => {
      const value = attributes[key];
      if (typeof value === 'string') {
        return `${encodeURIComponent(key)}=${encodeURIComponent(value)}`;
      } else {
        return `${encodeURIComponent(key)}=${encodeURIComponent(JSON.stringify(value))}`;
      }
    }).join('&');
  }
  
  /**
   * Create a semantic ID from an embedding
   * @private
   * @param {MultivectorRepresentation} embedding - Semantic embedding
   * @returns {string} Semantic ID
   */
  _createSemanticId(embedding) {
    // Get key components of the embedding
    const keyComponents = this._extractKeyComponents(embedding);
    
    // Create hash from key components
    const bytes = new Uint8Array(keyComponents.length * 4);
    const view = new DataView(bytes.buffer);
    
    for (let i = 0; i < keyComponents.length; i++) {
      view.setFloat32(i * 4, keyComponents[i], true);
    }
    
    // Simple hash for reference implementation
    let hash = 0;
    for (let i = 0; i < bytes.length; i++) {
      hash = ((hash << 5) - hash) + bytes[i];
      hash |= 0;
    }
    
    // Create a 16-character hexadecimal hash
    return Math.abs(hash).toString(16).padStart(8, '0') + 
           Date.now().toString(16).substr(-8);
  }
  
  /**
   * Extract key components from embedding
   * @private
   * @param {MultivectorRepresentation} embedding - Semantic embedding
   * @returns {number[]} Key components
   */
  _extractKeyComponents(embedding) {
    // For the reference implementation, use the most significant components
    const components = Array.from(embedding.components);
    
    // Sort components by absolute magnitude
    const indices = components.map((val, idx) => [idx, Math.abs(val)]);
    indices.sort((a, b) => b[1] - a[1]);
    
    // Take top components
    return indices.slice(0, 16).map(([idx, _]) => components[idx]);
  }
  
  /**
   * Encode embedding for storage
   * @private
   * @param {MultivectorRepresentation} embedding - Semantic embedding
   * @returns {string} Encoded embedding
   */
  _encodeEmbedding(embedding) {
    // Simple base64 encoding for the reference implementation
    const jsonStr = JSON.stringify(Array.from(embedding.components));
    return `base64:${btoa(jsonStr)}`;
  }
  
  /**
   * Decode embedding from storage
   * @private
   * @param {string} encoded - Encoded embedding
   * @returns {MultivectorRepresentation} Decoded embedding
   */
  _decodeEmbedding(encoded) {
    if (!encoded.startsWith('base64:')) {
      throw new Error('Invalid encoding format');
    }
    
    // Remove prefix
    const base64 = encoded.substring(7);
    
    // Decode base64
    const jsonStr = atob(base64);
    
    // Parse JSON
    const components = JSON.parse(jsonStr);
    
    // Create multivector
    const dimension = Math.log2(components.length);
    const multivector = new MultivectorRepresentation(dimension);
    
    // Copy components
    for (let i = 0; i < components.length; i++) {
      multivector.components[i] = components[i];
    }
    
    return multivector;
  }
  
  /**
   * Get a cache key for an object
   * @private
   * @param {*} object - Object to get key for
   * @returns {string} Cache key
   */
  _getCacheKey(object) {
    if (typeof object === 'string') {
      return `str:${object}`;
    } else if (typeof object === 'number') {
      return `num:${object}`;
    } else if (typeof object === 'object' && object !== null) {
      if (object.id) {
        return `obj:${object.id}`;
      } else {
        try {
          return `obj:${JSON.stringify(object)}`;
        } catch (error) {
          return `obj:${Date.now()}`;
        }
      }
    } else {
      return `other:${String(object)}`;
    }
  }
 }

 /**
 * Object Manifold
 * Organizes objects in a manifold structure
 */
 class ObjectManifold {
  /**
   * Create a new object manifold
   * @param {Base0} base0 - Base0 instance
   */
  constructor(base0) {
    this.base0 = base0;
    this.objects = new Map();
    this.relations = new Map();
    this.metrics = new Map();
    this.depthCalculator = new ManifoldDepthCalculator();
    
    // Initialize standard metrics
    this._initializeMetrics();
  }
  
  /**
   * Initialize standard metrics
   * @private
   */
  _initializeMetrics() {
    // Euclidean metric
    this.registerMetric('euclidean', (p1, p2) => {
      let sum = 0;
      for (let i = 0; i < p1.length; i++) {
        const diff = p1[i] - p2[i];
        sum += diff * diff;
      }
      return Math.sqrt(sum);
    });
    
    // Cosine similarity metric
    this.registerMetric('cosine', (p1, p2) => {
      let dotProduct = 0;
      let norm1 = 0;
      let norm2 = 0;
      
      for (let i = 0; i < p1.length; i++) {
        dotProduct += p1[i] * p2[i];
        norm1 += p1[i] * p1[i];
        norm2 += p2[i] * p2[i];
      }
      
      norm1 = Math.sqrt(norm1);
      norm2 = Math.sqrt(norm2);
      
      if (norm1 === 0 || norm2 === 0) return 0;
      
      return dotProduct / (norm1 * norm2);
    });
    
    // Manhattan metric
    this.registerMetric('manhattan', (p1, p2) => {
      let sum = 0;
      for (let i = 0; i < p1.length; i++) {
        sum += Math.abs(p1[i] - p2[i]);
      }
      return sum;
    });
  }
  
  /**
   * Register a metric
   * @param {string} name - Metric name
   * @param {function} metricFn - Metric function
   * @returns {ObjectManifold} This manifold for chaining
   */
  registerMetric(name, metricFn) {
    this.metrics.set(name, metricFn);
    return this;
  }
  
  /**
   * Add an object to the manifold
   * @param {*} object - Object to add
   * @param {Object} address - Universal address
   * @returns {Promise<Object>} Manifold point
   */
  async addObject(object, address) {
    // Calculate object manifold coordinates
    const coordinates = await this._calculateCoordinates(object, address);
    
    // Calculate manifold depth
    const depth = this.depthCalculator.calculate(object);
    
    // Create manifold point
    const point = {
      object,
      address,
      coordinates,
      depth,
      relations: new Set()
    };
    
    // Add to manifold
    this.objects.set(address.universal.id, point);
    
    return point;
  }
  
  /**
   * Create a relation between objects
   * @param {string} sourceId - Source object ID
   * @param {string} targetId - Target object ID
   * @param {string} type - Relation type
   * @param {Object} properties - Relation properties
   * @returns {Promise<Object>} Relation object
   */
  async createRelation(sourceId, targetId, type, properties = {}) {
    // Verify objects exist
    if (!this.objects.has(sourceId)) {
      throw new Error(`Source object not found: ${sourceId}`);
    }
    
    if (!this.objects.has(targetId)) {
      throw new Error(`Target object not found: ${targetId}`);
    }
    
    // Get manifold points
    const source = this.objects.get(sourceId);
    const target = this.objects.get(targetId);
    
    // Verify depth constraints
    if (!this._verifyDepthAccess(source, target, type)) {
      throw new Error(
        `Depth violation: ${sourceId} cannot relate to ${targetId} with type ${type}`
      );
    }
    
    // Create relation ID
    const relationId = `${sourceId}|${type}|${targetId}`;
    
    // Create relation object
    const relation = {
      id: relationId,
      sourceId,
      targetId,
      type,
      properties,
      created: Date.now()
    };
    
    // Add to relations
    this.relations.set(relationId, relation);
    
    // Update object relation sets
    source.relations.add(relationId);
    target.relations.add(relationId);
    
    return relation;
  }
  
  /**
   * Find objects by attribute query
   * @param {Object} query - Query parameters
   * @returns {Promise<Object[]>} Found objects
   */
  async findObjects(query) {
    const results = [];
    
    // Get initial search region in manifold
    const searchRegion = await this._calculateSearchRegion(query);
    
    // Find candidate objects in region
    const candidates = this._findCandidatesInRegion(searchRegion);
    
    // Filter candidates by query
    for (const object of candidates) {
      if (this._matchesQuery(object, query)) {
        results.push(object);
      }
    }
    
    return results;
  }
  
  /**
   * Find similar objects by universal ID
   * @param {string} universalId - Universal ID
   * @param {Object} options - Search options
   * @returns {Promise<Object[]>} Similar objects
   */
  async findSimilarObjects(universalId, options = {}) {
    // Get source object
    if (!this.objects.has(universalId)) {
      throw new Error(`Object not found: ${universalId}`);
    }
    
    const source = this.objects.get(universalId);
    
    // Get limit and threshold
    const limit = options.limit || 10;
    const threshold = options.threshold || 0.7;
    
    // Select metric
    const metricName = options.metric || 'cosine';
    if (!this.metrics.has(metricName)) {
      throw new Error(`Unknown metric: ${metricName}`);
    }
    
    const metricFn = this.metrics.get(metricName);
    
    // Find similar objects by coordinate proximity
    const similarities = [];
    
    for (const [id, target] of this.objects.entries()) {
      if (id === universalId) continue;
      
      // Calculate similarity
      const similarity = metricFn(source.coordinates, target.coordinates);
      
      if (similarity >= threshold) {
        similarities.push({
          id,
          similarity,
          object: target.object,
          address: target.address
        });
      }
    }
    
    // Sort by similarity (descending)
    similarities.sort((a, b) => b.similarity - a.similarity);
    
    // Return top matches
    return similarities.slice(0, limit);
  }
  
  /**
   * Retrieve object by ID
   * @param {string} id - Object ID
   * @returns {Object} Object data
   */
  getObject(id) {
    const point = this.objects.get(id);
    if (!point) {
      throw new Error(`Object not found: ${id}`);
    }
    
    return {
      id,
      object: point.object,
      address: point.address,
      depth: point.depth,
      relationCount: point.relations.size
    };
  }
  
  /**
   * Find relations for an object
   * @param {string} objectId - Object ID
   * @param {Object} options - Filter options
   * @returns {Object[]} Relations
   */
  findRelations(objectId, options = {}) {
    const point = this.objects.get(objectId);
    if (!point) {
      throw new Error(`Object not found: ${objectId}`);
    }
    
    const results = [];
    
    for (const relationId of point.relations) {
      const relation = this.relations.get(relationId);
      
      // Apply type filter
      if (options.type && relation.type !== options.type) {
        continue;
      }
      
      // Apply direction filter
      if (options.direction === 'outgoing' && relation.sourceId !== objectId) {
        continue;
      }
      
      if (options.direction === 'incoming' && relation.targetId !== objectId) {
        continue;
      }
      
      // Add related object info
      const relatedId = relation.sourceId === objectId ? relation.targetId : relation.sourceId;
      const relatedPoint = this.objects.get(relatedId);
      
      results.push({
        relation,
        object: relatedPoint ? relatedPoint.object : null,
        address: relatedPoint ? relatedPoint.address : null,
        isSource: relation.sourceId === objectId
      });
    }
    
    // Apply limit
    if (options.limit && options.limit > 0) {
      return results.slice(0, options.limit);
    }
    
    return results;
  }
  
  /**
   * Calculate coordinates for an object
   * @private
   * @param {*} object - Object to calculate coordinates for
   * @param {Object} address - Universal address
   * @returns {Promise<number[]>} Manifold coordinates
   */
  async _calculateCoordinates(object, address) {
    // Default coordinates dimension
    const dimension = 8;
    const coordinates = new Array(dimension).fill(0);
    
    // Use semantic embedding if available
    if (address.semantic && address.semantic.embedding) {
      try {
        // Decode embedding
        const embedding = this._decodeEmbedding(address.semantic.embedding);
        
        // Project to target dimension using spectral operator
        const projection = this.base0.spectralOperator.project(embedding);
        
        // Use projection for coordinates
        for (let i = 0; i < dimension; i++) {
          if (i < projection.length) {
            coordinates[i] = projection[i];
          }
        }
        
        return coordinates;
      } catch (error) {
        console.error("Error using semantic embedding for coordinates:", error);
      }
    }
    
    // Fallback: hash-based coordinates
    // Use content address hash if available
    if (address.content && address.content.id) {
      const hashPart = address.content.id.split(':').pop();
      
      // Convert first bytes of hash to coordinates
      for (let i = 0; i < Math.min(dimension, hashPart.length / 2); i++) {
        const byte = parseInt(hashPart.substr(i * 2, 2), 16);
        coordinates[i] = (byte / 255) * 2 - 1;  // Scale to [-1, 1]
      }
    }
    
    return coordinates;
  }
  
  /**
   * Decode embedding from storage
   * @private
   * @param {string} encoded - Encoded embedding
   * @returns {MultivectorRepresentation} Decoded embedding
   */
  _decodeEmbedding(encoded) {
    if (!encoded.startsWith('base64:')) {
      throw new Error('Invalid encoding format');
    }
    
    // Remove prefix
    const base64 = encoded.substring(7);
    
    // Decode base64
    const jsonStr = atob(base64);
    
    // Parse JSON
    const components = JSON.parse(jsonStr);
    
    // Create multivector
    const dimension = Math.log2(components.length);
    const multivector = new MultivectorRepresentation(dimension);
    
    // Copy components
    for (let i = 0; i < components.length; i++) {
      multivector.components[i] = components[i];
    }
    
    return multivector;
  }
  
  /**
   * Calculate search region
   * @private
   * @param {Object} query - Search query
   * @returns {Object} Search region
   */
  _calculateSearchRegion(query) {
    // Default region is entire manifold
    const region = {
      center: null,
      radius: Infinity,
      bounds: null
    };
    
    // If semantic search is specified
    if (query.semantic) {
      // Use semantic vector as center
      // For the reference implementation, we'd need an embedding model
      
      // Set a reasonable radius for semantic search
      region.radius = 0.5;
    }
    
    // If attribute search is specified
    if (query.attributes) {
      // Currently, we don't adjust the region for attributes
      // In a real implementation, we'd use attribute indexes
    }
    
    return region;
  }
  
  /**
   * Find candidates in a region
   * @private
   * @param {Object} region - Search region
   * @returns {Object[]} Candidate objects
   */
  _findCandidatesInRegion(region) {
    const candidates = [];
    
    // If no center specified, return all objects
    if (!region.center) {
      return Array.from(this.objects.values());
    }
    
    // Select metric
    const metricFn = this.metrics.get('euclidean');
    
    // Filter objects by distance
    for (const point of this.objects.values()) {
      const distance = metricFn(region.center, point.coordinates);
      
      if (distance <= region.radius) {
        candidates.push(point);
      }
    }
    
    return candidates;
  }
  
  /**
   * Check if an object matches a query
   * @private
   * @param {Object} point - Manifold point
   * @param {Object} query - Search query
   * @returns {boolean} True if matches
   */
  _matchesQuery(point, query) {
    // Check attribute constraints
    if (query.attributes) {
      const attrs = point.address.attribute.attributes;
      
      for (const [key, value] of Object.entries(query.attributes)) {
        if (attrs[key] !== value) {
          return false;
        }
      }
    }
    
    // Check semantic constraints
    if (query.semantic && query.embedding) {
      // Calculate semantic similarity
      // For the reference implementation, we'd need an embedding model
      
      // Placeholder for real implementation
      return true;
    }
    
    // Check depth constraints
    if (query.minDepth !== undefined && point.depth < query.minDepth) {
      return false;
    }
    
    if (query.maxDepth !== undefined && point.depth > query.maxDepth) {
      return false;
    }
    
    return true;
  }
  
  /**
   * Verify depth access constraints
   * @private
   * @param {Object} source - Source object
   * @param {Object} target - Target object
   * @param {string} relationType - Relation type
   * @returns {boolean} True if access is allowed
   */
  _verifyDepthAccess(source, target, relationType) {
    // Get relation constraints
    const constraints = this._getRelationConstraints(relationType);
    
    // Check depth constraints
    if (constraints.requiresEqualDepth) {
      return Math.abs(source.depth - target.depth) < 0.001;
    }
    
    if (constraints.requiresSourceDeeper) {
      return source.depth > target.depth;
    }
    
    if (constraints.requiresTargetDeeper) {
      return target.depth > source.depth;
    }
    
    // Default constraint: source must be at least as deep as target
    return source.depth >= target.depth;
  }
  
  /**
   * Get constraints for a relation type
   * @private
   * @param {string} relationType - Relation type
   * @returns {Object} Relation constraints
   */
  _getRelationConstraints(relationType) {
    // Default constraints
    const constraints = {
      requiresEqualDepth: false,
      requiresSourceDeeper: false,
      requiresTargetDeeper: false
    };
    
    // Apply type-specific constraints
    switch (relationType) {
      case 'equals':
        constraints.requiresEqualDepth = true;
        break;
        
      case 'contains':
        constraints.requiresSourceDeeper = true;
        break;
        
      case 'partOf':
        constraints.requiresTargetDeeper = true;
        break;
        
      case 'references':
        // No special constraints
        break;
    }
    
    return constraints;
  }
 }

 /**
 * Base 3: Application (Userspace)
 * Represents the user-space of the system
 */
 class Base3 extends Base2 {
  /**
   * Create a new Base3 instance
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    super(config);
    
    // Create behavior model (similar to JavaScript)
    this.behaviorModel = new BehaviorModel(this, config.behavior || {});
    
    // Create framework model (similar to CSS)
    this.frameworkModel = new FrameworkModel(this, config.framework || {});
    
    // Create structure model (similar to HTML)
    this.structureModel = new StructureModel(this, config.structure || {});
  }
  
  /**
   * Create application interface
   * @param {Object} spec - Application specification
   * @returns {Promise<Object>} Application interface
   */
  async createApplication(spec) {
    // Validate specification coherence
    const coherence = await this._validateSpecCoherence(spec);
    if (coherence < this.config.coherenceThreshold) {
      throw new Error(
        `Application specification failed coherence validation: ${coherence}`
      );
    }
    
    // Create structure from specification
    const structure = await this.structureModel.createFromSpec(spec.structure);
    
    // Apply framework to structure
    const styledStructure = await this.frameworkModel.applyToStructure(
      structure, 
      spec.framework
    );
    
    // Attach behavior to structure
    const application = await this.behaviorModel.attachToStructure(
      styledStructure, 
      spec.behavior
    );
    
    // Return the assembled application
    return {
      id: application.id,
      interface: application.interface,
      execute: (action, params) => this.executeApplication(application.id, action, params)
    };
  }
  
  /**
   * Validate specification coherence
   * @private
   * @param {Object} spec - Application specification
   * @returns {Promise<number>} Coherence value
   */
  async _validateSpecCoherence(spec) {
    if (!spec) return 0;
    
    const scores = [];
    
    // Check structure validity
    if (spec.structure && typeof spec.structure === 'object') {
      scores.push(1.0);
    } else {
      scores.push(0.0);
    }
    
    // Check framework validity
    if (spec.framework && typeof spec.framework === 'object') {
      scores.push(1.0);
    } else {
      scores.push(0.5);  // Optional
    }
    
    // Check behavior validity
    if (spec.behavior && typeof spec.behavior === 'object') {
      scores.push(1.0);
    } else {
      scores.push(0.5);  // Optional
    }
    
    // Calculate average score
    const total = scores.reduce((sum, score) => sum + score, 0);
    return total / scores.length;
  }
  
  /**
   * Execute application action
   * @param {string} appId - Application ID
   * @param {string} action - Action to execute
   * @param {Object} params - Action parameters
   * @returns {Promise<Object>} Action result
   */
  async executeApplicationAction(appId, action, params = {}) {
    return this.executeApplication(appId, action, params);
  }
 }

 /**
 * Behavior Model for Base3
 * Controls application behavior
 */
 class BehaviorModel {
  /**
   * Create a new behavior model
   * @param {Base3} base - Base3 instance
   * @param {Object} config - Configuration options
   */
  constructor(base, config = {}) {
    this.base = base;
    this.scriptEngine = new ScriptEngine(config.script || {});
    this.eventSystem = new EventSystem(config.events || {});
    this.globalScope = config.globalScope || {};
  }
  
  /**
   * Attach behavior to structure
   * @param {Object} structure - Structure to attach behavior to
   * @param {Object} behavior - Behavior specification
   * @returns {Promise<Object>} Structure with behavior
   */
  async attachToStructure(structure, behavior) {
    if (!behavior) {
      return structure;
    }
    
    // Create a copy of the structure
    const result = JSON.parse(JSON.stringify(structure));
    
    // Add event handlers
    if (behavior.eventHandlers) {
      for (const [eventName, handler] of Object.entries(behavior.eventHandlers)) {
        this.eventSystem.registerHandler(
          result.id,
          eventName,
          this.scriptEngine.compile(handler)
        );
      }
    }
    
    // Add methods
    if (behavior.methods) {
      result.methods = {};
      
      for (const [methodName, methodCode] of Object.entries(behavior.methods)) {
        result.methods[methodName] = this.scriptEngine.compile(methodCode);
      }
    }
    
    // Add a reference to the script engine and event system
    result._scriptEngine = this.scriptEngine;
    result._eventSystem = this.eventSystem;
    
    // Create public interface
    result.interface = this._createInterface(result, behavior);
    
    return result;
  }
  
  /**
   * Create application interface
   * @private
   * @param {Object} structure - Structure with behavior
   * @param {Object} behavior - Behavior specification
   * @returns {Object} Application interface
   */
  _createInterface(structure, behavior) {
    const interface = {};
    
    // Add exported methods to interface
    if (behavior.exports && behavior.methods) {
      for (const methodName of behavior.exports) {
        if (structure.methods[methodName]) {
          interface[methodName] = async (...args) => {
            const context = {
              structure,
              base: this.base,
              globals: this.globalScope
            };
            
            return structure.methods[methodName](context, ...args);
          };
        }
      }
    }
    
    // Add event triggering to interface
    interface.trigger = async (eventName, eventData) => {
      return this.eventSystem.trigger(structure.id, eventName, {
        structure,
        eventData,
        base: this.base,
        globals: this.globalScope
      });
    };
    
    return interface;
  }
 }

 /**
 * Script Engine for Behavior Model
 * Compiles and executes scripts
 */
 class ScriptEngine {
  /**
   * Create a new script engine
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.sandbox = config.sandbox !== false;
    this.enabledApis = config.enabledApis || ['math', 'json', 'date', 'string'];
    this.disabledGlobals = config.disabledGlobals || ['process', 'require', 'module', 'eval'];
  }
  
  /**
   * Compile a script into a function
   * @param {string} code - Script code
   * @returns {function} Compiled function
   */
  compile(code) {
    if (typeof code === 'function') {
      return code;  // Already a function
    }
    
    // Validate code
    this._validateCode(code);
    
    // Create function using the code
    try {
      return new Function('context', ...this._extractParams(code), code);
    } catch (error) {
      throw new Error(`Script compilation error: ${error.message}`);
    }
  }
  
  /**
   * Execute a compiled script
   * @param {function} script - Compiled script
   * @param {Object} context - Execution context
   * @param {...*} args - Script arguments
   * @returns {*} Script result
   */
  execute(script, context, ...args) {
    if (typeof script !== 'function') {
      throw new Error('Invalid script: must be a function');
    }
    
    // Prepare sandbox if enabled
    if (this.sandbox) {
      context = this._createSandbox(context);
    }
    
    // Execute the script
    try {
      return script(context, ...args);
    } catch (error) {
      throw new Error(`Script execution error: ${error.message}`);
    }
  }
  
  /**
   * Validate script code
   * @private
   * @param {string} code - Script code
   */
  _validateCode(code) {
    if (typeof code !== 'string') {
      throw new Error('Invalid code: must be a string');
    }
    
    // Check for disallowed constructs
    for (const disallowed of this.disabledGlobals) {
      if (code.includes(disallowed)) {
        throw new Error(`Disallowed construct in code: ${disallowed}`);
      }
    }
    
    // Advanced validation would use a JavaScript parser
    // For the reference implementation, this simple check is sufficient
  }
  
  /**
   * Extract parameter names from function code
   * @private
   * @param {string} code - Function code
   * @returns {string[]} Parameter names
   */
  _extractParams(code) {
    // Simple regex to extract parameter names
    const match = code.match(/^\s*function\s*\(([^)]*)\)/);
    if (match) {
      return match[1].split(',').map(p => p.trim()).filter(p => p.length > 0);
    }
    
    return [];
  }
  
  /**
   * Create a sandbox for script execution
   * @private
   * @param {Object} context - Execution context
   * @returns {Object} Sandboxed context
   */
  _createSandbox(context) {
    // Create a restricted context
    const sandbox = {
      ...context,
      console: {
        log: (...args) => console.log('[ScriptEngine]', ...args),
        warn: (...args) => console.warn('[ScriptEngine]', ...args),
        error: (...args) => console.error('[ScriptEngine]', ...args)
      }
    };
    
    // Add enabled APIs
    if (this.enabledApis.includes('math')) {
      sandbox.Math = Math;
    }
    
    if (this.enabledApis.includes('json')) {
      sandbox.JSON = JSON;
    }
    
    if (this.enabledApis.includes('date')) {
      sandbox.Date = Date;
    }
    
    if (this.enabledApis.includes('string')) {
      sandbox.String = String;
    }
    
    return sandbox;
  }
 }

 /**
 * Event System for Behavior Model
 * Manages event registration and triggering
 */
 class EventSystem {
  /**
   * Create a new event system
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.handlers = new Map();
    this.maxHandlers = config.maxHandlers || 100;
  }
  
  /**
   * Register an event handler
   * @param {string} objectId - Object ID
   * @param {string} eventName - Event name
   * @param {function} handler - Event handler
   * @returns {EventSystem} This event system for chaining
   */
  registerHandler(objectId, eventName, handler) {
    const key = `${objectId}:${eventName}`;
    
    if (!this.handlers.has(key)) {
      this.handlers.set(key, []);
    }
    
    const handlers = this.handlers.get(key);
    
    // Check for handler limit
    if (handlers.length >= this.maxHandlers) {
      throw new Error(`Maximum number of handlers (${this.maxHandlers}) reached for ${key}`);
    }
    
    handlers.push(handler);
    
    return this;
  }
  
  /**
   * Unregister event handlers
   * @param {string} objectId - Object ID
   * @param {string} eventName - Event name
   * @param {function} [handler] - Specific handler to unregister
   * @returns {boolean} True if handlers were removed
   */
  unregisterHandler(objectId, eventName, handler = null) {
    const key = `${objectId}:${eventName}`;
    
    if (!this.handlers.has(key)) {
      return false;
    }
    
    if (handler === null) {
      // Remove all handlers
      this.handlers.delete(key);
      return true;
    }
    
    // Remove specific handler
    const handlers = this.handlers.get(key);
    const initialLength = handlers.length;
    
    for (let i = handlers.length - 1; i >= 0; i--) {
      if (handlers[i] === handler) {
        handlers.splice(i, 1);
      }
    }
    
    // Clean up empty arrays
    if (handlers.length === 0) {
      this.handlers.delete(key);
    }
    
    return initialLength > handlers.length;
  }
  
  /**
   * Trigger an event
   * @param {string} objectId - Object ID
   * @param {string} eventName - Event name
   * @param {Object} context - Event context
   * @returns {Promise<Array>} Array of handler results
   */
  async trigger(objectId, eventName, context) {
    const key = `${objectId}:${eventName}`;
    
    if (!this.handlers.has(key)) {
      return [];
    }
    
    const handlers = this.handlers.get(key);
    const results = [];
    
    // Add event information to context
    const eventContext = {
      ...context,
      event: {
        name: eventName,
        target: objectId,
        timestamp: Date.now()
      }
    };
    
    // Execute handlers
    for (const handler of handlers) {
      try {
        results.push(await handler(eventContext));
      } catch (error) {
        console.error(`Error in event handler for ${key}:`, error);
        results.push({ error: error.message });
      }
    }
    
    return results;
  }
 }

 /**
 * Framework Model for Base3
 * Manages styling and layout
 */
 class FrameworkModel {
  /**
   * Create a new framework model
   * @param {Base3} base - Base3 instance
   * @param {Object} config - Configuration options
   */
  constructor(base, config = {}) {
    this.base = base;
    this.styleEngine = new StyleEngine(config.style || {});
    this.layouts = new Map();
    
    // Initialize standard layouts
    this._initializeLayouts();
  }
  
  /**
   * Initialize standard layouts
   * @private
   */
  _initializeLayouts() {
    // Standard flow layout
    this.registerLayout('flow', {
      apply: (container, children) => {
        if (!container.style) {
          container.style = {};
        }
        
        container.style.display = 'flex';
        container.style.flexDirection = 'column';
        
        return container;
      }
    });
    
    // Grid layout
    this.registerLayout('grid', {
      apply: (container, children, options = {}) => {
        if (!container.style) {
          container.style = {};
        }
        
        container.style.display = 'grid';
        container.style.gridTemplateColumns = options.columns || 'repeat(1, 1fr)';
        container.style.gridTemplateRows = options.rows || 'auto';
        container.style.gridGap = options.gap || '0';
        
        return container;
      }
    });
    
    // Flex layout
    this.registerLayout('flex', {
      apply: (container, children, options = {}) => {
        if (!container.style) {
          container.style = {};
        }
        
        container.style.display = 'flex';
        container.style.flexDirection = options.direction || 'row';
        container.style.justifyContent = options.justify || 'flex-start';
        container.style.alignItems = options.align || 'stretch';
        container.style.flexWrap = options.wrap || 'nowrap';
        
        return container;
      }
    });
  }
  
  /**
   * Register a layout
   * @param {string} name - Layout name
   * @param {Object} layout - Layout object
   * @returns {FrameworkModel} This framework model for chaining
   */
  registerLayout(name, layout) {
    if (typeof layout.apply !== 'function') {
      throw new Error(`Layout must implement apply method`);
    }
    
    this.layouts.set(name, layout);
    return this;
  }
  
  /**
   * Apply framework to structure
   * @param {Object} structure - Structure to style
   * @param {Object} framework - Framework specification
   * @returns {Promise<Object>} Styled structure
   */
  async applyToStructure(structure, framework) {
    if (!framework) {
      return structure;
    }
    
    // Create a copy of the structure
    const result = JSON.parse(JSON.stringify(structure));
    
    // Apply styles
    if (framework.styles) {
      this._applyStylesToNode(result, framework.styles);
    }
    
    // Apply layouts
    if (framework.layouts) {
      this._applyLayoutsToNode(result, framework.layouts);
    }
    
    return result;
  }
  
  /**
   * Apply styles to a node
   * @private
   * @param {Object} node - Node to style
   * @param {Object} styles - Style definitions
   */
  _applyStylesToNode(node, styles) {
    // Apply style to current node
    if (styles.default) {
      node.style = this.styleEngine.applyStyle(node.style || {}, styles.default);
    }
    
    // Apply style by node type
    if (node.type && styles[node.type]) {
      node.style = this.styleEngine.applyStyle(node.style || {}, styles[node.type]);
    }
    
    // Apply style by node ID
    if (node.id && styles[`#${node.id}`]) {
      node.style = this.styleEngine.applyStyle(node.style || {}, styles[`#${node.id}`]);
    }
    
    // Apply style by node class
    if (node.class) {
      const classes = node.class.split(' ');
      for (const cls of classes) {
        if (styles[`.${cls}`]) {
          node.style = this.styleEngine.applyStyle(node.style || {}, styles[`.${cls}`]);
        }
      }
    }
    
    // Apply styles to children
    if (node.children) {
      for (const child of node.children) {
        this._applyStylesToNode(child, styles);
      }
    }
  }
  
  /**
   * Apply layouts to a node
   * @private
   * @param {Object} node - Node to apply layout to
   * @param {Object} layouts - Layout definitions
   */
  _applyLayoutsToNode(node, layouts) {
    // Apply layout to current node
    if (node.id && layouts[node.id]) {
      const layoutConfig = layouts[node.id];
      const layout = this.layouts.get(layoutConfig.type);
      
      if (layout) {
        layout.apply(node, node.children, layoutConfig.options);
      }
    }
    
    // Apply layout by node type
    if (node.type && layouts[node.type]) {
      const layoutConfig = layouts[node.type];
      const layout = this.layouts.get(layoutConfig.type);
      
      if (layout) {
        layout.apply(node, node.children, layoutConfig.options);
      }
    }
    
    // Apply layouts to children
    if (node.children) {
      for (const child of node.children) {
        this._applyLayoutsToNode(child, layouts);
      }
    }
  }
 }

 /**
 * Style Engine for Framework Model
 * Manages style application
 */
 class StyleEngine {
  /**
   * Create a new style engine
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.preprocessors = new Map();
    this.propertyHandlers = new Map();
    
    // Initialize standard preprocessors
    this._initializePreprocessors();
    
    // Initialize standard property handlers
    this._initializePropertyHandlers();
  }
  
  /**
   * Initialize standard preprocessors
   * @private
   */
  _initializePreprocessors() {
    // Variables preprocessor
    this.registerPreprocessor('variables', (style, context) => {
      // Replace variables in style properties
      for (const [key, value] of Object.entries(style)) {
        if (typeof value === 'string' && value.includes('var(')) {
          style[key] = this._replaceVariables(value, context.variables || {});
        }
      }
      
      return style;
    });
    
    // Units preprocessor
    this.registerPreprocessor('units', (style, context) => {
      // Add default units to numeric properties
      const unitProperties = [
        'width', 'height', 'margin', 'padding', 'top', 'right', 'bottom', 'left',
        'font-size', 'line-height', 'border-width'
      ];
      
      for (const prop of unitProperties) {
        if (style[prop] !== undefined && typeof style[prop] === 'number') {
          style[prop] = `${style[prop]}px`;
        }
      }
      
      return style;
    });
  }
  
  /**
   * Initialize standard property handlers
   * @private
   */
  _initializePropertyHandlers() {
    // Margin handler
    this.registerPropertyHandler('margin', (value, style) => {
      if (typeof value === 'string') {
        // Parse CSS-style margin
        const parts = value.split(/\s+/);
        
        if (parts.length === 1) {
          style['margin-top'] = parts[0];
          style['margin-right'] = parts[0];
          style['margin-bottom'] = parts[0];
          style['margin-left'] = parts[0];
        } else if (parts.length === 2) {
          style['margin-top'] = parts[0];
          style['margin-right'] = parts[1];
          style['margin-bottom'] = parts[0];
          style['margin-left'] = parts[1];
        } else if (parts.length === 3) {
          style['margin-top'] = parts[0];
          style['margin-right'] = parts[1];
          style['margin-bottom'] = parts[2];
          style['margin-left'] = parts[1];
        } else if (parts.length === 4) {
          style['margin-top'] = parts[0];
          style['margin-right'] = parts[1];
          style['margin-bottom'] = parts[2];
          style['margin-left'] = parts[3];
        }
      } else {
        style['margin-top'] = value;
        style['margin-right'] = value;
        style['margin-bottom'] = value;
        style['margin-left'] = value;
      }
    });
    
    // Padding handler
    this.registerPropertyHandler('padding', (value, style) => {
      if (typeof value === 'string') {
        // Parse CSS-style padding
        const parts = value.split(/\s+/);
        
        if (parts.length === 1) {
          style['padding-top'] = parts[0];
          style['padding-right'] = parts[0];
          style['padding-bottom'] = parts[0];
          style['padding-left'] = parts[0];
        } else if (parts.length === 2) {
          style['padding-top'] = parts[0];
          style['padding-right'] = parts[1];
          style['padding-bottom'] = parts[0];
          style['padding-left'] = parts[1];
        } else if (parts.length === 3) {
          style['padding-top'] = parts[0];
          style['padding-right'] = parts[1];
          style['padding-bottom'] = parts[2];
          style['padding-left'] = parts[1];
        } else if (parts.length === 4) {
          style['padding-top'] = parts[0];
          style['padding-right'] = parts[1];
          style['padding-bottom'] = parts[2];
          style['padding-left'] = parts[3];
        }
      } else {
        style['padding-top'] = value;
        style['padding-right'] = value;
        style['padding-bottom'] = value;
        style['padding-left'] = value;
      }
    });
  }
  
  /**
   * Register a style preprocessor
   * @param {string} name - Preprocessor name
   * @param {function} processor - Preprocessor function
   * @returns {StyleEngine} This style engine for chaining
   */
  registerPreprocessor(name, processor) {
    this.preprocessors.set(name, processor);
    return this;
  }
  
  /**
   * Register a property handler
   * @param {string} property - Property name
   * @param {function} handler - Property handler
   * @returns {StyleEngine} This style engine for chaining
   */
  registerPropertyHandler(property, handler) {
    this.propertyHandlers.set(property, handler);
    return this;
  }
  
  /**
   * Apply a style to a node
   * @param {Object} baseStyle - Base style object
   * @param {Object} newStyle - Style to apply
   * @param {Object} context - Style context
   * @returns {Object} Combined style
   */
  applyStyle(baseStyle = {}, newStyle = {}, context = {}) {
    // Create a copy of the base style
    const result = { ...baseStyle };
    
    // Apply preprocessors to new style
    let processedStyle = { ...newStyle };
    
    for (const processor of this.preprocessors.values()) {
      processedStyle = processor(processedStyle, context);
    }
    
    // Apply property handlers
    for (const [prop, value] of Object.entries(processedStyle)) {
      if (this.propertyHandlers.has(prop)) {
        // Use property handler
        this.propertyHandlers.get(prop)(value, result);
      } else {
        // Direct assignment
        result[prop] = value;
      }
    }
    
    return result;
  }
  
  /**
   * Replace variable references in a string
   * @private
   * @param {string} value - String with variable references
   * @param {Object} variables - Variable definitions
   * @returns {string} String with variables replaced
   */
  _replaceVariables(value, variables) {
    return value.replace(/var\(--([a-zA-Z0-9-_]+)(?:,\s*([^)]+))?\)/g, (match, name, fallback) => {
      if (variables[name] !== undefined) {
        return variables[name];
      }
      return fallback || '';
    });
  }
 }

 /**
 * Structure Model for Base3
 * Manages component structure
 */
 class StructureModel {
  /**
   * Create a new structure model
   * @param {Base3} base - Base3 instance
   * @param {Object} config - Configuration options
   */
  constructor(base, config = {}) {
    this.base = base;
    this.componentTypes = new Map();
    this.templates = new Map();
    
    // Initialize standard component types
    this._initializeComponentTypes();
  }
  
  /**
   * Initialize standard component types
   * @private
   */
  _initializeComponentTypes() {
    // Container component
    this.registerComponentType('container', {
      create: (spec) => ({
        type: 'container',
        id: spec.id,
        class: spec.class,
        children: [],
        style: spec.style || {}
      })
    });
    
    // Text component
    this.registerComponentType('text', {
      create: (spec) => ({
        type: 'text',
        id: spec.id,
        class: spec.class,
        content: spec.content || '',
        style: spec.style || {}
      })
    });
    
    // Input component
    this.registerComponentType('input', {
      create: (spec) => ({
        type: 'input',
        id: spec.id,
        class: spec.class,
        inputType: spec.inputType || 'text',
        value: spec.value || '',
        placeholder: spec.placeholder || '',
        style: spec.style || {}
      })
    });
    
    // Button component
    this.registerComponentType('button', {
      create: (spec) => ({
        type: 'button',
        id: spec.id,
        class: spec.class,
        label: spec.label || '',
        disabled: spec.disabled || false,
        style: spec.style || {}
      })
    });
    
    // Image component
    this.registerComponentType('image', {
      create: (spec) => ({
        type: 'image',
        id: spec.id,
        class: spec.class,
        src: spec.src || '',
        alt: spec.alt || '',
        style: spec.style || {}
      })
    });
  }
  
  /**
   * Register a component type
   * @param {string} name - Component type name
   * @param {Object} factory - Component factory
   * @returns {StructureModel} This structure model for chaining
   */
  registerComponentType(name, factory) {
    if (typeof factory.create !== 'function') {
      throw new Error(`Component factory must implement create method`);
    }
    
    this.componentTypes.set(name, factory);
    return this;
  }
  
  /**
   * Register a template
   * @param {string} name - Template name
   * @param {Object} template - Template specification
   * @returns {StructureModel} This structure model for chaining
   */
  registerTemplate(name, template) {
    this.templates.set(name, template);
    return this;
  }
  
  /**
   * Create structure from specification
   * @param {Object} spec - Structure specification
   * @returns {Promise<Object>} Created structure
   */
  async createFromSpec(spec) {
    if (!spec) {
      throw new Error('Invalid structure specification');
    }
    
    // Check if using a template
    if (typeof spec === 'string' && this.templates.has(spec)) {
      return this.createFromSpec(this.templates.get(spec));
    }
    
    // Create the component
    const result = await this._createComponent(spec);
    
    // Process children if any
    if (spec.children && Array.isArray(spec.children)) {
      result.children = [];
      
      for (const childSpec of spec.children) {
        const child = await this.createFromSpec(childSpec);
        result.children.push(child);
      }
    }
    
    return result;
  }
  
  /**
   * Create a component
   * @private
   * @param {Object} spec - Component specification
   * @returns {Promise<Object>} Created component
   */
  async _createComponent(spec) {
    // Validate component type
    if (!spec.type) {
      throw new Error('Component specification must include a type');
    }
    
    if (!this.componentTypes.has(spec.type)) {
      throw new Error(`Unknown component type: ${spec.type}`);
    }
    
    // Create component using factory
    const factory = this.componentTypes.get(spec.type);
    return factory.create(spec);
  }
 }

 /**
 * Security Manager for Base2
 * Manages access control and security policies
 */
 class SecurityManager {
  /**
   * Create a new security manager
   * @param {Base2} kernel - Kernel instance
   * @param {Object} config - Configuration options
   */
  constructor(kernel, config = {}) {
    this.kernel = kernel;
    this.bundles = new Map();
    this.policies = new Map();
    this.depthCalculator = new ManifoldDepthCalculator();
    this.mda = new ManifoldDepthAttention();
    
    // Initialize standard security policies
    this._initializePolicies(config);
  }
  
  /**
   * Initialize standard security policies
   * @private
   * @param {Object} config - Configuration options
   */
  _initializePolicies(config) {
    // System policy - system bundles have elevated privileges
    this.registerPolicy('system', {
      validate: async (bundleId, action) => {
        // System bundles start with "system."
        if (bundleId.startsWith('system.')) {
          return {
            allowed: true,
            reason: 'System bundle'
          };
        }
        
        return null;  // Not applicable
      }
    });
    
    // Manifest policy - check bundle manifest for allowed actions
    this.registerPolicy('manifest', {
      validate: async (bundleId, action) => {
        const bundle = this.bundles.get(bundleId);
        if (!bundle) return null;  // Not applicable
        
        // Check if action is in the declared interfaces
        if (bundle.meta.interfaces && bundle.meta.interfaces[action]) {
          return {
            allowed: true,
            reason: 'Action in manifest'
          };
        }
        
        return {
          allowed: false,
          reason: 'Action not in manifest'
        };
      }
    });
    
    // Depth policy - check manifold depth for access
    this.registerPolicy('depth', {
      validate: async (bundleId, action) => {
        const bundle = this.bundles.get(bundleId);
        if (!bundle) return null;  // Not applicable
        
        // Get bundle depth
        const bundleDepth = this.depthCalculator.calculate(bundle);
        
        // System actions require deep manifold depth
        if (action.startsWith('system.') && bundleDepth < 3.0) {
          return {
            allowed: false,
            reason: 'Insufficient depth for system action'
          };
        }
        
        // Resource actions require moderate depth
        if (action.startsWith('resource.') && bundleDepth < 2.0) {
          return {
            allowed: false,
            reason: 'Insufficient depth for resource action'
          };
        }
        
        return null;  // Not applicable
      }
    });
  }
  
  /**
   * Register a security policy
   * @param {string} name - Policy name
   * @param {Object} policy - Policy object
   * @returns {SecurityManager} This manager for chaining
   */
  registerPolicy(name, policy) {
    if (typeof policy.validate !== 'function') {
      throw new Error(`Policy must implement validate method`);
    }
    
    this.policies.set(name, policy);
    return this;
  }
  
  /**
   * Register a bundle with the security manager
   * @param {Object} bundle - Application bundle
   * @returns {Promise<Object>} Registration result
   */
  async registerBundle(bundle) {
    // Store bundle security information
    this.bundles.set(bundle.id, {
      id: bundle.id,
      meta: bundle.meta,
      depth: this._calculateBundleDepth(bundle),
      registered: Date.now(),
      permissions: bundle.meta.permissions || {}
    });
    
    return {
      id: bundle.id,
      registered: true
    };
  }
  
  /**
   * Unregister a bundle from the security manager
   * @param {string} bundleId - Bundle ID
   * @returns {Promise<boolean>} True if unregistered
   */
  async unregisterBundle(bundleId) {
    return this.bundles.delete(bundleId);
  }
  
  /**
   * Verify access permission
   * @param {string} bundleId - Bundle ID
   * @param {string} action - Action to verify
   * @returns {Promise<Object>} Verification result
   */
  async verifyAccess(bundleId, action) {
    // Check if bundle is registered
    if (!this.bundles.has(bundleId)) {
      throw new Error(`Bundle not registered: ${bundleId}`);
    }
    
    const bundle = this.bundles.get(bundleId);
    
    // Apply security policies
    let allowed = true;
    let reason = 'Default allow';
    
    for (const [name, policy] of this.policies.entries()) {
      try {
        const result = await policy.validate(bundleId, action);
        
        // Skip non-applicable policies
        if (!result) continue;
        
        // If any policy explicitly denies, access is denied
        if (!result.allowed) {
          allowed = false;
          reason = `Policy '${name}': ${result.reason}`;
          break;
        }
        
        // Record reason for latest allowing policy
        if (result.allowed) {
          reason = `Policy '${name}': ${result.reason}`;
        }
      } catch (error) {
        console.error(`Error in security policy ${name}:`, error);
      }
    }
    
    // If access is denied, throw error
    if (!allowed) {
      throw new Error(`Access denied: ${reason}`);
    }
    
    // Return verification result
    return {
      bundleId,
      action,
      allowed,
      reason
    };
  }
  
  /**
   * Create a security boundary at a specified depth
   * @param {number} depth - Boundary depth
   * @param {Object} options - Boundary options
   * @returns {Object} Boundary object
   */
  createBoundary(depth, options = {}) {
    return {
      depth,
      name: options.name || `boundary-${depth}`,
      
      // Verifier function
      verifier: (source) => {
        const sourceDepth = this.depthCalculator.calculate(source);
        return sourceDepth >= depth;
      },
      
      // Attention calculator
      attention: (source) => {
        const sourceDepth = this.depthCalculator.calculate(source);
        return this.mda.calculateAttention(
          { depth: sourceDepth },
          { depth }
        );
      }
    };
  }
  
  /**
   * Verify a component can cross a boundary
   * @param {Object} component - Component to check
   * @param {Object} boundary - Security boundary
   * @returns {Object} Verification result
   */
  verifyBoundaryCrossing(component, boundary) {
    const componentDepth = this.depthCalculator.calculate(component);
    
    // Component can cross boundary if its depth is sufficient
    const permitted = componentDepth >= boundary.depth;
    
    if (!permitted) {
      throw new Error(
        `Boundary violation: component at depth ${componentDepth} ` +
        `cannot cross boundary at depth ${boundary.depth}`
      );
    }
    
    return {
      permitted,
      componentDepth,
      boundaryDepth: boundary.depth,
      attention: boundary.attention(component)
    };
  }
  
  /**
   * Calculate bundle security depth
   * @private
   * @param {Object} bundle - Application bundle
   * @returns {number} Bundle depth
   */
  _calculateBundleDepth(bundle) {
    // System bundles have maximum depth
    if (bundle.id.startsWith('system.')) {
      return 5.0;
    }
    
    // Calculate depth based on bundle characteristics
    let depth = 1.0;  // Default depth
    
    // Add depth for signing
    if (bundle.meta.signed) {
      depth += 1.0;
    }
    
    // Add depth for verification
    if (bundle.meta.verified) {
      depth += 1.0;
    }
    
    // Add depth for interface completeness
    if (bundle.meta.interfaces) {
      const interfaceCount = Object.keys(bundle.meta.interfaces).length;
      depth += Math.min(1.0, interfaceCount / 5);
    }
    
    // System interfaces add depth
    if (bundle.meta.interfaces && 
        Object.keys(bundle.meta.interfaces).some(i => i.startsWith('system.'))) {
      depth += 1.0;
    }
    
    return depth;
  }
 }

 /**
 * Manifold Depth Calculator
 * Calculates manifold depth for objects
 */
 class ManifoldDepthCalculator {
  /**
   * Create a new manifold depth calculator
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.defaultDepth = config.defaultDepth || 1.0;
    this.depthCache = new Map();
  }
  
  /**
   * Calculate manifold depth for an object
   * @param {Object} obj - Object to calculate depth for
   * @returns {number} Manifold depth
   */
  calculate(obj) {
    if (!obj) return 0;
    
    // Use object ID as cache key if available
    const cacheKey = obj.id || JSON.stringify(obj);
    
    // Check cache
    if (this.depthCache.has(cacheKey)) {
      return this.depthCache.get(cacheKey);
    }
    
    // Calculate depth based on object type
    let depth;
    
    if (typeof obj === 'number') {
      depth = this._calculateNumberDepth(obj);
    } else if (typeof obj === 'string') {
      depth = this._calculateStringDepth(obj);
    } else if (Array.isArray(obj)) {
      depth = this._calculateArrayDepth(obj);
    } else if (obj instanceof MultivectorRepresentation) {
      depth = this._calculateMultivectorDepth(obj);
    } else if (typeof obj === 'object') {
      depth = this._calculateObjectDepth(obj);
    } else {
      depth = this.defaultDepth;
    }
    
    // Cache the result
    if (cacheKey) {
      this.depthCache.set(cacheKey, depth);
    }
    
    return depth;
  }
  
  /**
   * Calculate depth for a number
   * @private
   * @param {number} num - Number to calculate depth for
   * @returns {number} Manifold depth
   */
  _calculateNumberDepth(num) {
    // Integers have higher depth than floating point
    if (Number.isInteger(num)) {
      return 1.0 + Math.min(1.0, Math.abs(num) / 1000);
    }
    
    return 0.8 + Math.min(0.5, Math.abs(num) / 1000);
  }
  
  /**
   * Calculate depth for a string
   * @private
   * @param {string} str - String to calculate depth for
   * @returns {number} Manifold depth
   */
  _calculateStringDepth(str) {
    // Empty strings have zero depth
    if (!str) return 0;
    
    // System identifiers have higher depth
    if (str.startsWith('system.')) {
      return 3.0;
    }
    
    // Calculate entropy as a measure of depth
    const entropy = this._calculateStringEntropy(str);
    
    // Scale entropy to a reasonable depth range
    return 0.5 + Math.min(1.5, entropy / 4);
  }
  
  /**
   * Calculate entropy of a string
   * @private
   * @param {string} str - String to calculate entropy for
   * @returns {number} Shannon entropy
   */
  _calculateStringEntropy(str) {
    const len = str.length;
    const counts = new Map();
    
    // Count character frequencies
    for (let i = 0; i < len; i++) {
      const char = str[i];
      counts.set(char, (counts.get(char) || 0) + 1);
    }
    
    // Calculate Shannon entropy
    let entropy = 0;
    for (const count of counts.values()) {
      const p = count / len;
      entropy -= p * Math.log2(p);
    }
    
    return entropy;
  }
  
  /**
   * Calculate depth for an array
   * @private
   * @param {Array} arr - Array to calculate depth for
   * @returns {number} Manifold depth
   */
  _calculateArrayDepth(arr) {
    if (arr.length === 0) return 0.5;
    
    // Calculate average element depth
    let totalDepth = 0;
    
    for (const item of arr) {
      totalDepth += this.calculate(item);
    }
    
    const avgDepth = totalDepth / arr.length;
    
    // Arrays add 0.3 to their contents' depth, up to 3.0 total
    return Math.min(3.0, avgDepth + 0.3);
  }
  
  /**
   * Calculate depth for a multivector
   * @private
   * @param {MultivectorRepresentation} mv - Multivector to calculate depth for
   * @returns {number} Manifold depth
   */
  _calculateMultivectorDepth(mv) {
    // Higher grades have higher depth
    let maxGrade = 0;
    let maxGradeNorm = 0;
    
    for (let i = 0; i < mv.bladeCount; i++) {
      if (Math.abs(mv.components[i]) > 1e-10) {
        const grade = mv._gradeOfIndex(i);
        if (grade > maxGrade) {
          maxGrade = grade;
          maxGradeNorm = Math.abs(mv.components[i]);
        }
      }
    }
    
    // Calculate coherence
    const coherence = CoherenceMetrics.normalizedCoherence(mv);
    
    // Combine grade and coherence for depth
    return 1.0 + maxGrade * 0.5 + coherence;
  }
  
  /**
   * Calculate depth for an object
   * @private
   * @param {Object} obj - Object to calculate depth for
   * @returns {number} Manifold depth
   */
  _calculateObjectDepth(obj) {
    // Check for explicit depth property
    if (typeof obj.depth === 'number') {
      return obj.depth;
    }
    
    // Check for depth calculation function
    if (typeof obj.calculateDepth === 'function') {
      try {
        return obj.calculateDepth();
      } catch (error) {
        console.error("Error calculating object depth:", error);
      }
    }
    
    // Calculate based on object properties
    const keys = Object.keys(obj);
    
    if (keys.length === 0) return 0.5;
    
    // Simple calculation based on number of properties and nesting
    let depthScore = Math.min(1.0, keys.length / 10);
    
    // Check for nesting
    let nestedObjects = 0;
    for (const key of keys) {
      if (typeof obj[key] === 'object' && obj[key] !== null) {
        nestedObjects++;
      }
    }
    
    depthScore += Math.min(1.0, nestedObjects / 5);
    
    // Special handling for common properties that indicate depth
    if (obj.id && typeof obj.id === 'string') {
      if (obj.id.startsWith('system.')) {
        depthScore += 1.0;
      }
    }
    
    if (obj.secure === true) {
      depthScore += 0.5;
    }
    
    if (obj.permission === 'admin' || obj.role === 'admin') {
      depthScore += 1.0;
    }
    
    return 1.0 + depthScore;
  }
 }

 /**
 * Manifold Depth Attention
 * Determines interaction strength based on manifold depth
 */
 class ManifoldDepthAttention {
  /**
   * Create a new manifold depth attention calculator
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.alpha = config.alpha || 1.0;
    this.depthCalculator = new ManifoldDepthCalculator(config.depth || {});
  }
  
  /**
   * Calculate attention between components
   * @param {Object} component1 - First component
   * @param {Object} component2 - Second component
   * @returns {number} Attention value
   */
  calculateAttention(component1, component2) {
    // Get manifold depths
    const depth1 = component1.depth || this.depthCalculator.calculate(component1);
    const depth2 = component2.depth || this.depthCalculator.calculate(component2);
    
    // Calculate attention using exponential decay with depth difference
    return Math.exp(-this.alpha * Math.abs(depth1 - depth2));
  }
  
  /**
   * Calculate multi-head attention
   * @param {Object} component1 - First component
   * @param {Object} component2 - Second component
   * @param {number} heads - Number of attention heads
   * @returns {number[]} Attention values for each head
   */
  calculateMultiHeadAttention(component1, component2, heads = 4) {
    const attentions = [];
    
    // Get manifold depths
    const depth1 = component1.depth || this.depthCalculator.calculate(component1);
    const depth2 = component2.depth || this.depthCalculator.calculate(component2);
    const depthDiff = Math.abs(depth1 - depth2);
    
    // Calculate attention with different alpha values
    for (let i = 0; i < heads; i++) {
      const headAlpha = this.alpha * (0.5 + i * 0.5);
      attentions.push(Math.exp(-headAlpha * depthDiff));
    }
    
    return attentions;
  }
  
  /**
   * Check if access is permitted based on depth
   * @param {Object} source - Source component
   * @param {Object} target - Target component
   * @returns {boolean} True if access is permitted
   */
  checkAccess(source, target) {
    // Get manifold depths
    const sourceDepth = source.depth || this.depthCalculator.calculate(source);
    const targetDepth = target.depth || this.depthCalculator.calculate(target);
    
    // Access is permitted if source is at least as deep as target
    return sourceDepth >= targetDepth;
  }
  
  /**
   * Calculate attention matrix for multiple components
   * @param {Object[]} components - Components to calculate attention for
   * @returns {number[][]} Attention matrix
   */
  calculateAttentionMatrix(components) {
    const n = components.length;
    const matrix = new Array(n);
    
    // Precalculate depths
    const depths = components.map(c => 
      c.depth || this.depthCalculator.calculate(c)
    );
    
    // Calculate attention for each pair
    for (let i = 0; i < n; i++) {
      matrix[i] = new Array(n);
      
      for (let j = 0; j < n; j++) {
        if (i === j) {
          matrix[i][j] = 1.0;  // Self-attention is 1.0
        } else {
          const depthDiff = Math.abs(depths[i] - depths[j]);
          matrix[i][j] = Math.exp(-this.alpha * depthDiff);
        }
      }
    }
    
    return matrix;
  }
 }

 /**
 * Resource Manager for Base2
 * Handles resource allocation and optimization
 */
 class ResourceManager {
  /**
   * Create a new resource manager
   * @param {Base2} kernel - Kernel instance
   * @param {Object} config - Configuration options
   */
  constructor(kernel, config = {}) {
    this.kernel = kernel;
    this.allocations = new Map();
    this.resourcePools = new Map();
    this.coherenceOptimizer = new ResourceCoherenceOptimizer(config.optimization || {});
    
    // Initialize resource pools
    this._initializeResourcePools(config);
  }
  
  /**
   * Initialize standard resource pools
   * @private
   * @param {Object} config - Configuration options
   */
  _initializeResourcePools(config) {
    // CPU resources
    this.registerResourcePool('cpu', {
      total: config.cpu?.total || 100,
      available: config.cpu?.available || 100,
      
      allocate: async (amount) => {
        const pool = this.resourcePools.get('cpu');
        
        if (pool.available < amount) {
          throw new Error(`Insufficient CPU resources: ${pool.available} < ${amount}`);
        }
        
        pool.available -= amount;
        
        return {
          id: `cpu-${Date.now()}-${Math.floor(Math.random() * 1000)}`,
          amount,
          resourceType: 'cpu'
        };
      },
      
      release: async (resource) => {
        const pool = this.resourcePools.get('cpu');
        pool.available += resource.amount;
        return true;
      }
    });
    
    // Memory resources
    this.registerResourcePool('memory', {
      total: config.memory?.total || 1024,
      available: config.memory?.available || 1024,
      
      allocate: async (amount) => {
        const pool = this.resourcePools.get('memory');
        
        if (pool.available < amount) {
          throw new Error(`Insufficient memory resources: ${pool.available} < ${amount}`);
        }
        
        pool.available -= amount;
        
        return {
          id: `memory-${Date.now()}-${Math.floor(Math.random() * 1000)}`,
          amount,
          resourceType: 'memory'
        };
      },
      
      release: async (resource) => {
        const pool = this.resourcePools.get('memory');
        pool.available += resource.amount;
        return true;
      }
    });
    
    // Storage resources
    this.registerResourcePool('storage', {
      total: config.storage?.total || 10240,
      available: config.storage?.available || 10240,
      
      allocate: async (amount) => {
        const pool = this.resourcePools.get('storage');
        
        if (pool.available < amount) {
          throw new Error(`Insufficient storage resources: ${pool.available} < ${amount}`);
        }
        
        pool.available -= amount;
        
        return {
          id: `storage-${Date.now()}-${Math.floor(Math.random() * 1000)}`,
          amount,
          resourceType: 'storage'
        };
      },
      
      release: async (resource) => {
        const pool = this.resourcePools.get('storage');
        pool.available += resource.amount;
        return true;
      }
    });
  }
  
  /**
   * Register a resource pool
   * @param {string} type - Resource type
   * @param {Object} pool - Resource pool object
   * @returns {ResourceManager} This manager for chaining
   */
  registerResourcePool(type, pool) {
    if (!pool.allocate || !pool.release) {
      throw new Error(`Resource pool must implement allocate and release methods`);
    }
    
    this.resourcePools.set(type, pool);
    return this;
  }
  
  /**
   * Allocate resources for application execution
   * @param {Object} bundle - Application bundle
   * @param {string} action - Action to execute
   * @returns {Promise<Object>} Allocation result
   */
  async allocateForExecution(bundle, action) {
    // Determine resource requirements
    const requirements = this._determineRequirements(bundle, action);
    
    // Optimize allocation for coherence
    const allocation = await this.coherenceOptimizer.optimize(requirements, {
      bundle,
      action,
      pools: this.resourcePools
    });
    
    // Perform actual allocation
    const resources = {};
    const usage = {};
    
    for (const [type, amount] of Object.entries(allocation)) {
      const pool = this.resourcePools.get(type);
      if (!pool) {
        throw new Error(`Resource pool not found: ${type}`);
      }
      
      const allocated = await pool.allocate(amount);
      resources[type] = allocated;
      usage[type] = amount;
    }
    
    // Generate allocation ID
    const id = `alloc-${Date.now()}-${Math.floor(Math.random() * 10000)}`;
    
    // Record allocation
    this.allocations.set(id, {
      id,
      resources,
      usage,
      timestamp: Date.now(),
      bundle: bundle.id,
      action
    });
    
    return {
      id,
      resources,
      usage
    };
  }
  
  /**
   * Release allocated resources
   * @param {string} allocationId - Allocation ID
   * @returns {Promise<boolean>} True if released
   */
  async release(allocationId) {
    const allocation = this.allocations.get(allocationId);
    if (!allocation) {
      throw new Error(`Allocation not found: ${allocationId}`);
    }
    
    // Release each resource
    for (const [type, resource] of Object.entries(allocation.resources)) {
      const pool = this.resourcePools.get(type);
      await pool.release(resource);
    }
    
    // Remove allocation record
    this.allocations.delete(allocationId);
    
    return true;
  }
  
  /**
   * Get resource usage statistics
   * @returns {Object} Resource usage stats
   */
  getResourceUsage() {
    const usage = {};
    
    for (const [type, pool] of this.resourcePools.entries()) {
      usage[type] = {
        total: pool.total,
        available: pool.available,
        used: pool.total - pool.available,
        utilization: ((pool.total - pool.available) / pool.total) * 100
      };
    }
    
    return usage;
  }
  
  /**
   * Determine resource requirements for an action
   * @private
   * @param {Object} bundle - Application bundle
   * @param {string} action - Action to execute
   * @returns {Object} Resource requirements
   */
  _determineRequirements(bundle, action) {
    // Check for explicit requirements in bundle metadata
    if (bundle.meta.resources && bundle.meta.resources[action]) {
      return bundle.meta.resources[action];
    }
    
    // Default requirements based on action complexity
    const actionFn = bundle.actions[action];
    const complexity = this._estimateComplexity(actionFn);
    
    return {
      cpu: 5 + complexity * 5,      // 5-25 CPU units
      memory: 10 + complexity * 20, // 10-110 memory units
      storage: 5 + complexity * 10  // 5-55 storage units
    };
  }
  
  /**
   * Estimate complexity of an action
   * @private
   * @param {function} actionFn - Action function
   * @returns {number} Complexity estimate (0-4)
   */
  _estimateComplexity(actionFn) {
    // In a reference implementation, we can't analyze function code
    // In a real implementation, this would analyze the function to estimate complexity
    
    // For this reference, just return a random complexity between 0 and 4
    return Math.floor(Math.random() * 5);
  }
 }

 /**
 * Resource Coherence Optimizer
 * Optimizes resource allocation for coherence
 */
 class ResourceCoherenceOptimizer {
  /**
   * Create a new resource coherence optimizer
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.strategies = new Map();
    this.defaultStrategy = config.defaultStrategy || 'balanced';
    
    // Initialize standard optimization strategies
    this._initializeStrategies();
  }
  
  /**
   * Initialize standard optimization strategies
   * @private
   */
  _initializeStrategies() {
    // Minimal strategy - allocate minimum resources
    this.registerStrategy('minimal', async (requirements, context) => {
      const result = {};
      
      for (const [type, amount] of Object.entries(requirements)) {
        // Allocate minimum resources (80% of requested)
        result[type] = Math.ceil(amount * 0.8);
      }
      
      return result;
    });
    
    // Balanced strategy - allocate requested resources
    this.registerStrategy('balanced', async (requirements, context) => {
      return { ...requirements };
    });
    
    // Performance strategy - allocate extra resources
    this.registerStrategy('performance', async (requirements, context) => {
      const result = {};
      
      for (const [type, amount] of Object.entries(requirements)) {
        // Allocate extra resources (120% of requested)
        result[type] = Math.ceil(amount * 1.2);
      }
      
      return result;
    });
    
    // Adaptive strategy - allocate based on system load
    this.registerStrategy('adaptive', async (requirements, context) => {
      const result = {};
      
      for (const [type, amount] of Object.entries(requirements)) {
        const pool = context.pools.get(type);
        if (!pool) {
          result[type] = amount;
          continue;
        }
        
        // Calculate utilization
        const utilization = (pool.total - pool.available) / pool.total;
        
        if (utilization > 0.8) {
          // High load - allocate minimum
          result[type] = Math.ceil(amount * 0.8);
        } else if (utilization > 0.5) {
          // Medium load - allocate requested
          result[type] = amount;
        } else {
          // Low load - allocate extra
          result[type] = Math.ceil(amount * 1.2);
        }
      }
      
      return result;
    });
  }
  
  /**
   * Register an optimization strategy
   * @param {string} name - Strategy name
   * @param {function} strategyFn - Strategy function
   * @returns {ResourceCoherenceOptimizer} This optimizer for chaining
   */
  registerStrategy(name, strategyFn) {
    this.strategies.set(name, strategyFn);
    return this;
  }
  
  /**
   * Optimize resource allocation
   * @param {Object} requirements - Resource requirements
   * @param {Object} context - Optimization context
   * @returns {Promise<Object>} Optimized allocation
   */
  async optimize(requirements, context) {
    // Determine which strategy to use
    let strategyName = this.defaultStrategy;
    
    // Check if bundle specifies a preferred strategy
    if (context.bundle.meta.resourceStrategy) {
      strategyName = context.bundle.meta.resourceStrategy;
    }
    
    // Check if strategy exists
    if (!this.strategies.has(strategyName)) {
      strategyName = this.defaultStrategy;
    }
    
    // Apply the strategy
    const strategy = this.strategies.get(strategyName);
    const allocation = await strategy(requirements, context);
    
    // Validate allocation
    this._validateAllocation(allocation, context);
    
    return allocation;
  }
  
  /**
   * Validate an allocation
   * @private
   * @param {Object} allocation - Resource allocation
   * @param {Object} context - Optimization context
   */
  _validateAllocation(allocation, context) {
    // Check that all required resource types are allocated
    for (const type of Object.keys(context.pools)) {
      if (!allocation[type]) {
        allocation[type] = 1;  // Default minimum allocation
      }
    }
    
    // Check for sufficient resources
    for (const [type, amount] of Object.entries(allocation)) {
      const pool = context.pools.get(type);
      if (!pool) continue;
      
      if (amount > pool.available) {
        throw new Error(`Insufficient ${type} resources: ${pool.available} < ${amount}`);
      }
    }
  }
 }

 /**
 * Application Manager for Base2
 * Handles application bundles
 */
 class ApplicationManager {
  /**
   * Create a new application manager
   * @param {Base2} kernel - Kernel instance
   * @param {Object} config - Configuration options
   */
  constructor(kernel, config = {}) {
    this.kernel = kernel;
    this.bundles = new Map();
    this.coherenceValidator = new ApplicationCoherenceValidator(config.validation || {});
    this.storage = config.storage || this._createDefaultStorage();
  }
  
  /**
   * Create default storage backend
   * @private
   * @returns {Object} Storage interface
   */
  _createDefaultStorage() {
    // In-memory storage for reference implementation
    const bundleStorage = new Map();
    
    return {
      load: async (bundleId) => {
        if (bundleStorage.has(bundleId)) {
          return bundleStorage.get(bundleId);
        }
        return null;
      },
      
      store: async (bundleId, bundleData) => {
        bundleStorage.set(bundleId, bundleData);
        return true;
      },
      
      remove: async (bundleId) => {
        return bundleStorage.delete(bundleId);
      },
      
      list: async () => {
        return Array.from(bundleStorage.keys());
      }
    };
  }
  
  /**
   * Get application bundle by ID
   * @param {string} bundleId - Bundle ID
   * @param {boolean} skipValidation - Skip coherence validation
   * @returns {Promise<Object>} Application bundle
   */
  async getBundle(bundleId, skipValidation = false) {
    // Check in-memory cache
    if (this.bundles.has(bundleId)) {
      return this.bundles.get(bundleId);
    }
    
    // Load from storage
    try {
      const bundleData = await this.storage.load(bundleId);
      
      if (!bundleData) {
        return null;
      }
      
      // Parse and validate bundle
      const bundle = this._parseBundle(bundleData);
      
      // Validate bundle coherence
      if (!skipValidation) {
        const coherence = await this.coherenceValidator.validateBundle(bundle);
        if (coherence < this.kernel.config.coherenceThreshold) {
          throw new Error(
            `Bundle ${bundleId} failed coherence validation: ${coherence}`
          );
        }
      }
      
      // Cache bundle
      this.bundles.set(bundleId, bundle);
      
      return bundle;
    } catch (error) {
      throw new Error(`Failed to load bundle ${bundleId}: ${error.message}`);
    }
  }
  
  /**
   * Create a new application bundle
   * @param {Object} bundleSpec - Bundle specification
   * @returns {Promise<Object>} Created bundle
   */
  async createBundle(bundleSpec) {
    // Validate bundle specification
    this._validateBundleSpec(bundleSpec);
    
    // Create bundle object
    const bundle = new ApplicationBundle(bundleSpec.id, bundleSpec);
    
    // Validate bundle coherence
    const coherence = await this.coherenceValidator.validateBundle(bundle);
    if (coherence < this.kernel.config.coherenceThreshold) {
      throw new Error(
        `Bundle ${bundleSpec.id} failed coherence validation: ${coherence}`
      );
    }
    
    // Store bundle
    await this.storage.store(bundleSpec.id, this._serializeBundle(bundle));
    
    // Cache bundle
    this.bundles.set(bundleSpec.id, bundle);
    
    return bundle;
  }
  
  /**
   * Remove an application bundle
   * @param {string} bundleId - Bundle ID
   * @returns {Promise<boolean>} True if removed
   */
  async removeBundle(bundleId) {
    // Remove from cache
    this.bundles.delete(bundleId);
    
    // Remove from storage
    return await this.storage.remove(bundleId);
  }
  
  /**
   * Execute an action within an application bundle
   * @param {Object} bundle - Application bundle
   * @param {string} action - Action to execute
   * @param {Object} parameters - Action parameters
   * @param {Object} resources - Allocated resources
   * @returns {Promise<*>} Action result
   */
  async executeAction(bundle, action, parameters, resources) {
    // Validate action exists
    if (!bundle.actions || !bundle.actions[action]) {
      throw new Error(`Action not found in bundle: ${action}`);
    }
    
    // Prepare execution context
    const context = this._createExecutionContext(bundle, resources);
    
    // Execute the action
    return await bundle.actions[action](parameters, context);
  }
  
  /**
   * Create execution context for an action
   * @private
   * @param {Object} bundle - Application bundle
   * @param {Object} resources - Allocated resources
   * @returns {Object} Execution context
   */
  _createExecutionContext(bundle, resources) {
    return {
      bundleId: bundle.id,
      meta: bundle.meta,
      resources: bundle.invariant.resources,
      state: bundle.variant.state,
      schemas: bundle.invariant.schemas,
      allocatedResources: resources,
      
      // System services
      services: {
        storage: {
          get: async (key) => {
            const fullKey = `${bundle.id}:${key}`;
            const storageService = this.kernel.systemManager.getService('storage');
            return await storageService.read(fullKey);
          },
          put: async (key, value) => {
            const fullKey = `${bundle.id}:${key}`;
            const storageService = this.kernel.systemManager.getService('storage');
            return await storageService.write(fullKey, value);
          },
          remove: async (key) => {
            const fullKey = `${bundle.id}:${key}`;
            const storageService = this.kernel.systemManager.getService('storage');
            return await storageService.delete(fullKey);
          },
          list: async (prefix) => {
            const fullPrefix = `${bundle.id}:${prefix}`;
            const storageService = this.kernel.systemManager.getService('storage');
            const keys = await storageService.list(fullPrefix);
            
            // Remove bundle ID prefix from keys
            return keys.map(key => key.substring(bundle.id.length + 1));
          }
        },
        coherence: {
          measure: async () => {
            const coherenceService = this.kernel.systemManager.getService('coherence');
            return await coherenceService.measure();
          },
          validate: async (obj, threshold) => {
            const coherenceService = this.kernel.systemManager.getService('coherence');
            return await coherenceService.validate(obj, threshold);
          }
        }
      }
    };
  }
  
  /**
   * Parse a bundle from serialized data
   * @private
   * @param {Object} bundleData - Serialized bundle data
   * @returns {Object} Application bundle
   */
  _parseBundle(bundleData) {
    if (!bundleData || !bundleData.id) {
      throw new Error("Invalid bundle data");
    }
    
    // Create bundle object from serialized data
    return new ApplicationBundle(bundleData.id, bundleData);
  }
  
  /**
   * Serialize a bundle for storage
   * @private
   * @param {Object} bundle - Application bundle
   * @returns {Object} Serialized bundle
   */
  _serializeBundle(bundle) {
    // Basic serialization for reference implementation
    // In a real implementation, this would handle code serialization better
    
    return {
      id: bundle.id,
      meta: bundle.meta,
      invariant: {
        resources: bundle.invariant.resources,
        schemas: bundle.invariant.schemas,
        // Code is not easily serializable, so we'd handle this differently
        // in a real implementation
        codeSignatures: Object.keys(bundle.invariant.code || {})
      },
      variant: {
        preferences: bundle.variant.preferences
      }
    };
  }
  
  /**
   * Validate a bundle specification
   * @private
   * @param {Object} spec - Bundle specification
   */
  _validateBundleSpec(spec) {
    if (!spec.id) {
      throw new Error("Bundle must have an ID");
    }
    
    if (!spec.name) {
      throw new Error("Bundle must have a name");
    }
    
    if (!spec.version) {
      throw new Error("Bundle must have a version");
    }
    
    // Validate bundle ID format
    if (!/^[a-zA-Z0-9._-]+$/.test(spec.id)) {
      throw new Error("Bundle ID must contain only alphanumeric characters, dots, hyphens, and underscores");
    }
    
    // Validate code if present
    if (spec.code) {
      if (typeof spec.code !== 'object') {
        throw new Error("Bundle code must be an object");
      }
      
      // Validate code functions
      for (const [name, fn] of Object.entries(spec.code)) {
        if (typeof fn !== 'function') {
          throw new Error(`Bundle code '${name}' must be a function`);
        }
      }
    }
  }
 }

 /**
 * Application Coherence Validator
 * Validates coherence of application bundles
 */
 class ApplicationCoherenceValidator {
  /**
   * Create a new application coherence validator
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.rules = new Map();
    
    // Initialize standard validation rules
    this._initializeRules();
  }
  
  /**
   * Initialize standard validation rules
   * @private
   */
  _initializeRules() {
    // Meta section validation
    this.registerRule('meta', (bundle) => {
      if (!bundle.meta) return 0;
      
      let score = 0;
      
      // Required fields
      if (bundle.meta.id) score += 0.2;
      if (bundle.meta.name) score += 0.2;
      if (bundle.meta.version) score += 0.2;
      
      // Optional fields
      if (bundle.meta.description) score += 0.1;
      if (bundle.meta.interfaces && Object.keys(bundle.meta.interfaces).length > 0) score += 0.2;
      if (bundle.meta.dependencies && Array.isArray(bundle.meta.dependencies)) score += 0.1;
      
      return score;
    });
    
    // Invariant section validation
    this.registerRule('invariant', (bundle) => {
      if (!bundle.invariant) return 0;
      
      let score = 0;
      
      // Code
      if (bundle.invariant.code && typeof bundle.invariant.code === 'object') {
        score += 0.3;
        
        // Check if code contains functions
        const functions = Object.values(bundle.invariant.code).filter(v => typeof v === 'function');
        if (functions.length > 0) score += 0.2;
      }
      
      // Resources
      if (bundle.invariant.resources && typeof bundle.invariant.resources === 'object') {
        score += 0.2;
      }
      
      // Schemas
      if (bundle.invariant.schemas && typeof bundle.invariant.schemas === 'object') {
        score += 0.2;
      }
      
      // Transforms
      if (bundle.invariant.transforms && typeof bundle.invariant.transforms === 'object') {
        score += 0.1;
      }
      
      return score;
    });
    
    // Variant section validation
    this.registerRule('variant', (bundle) => {
      if (!bundle.variant) return 0;
      
      let score = 0;
      
      // State
      if (bundle.variant.state && typeof bundle.variant.state === 'object') {
        score += 0.3;
      }
      
      // Cache
      if (bundle.variant.cache && typeof bundle.variant.cache === 'object') {
        score += 0.3;
      }
      
      // Preferences
      if (bundle.variant.preferences && typeof bundle.variant.preferences === 'object') {
        score += 0.4;
      }
      
      return score;
    });
    
    // Actions validation
    this.registerRule('actions', (bundle) => {
      if (!bundle.actions) return 0;
      
      let score = 0;
      
      // Check if actions object exists
      if (typeof bundle.actions === 'object') {
        score += 0.3;
        
        // Check if it has any functions
        const actionCount = Object.values(bundle.actions).filter(v => typeof v === 'function').length;
        if (actionCount > 0) {
          score += 0.7 * Math.min(1, actionCount / 3);  // Scale up to 3 actions
        }
      }
      
      return score;
    });
    
    // Interface coherence - check if declared interfaces match actions
    this.registerRule('interfaces', (bundle) => {
      if (!bundle.meta || !bundle.meta.interfaces || !bundle.actions) return 0;
      
      let score = 0;
      const interfaces = bundle.meta.interfaces;
      const actions = bundle.actions;
      
      // Count matching interfaces
      let matchCount = 0;
      let totalInterfaces = Object.keys(interfaces).length;
      
      if (totalInterfaces === 0) return 0.5;  // Neutral score if no interfaces declared
      
      for (const name of Object.keys(interfaces)) {
        if (typeof actions[name] === 'function') {
          matchCount++;
        }
      }
      
      // Calculate match ratio
      score = matchCount / totalInterfaces;
      
      return score;
    });
  }
  
  /**
   * Register a validation rule
   * @param {string} name - Rule name
   * @param {function} ruleFn - Rule function
   * @returns {ApplicationCoherenceValidator} This validator for chaining
   */
  registerRule(name, ruleFn) {
    this.rules.set(name, ruleFn);
    return this;
  }
  
  /**
   * Validate coherence of an application bundle
   * @param {Object} bundle - Application bundle
   * @returns {Promise<number>} Coherence value
   */
  async validateBundle(bundle) {
    if (!bundle) return 0;
    
    const scores = [];
    const weights = [];
    
    // Apply all rules
    for (const [name, ruleFn] of this.rules.entries()) {
      try {
        const score = ruleFn(bundle);
        scores.push(score);
        
        // Set weights based on rule importance
        let weight = 1.0;
        
        switch (name) {
          case 'meta':
            weight = 1.0;
            break;
          case 'invariant':
            weight = 1.5;
            break;
          case 'variant':
            weight = 0.8;
            break;
          case 'actions':
            weight = 2.0;
            break;
          case 'interfaces':
            weight = 1.2;
            break;
        }
        
        weights.push(weight);
      } catch (error) {
        console.error(`Error in validation rule ${name}:`, error);
        scores.push(0);
        weights.push(1.0);
      }
    }
    
    // Calculate weighted average
    let totalWeight = 0;
    let weightedSum = 0;
    
    for (let i = 0; i < scores.length; i++) {
      weightedSum += scores[i] * weights[i];
      totalWeight += weights[i];
    }
    
    return totalWeight > 0 ? weightedSum / totalWeight : 0;
  }
 }

 /**
 * Application Bundle
 * Represents a deployable application package
 */
 class ApplicationBundle {
  /**
   * Create a new application bundle
   * @param {string} id - Bundle ID
   * @param {Object} spec - Bundle specification
   */
  constructor(id, spec) {
    this.id = id;
    
    // Meta component: contextual information
    this.meta = {
      id: spec.id || id,
      name: spec.name,
      version: spec.version,
      description: spec.description,
      dependencies: spec.dependencies || [],
      interfaces: spec.interfaces || {}
    };
    
    // Invariant component: static code and resources
    this.invariant = {
      code: spec.code || {},
      resources: spec.resources || {},
      schemas: spec.schemas || {},
      transforms: spec.transforms || {}
    };
    
    // Variant component: dynamic state
    this.variant = {
      state: {},
      cache: {},
      preferences: spec.preferences || {}
    };
    
    // Actions provided by the bundle
    this.actions = {};
    
    // Validators for result coherence
    this.validators = {};
    
    // Initialize actions from code
    this._initializeActions();
  }
  
  /**
   * Initialize callable actions from code
   * @private
   */
  _initializeActions() {
    for (const [name, fn] of Object.entries(this.invariant.code)) {
      if (typeof fn === 'function') {
        this.actions[name] = async (params, context) => {
          // Create action-specific context
          const actionContext = {
            ...context,
            meta: this.meta,
            resources: this.invariant.resources,
            state: this.variant.state,
            schemas: this.invariant.schemas
          };
          
          // Execute the action function
          return await fn(params, actionContext);
        };
      }
    }
  }
  
  /**
   * Get bundle interface for external use
   * @returns {Object} External interface
   */
  getInterface() {
    const interface = {};
    
    // Expose only the declared interfaces
    for (const [name, spec] of Object.entries(this.meta.interfaces)) {
      if (this.actions[name]) {
        interface[name] = async (params) => this.actions[name](params, {});
      }
    }
    
    return interface;
  }
  
  /**
   * Register a result validator
   * @param {string} actionName - Action name
   * @param {function} validatorFn - Validator function
   * @returns {ApplicationBundle} This bundle for chaining
   */
  registerValidator(actionName, validatorFn) {
    this.validators[actionName] = validatorFn;
    return this;
  }
 }

 /**
 * System Manager for Base2
 * Provides core services
 */
 class SystemManager {
  /**
   * Create a new system manager
   * @param {Base2} kernel - Kernel instance
   * @param {Object} config - Configuration options
   */
  constructor(kernel, config = {}) {
    this.kernel = kernel;
    this.services = new Map();
    this.coherenceMonitor = new CoherenceMonitor(config.coherence || {});
    
    // Initialize core services
    this._initializeServices();
  }
  
  /**
   * Initialize core services
   * @private
   */
  _initializeServices() {
    // Memory service
    this.registerService('memory', {
      allocate: (size) => this.initializeMemory(size),
      free: (memory) => { /* memory cleanup logic */ },
      stats: () => ({
        available: 1024 * 1024 * 1024,  // Mock 1GB available
        used: 256 * 1024 * 1024         // Mock 256MB used
      })
    });
    
    // Storage service
    this.registerService('storage', {
      read: async (key) => {
        // Mock storage implementation
        return { key, value: `mock-value-for-${key}` };
      },
      write: async (key, value) => {
        // Mock storage implementation
        return { key, stored: true };
      },
      delete: async (key) => {
        // Mock storage implementation
        return { key, deleted: true };
      },
      list: async (prefix) => {
        // Mock storage implementation
        return [
          `${prefix}-1`,
          `${prefix}-2`,
          `${prefix}-3`
        ];
      }
    });
    
    // Coherence service
    this.registerService('coherence', {
      measure: async () => this.measureCoherence(),
      validate: async (obj, threshold = 0.8) => {
        const coherence = await this.coherenceMonitor.measureObject(obj);
        return {
          coherence,
          valid: coherence >= threshold,
          threshold
        };
      }
    });
    
    // Scheduler service
    this.registerService('scheduler', {
      schedule: async (task, options) => {
        // Mock scheduler implementation
        return {
          id: `task-${Date.now()}`,
          scheduled: true,
          executionTime: Date.now() + (options.delay || 0)
        };
      },
      cancel: async (taskId) => {
        // Mock cancel implementation
        return { id: taskId, cancelled: true };
      },
      list: async () => {
        // Mock task list
        return [
          { id: 'task-1', status: 'pending' },
          { id: 'task-2', status: 'running' }
        ];
      }
    });
  }
  
  /**
   * Get a system service
   * @param {string} name - Service name
   * @returns {Object} Service object
   */
  getService(name) {
    if (!this.services.has(name)) {
      throw new Error(`Service not found: ${name}`);
    }
    
    return this.services.get(name);
  }
  
  /**
   * Register a system service
   * @param {string} name - Service name
   * @param {Object} service - Service object
   * @returns {SystemManager} This manager for chaining
   */
  registerService(name, service) {
    // Validate service interface
    this._validateService(name, service);
    
    // Add to services
    this.services.set(name, service);
    
    return this;
  }
  
  /**
   * Measure system coherence
   * @returns {Promise<number>} Coherence value
   */
  async measureCoherence() {
    return this.coherenceMonitor.measureGlobal();
  }
  
  /**
   * Initialize memory with Kahan summation for numerical stability
   * @param {number} size - Memory size
   * @returns {Object} Memory object
   */
  initializeMemory(size) {
    let memory = new Float64Array(size);
    let compensation = new Float64Array(size);
    
    return {
      memory,
      compensation,
      
      // Read value
      read: (index) => {
        if (index < 0 || index >= size) {
          throw new Error(`Memory index out of bounds: ${index}`);
        }
        return memory[index];
      },
      
      // Write value with Kahan summation for numerical stability
      write: (index, value) => {
        if (index < 0 || index >= size) {
          throw new Error(`Memory index out of bounds: ${index}`);
        }
        
        // Kahan summation for numerical stability
        const y = value - compensation[index];
        const t = memory[index] + y;
        compensation[index] = (t - memory[index]) - y;
        memory[index] = t;
      },
      
      // Fill range with value
      fill: (value, start = 0, end = size) => {
        if (start < 0 || end > size || start >= end) {
          throw new Error(`Invalid range: ${start}-${end}`);
        }
        
        for (let i = start; i < end; i++) {
          memory[i] = value;
          compensation[i] = 0;
        }
      },
      
      // Get memory size
      size: () => size
    };
  }
  
  /**
   * Validate a service interface
   * @private
   * @param {string} name - Service name
   * @param {Object} service - Service object
   */
  _validateService(name, service) {
    // Basic validation - ensure service is an object
    if (typeof service !== 'object' || service === null) {
      throw new Error(`Invalid service '${name}': must be an object`);
    }
    
    // Validate required methods based on service type
    switch (name) {
      case 'memory':
        this._validateMethods(service, ['allocate', 'free', 'stats']);
        break;
        
      case 'storage':
        this._validateMethods(service, ['read', 'write', 'delete', 'list']);
        break;
        
      case 'coherence':
        this._validateMethods(service, ['measure', 'validate']);
        break;
        
      case 'scheduler':
        this._validateMethods(service, ['schedule', 'cancel', 'list']);
        break;
    }
  }
  
  /**
   * Validate that an object has the required methods
   * @private
   * @param {Object} obj - Object to validate
   * @param {string[]} methods - Required method names
   */
  _validateMethods(obj, methods) {
    for (const method of methods) {
      if (typeof obj[method] !== 'function') {
        throw new Error(`Missing required method: ${method}`);
      }
    }
  }
 }

 /**
 * Coherence Monitor
 * Monitors and measures system coherence
 */
 class CoherenceMonitor {
  /**
   * Create a new coherence monitor
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.samplingRate = config.samplingRate || 0.1;
    this.historySize = config.historySize || 100;
    this.coherenceHistory = [];
    this.componentMonitors = new Map();
    
    // Initialize standard component monitors
    this._initializeComponentMonitors();
  }
  
  /**
   * Initialize standard component monitors
   * @private
   */
  _initializeComponentMonitors() {
    // Resource coherence
    this.registerComponentMonitor('resources', {
      measure: (state) => {
        // If no state available, return perfect coherence
        if (!state || !state.resources) return 1.0;
        
        const resources = state.resources;
        
        // Check for negative resource counts (indicates incoherence)
        let negativeCounts = 0;
        
        for (const [type, resource] of resources.entries()) {
          if (resource.available < 0 || resource.allocated < 0) {
            negativeCounts++;
          }
        }
        
        if (resources.size === 0) return 1.0;
        
        // Scale coherence based on negative counts
        return 1.0 - (negativeCounts / resources.size);
      }
    });
    
    // Memory coherence
    this.registerComponentMonitor('memory', {
      measure: (state) => {
        // If no memory stats available, return perfect coherence
        if (!state || !state.memoryStats) return 1.0;
        
        const { available, used, total } = state.memoryStats;
        
        // Check for memory accounting errors
        if (available + used > total * 1.01) {  // Allow 1% error margin
          return 0.5;  // Significant incoherence
        }
        
        // Memory usage should be within limits
        if (used > total) {
          return 0.0;  // Complete incoherence
        }
        
        // Good coherence
        return 1.0;
      }
    });
  }
  
  /**
   * Register a component monitor
   * @param {string} name - Component name
   * @param {Object} monitor - Component monitor
   * @returns {CoherenceMonitor} This monitor for chaining
   */
  registerComponentMonitor(name, monitor) {
    if (typeof monitor.measure !== 'function') {
      throw new Error(`Component monitor must have a measure function`);
    }
    
    this.componentMonitors.set(name, monitor);
    return this;
  }
  
  /**
   * Measure global system coherence
   * @returns {Promise<number>} Coherence value
   */
  async measureGlobal() {
    // Collect state for coherence measurement
    const state = await this._collectState();
    
    // Measure component coherence
    const componentCoherences = [];
    
    for (const [name, monitor] of this.componentMonitors.entries()) {
      try {
        const coherence = monitor.measure(state);
        componentCoherences.push({ name, coherence });
      } catch (error) {
        console.error(`Error measuring coherence for ${name}:`, error);
        componentCoherences.push({ name, coherence: 0.5 });  // Default to medium coherence on error
      }
    }
    
    // Calculate weighted coherence
    let totalCoherence = 0;
    let weightSum = 0;
    
    for (const component of componentCoherences) {
      let weight = 1.0;
      
      // Assign weights based on importance
      switch (component.name) {
        case 'resources':
          weight = 2.0;
          break;
        case 'memory':
          weight = 1.5;
          break;
      }
      
      totalCoherence += component.coherence * weight;
      weightSum += weight;
    }
    
    // Compute final coherence
    const globalCoherence = weightSum > 0 ? totalCoherence / weightSum : 1.0;
    
    // Add to history
    this.coherenceHistory.push({
      timestamp: Date.now(),
      coherence: globalCoherence,
      components: componentCoherences
    });
    
    // Trim history if needed
    if (this.coherenceHistory.length > this.historySize) {
      this.coherenceHistory = this.coherenceHistory.slice(-this.historySize);
    }
    
    return globalCoherence;
  }
  
  /**
   * Measure coherence of a specific object
   * @param {*} obj - Object to measure
   * @returns {Promise<number>} Coherence value
   */
  async measureObject(obj) {
    if (obj === null || obj === undefined) {
      return 1.0;  // Null/undefined are coherent with themselves
    }
    
    if (typeof obj !== 'object') {
      return 1.0;  // Primitive values are perfectly coherent
    }
    
    // For objects, check internal consistency
    try {
      // Calculate object properties size consistency
      const propertyCoherence = this._calculatePropertyCoherence(obj);
      
      // Check for circular references (decreases coherence)
      const circularCoherence = this._checkCircularReferences(obj) ? 0.7 : 1.0;
      
      // Check type consistency for array elements
      const typeCoherence = Array.isArray(obj) ? this._calculateArrayTypeCoherence(obj) : 1.0;
      
      // Combine coherence measures
      return 0.4 * propertyCoherence + 0.3 * circularCoherence + 0.3 * typeCoherence;
    } catch (error) {
      console.error("Error measuring object coherence:", error);
      return 0.5;  // Default to medium coherence on error
    }
  }
  
  /**
   * Collect system state for coherence measurement
   * @private
   * @returns {Promise<Object>} System state
   */
  async _collectState() {
    // In a real implementation, this would collect actual system state
    // For the reference implementation, we create mock state
    
    return {
      resources: new Map([
        ['cpu', { available: 90, allocated: 10, total: 100 }],
        ['memory', { available: 800, allocated: 200, total: 1000 }],
        ['storage', { available: 9000, allocated: 1000, total: 10000 }]
      ]),
      
      memoryStats: {
        available: 800,
        used: 200,
        total: 1000
      },
      
      // Use sampling to avoid measuring everything
      sampling: this.samplingRate
    };
  }
  
  /**
   * Calculate property coherence for an object
   * @private
   * @param {Object} obj - Object to check
   * @returns {number} Property coherence
   */
  _calculatePropertyCoherence(obj) {
    if (!obj || typeof obj !== 'object') return 1.0;
    
    // Check for property size reasonableness
    const keys = Object.keys(obj);
    
    // Extremely large objects might indicate an issue
    if (keys.length > 10000) return 0.5;
    
    // Check property name patterns
    let unusualNames = 0;
    
    for (const key of keys) {
      // Check for unusual property naming (empty, very long, or non-alphanumeric)
      if (key === '' || key.length > 50 || !/^[a-zA-Z0-9_]+$/.test(key)) {
        unusualNames++;
      }
    }
    
    // Calculate unusual name ratio
    const unusualRatio = keys.length > 0 ? unusualNames / keys.length : 0;
    
    // Higher coherence for fewer unusual names
    return 1.0 - unusualRatio;
  }
  
  /**
   * Check for circular references in an object
   * @private
   * @param {Object} obj - Object to check
   * @returns {boolean} True if circular references found
   */
  _checkCircularReferences(obj) {
    try {
      JSON.stringify(obj);
      return false;  // No circular references
    } catch (error) {
      if (error.message.includes('circular')) {
        return true;  // Circular reference detected
      }
      // Other error
      return false;
    }
  }
  
  /**
   * Calculate type coherence for array elements
   * @private
   * @param {Array} arr - Array to check
   * @returns {number} Type coherence
   */
  _calculateArrayTypeCoherence(arr) {
    if (!Array.isArray(arr) || arr.length === 0) return 1.0;
    
    // Check if array elements have consistent types
    const types = new Map();
    
    for (const item of arr) {
      const type = typeof item;
      types.set(type, (types.get(type) || 0) + 1);
    }
    
    // Perfect coherence if all elements have the same type
    if (types.size === 1) return 1.0;
    
    // Calculate dominant type ratio
    let maxCount = 0;
    for (const count of types.values()) {
      maxCount = Math.max(maxCount, count);
    }
    
    // Higher coherence for more consistent types
    return maxCount / arr.length;
  }
 }

 /**
 * Base 2: Kernel (Orchestrator) Implementation
 * Functions as the orchestrator of the system
 */
 class Base2 extends Base1 {
  /**
   * Create a new Base2 instance
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    super(config);
    
    // Create system manager for core services
    this.systemManager = new SystemManager(this, config.system || {});
    
    // Create application manager for bundle handling
    this.applicationManager = new ApplicationManager(this, config.application || {});
    
    // Create resource manager for allocation
    this.resourceManager = new ResourceManager(this, config.resource || {});
    
    // Create security manager for access control
    this.securityManager = new SecurityManager(this, config.security || {});
  }
  
  /**
   * Execute an application
   * @param {string} bundleId - Bundle ID to execute
   * @param {string} action - Action to execute
   * @param {Object} parameters - Action parameters
   * @returns {Promise<Object>} Execution result
   */
  async executeApplication(bundleId, action, parameters = {}) {
    // Verify security first
    await this.securityManager.verifyAccess(bundleId, action);
    
    // Get application bundle
    const bundle = await this.applicationManager.getBundle(bundleId);
    if (!bundle) {
      throw new Error(`Bundle not found: ${bundleId}`);
    }
    
    // Allocate resources
    const resources = await this.resourceManager.allocateForExecution(bundle, action);
    
    try {
      // Execute the application action
      const result = await this.applicationManager.executeAction(
        bundle, action, parameters, resources
      );
      
      // Validate coherence of the result
      const coherence = await this._validateResultCoherence(bundle, action, result);
      
      return {
        result,
        coherence,
        resources: resources.usage
      };
    } finally {
      // Release resources
      await this.resourceManager.release(resources.id);
    }
  }
  
  /**
   * Validate result coherence
   * @private
   * @param {Object} bundle - Application bundle
   * @param {string} action - Action that was executed
   * @param {*} result - Action result
   * @returns {Promise<number>} Coherence value
   */
  async _validateResultCoherence(bundle, action, result) {
    // Check if the bundle has a coherence validator for this action
    const bundleValidator = bundle.validators && bundle.validators[action];
    if (bundleValidator) {
      return bundleValidator(result);
    }
    
    // Use default coherence validation
    return this.computeCoherence();
  }
  
  /**
   * System call implementation for Base 3
   * @param {string} name - System call name
   * @param {Object} parameters - System call parameters
   * @returns {Promise<Object>} System call result
   */
  async syscall(name, parameters = {}) {
    // System calls are implemented as internal applications
    return this.executeApplication(
      'system.core.syscalls', 
      name, 
      parameters
    );
  }
  
  /**
   * Install a bundle
   * @param {Object} bundleSpec - Bundle specification
   * @returns {Promise<Object>} Installation result
   */
  async installBundle(bundleSpec) {
    // Verify bundle specification
    if (!bundleSpec.id) {
      throw new Error("Bundle must have an ID");
    }
    
    // Check for existing bundle
    const existingBundle = await this.applicationManager.getBundle(bundleSpec.id, true);
    if (existingBundle) {
      throw new Error(`Bundle already exists: ${bundleSpec.id}`);
    }
    
    // Create and register the bundle
    const bundle = await this.applicationManager.createBundle(bundleSpec);
    
    // Register bundle with security manager
    await this.securityManager.registerBundle(bundle);
    
    return {
      id: bundle.id,
      installed: true,
      interfaces: Object.keys(bundle.meta.interfaces || {})
    };
  }
  
  /**
   * Uninstall a bundle
   * @param {string} bundleId - Bundle ID to uninstall
   * @returns {Promise<Object>} Uninstallation result
   */
  async uninstallBundle(bundleId) {
    // Check if bundle exists
    const bundle = await this.applicationManager.getBundle(bundleId, true);
    if (!bundle) {
      throw new Error(`Bundle not found: ${bundleId}`);
    }
    
    // Unregister bundle from security manager
    await this.securityManager.unregisterBundle(bundleId);
    
    // Remove bundle from application manager
    await this.applicationManager.removeBundle(bundleId);
    
    return {
      id: bundleId,
      uninstalled: true
    };
  }
 }

 /**
 * Enhanced Representation Model for Base1
 * Extends Base0 representation with additional capabilities
 */
 class EnhancedRepresentationModel {
  /**
   * Create a new enhanced representation model
   * @param {Object} config - Configuration options
   * @param {RepresentationModel} baseModel - Base representation model
   */
  constructor(config = {}, baseModel) {
    this.baseModel = baseModel;
    this.formats = new Map();
    this.transformers = new Map();
    
    // Copy formats from base model
    for (const [name, format] of baseModel.formats.entries()) {
      this.formats.set(name, format);
    }
    
    // Initialize enhanced formats
    this._initializeFormats(config);
  }
  
  /**
   * Initialize enhanced formats
   * @private
   * @param {Object} config - Configuration options
   */
  _initializeFormats(config) {
    // Add structured format (for nested data)
    this.registerFormat('structured', {
      format: data => {
        if (typeof data !== 'object' || data === null) {
          return this.baseModel.represent(data, 'standard');
        }
        
        // Format nested objects with indentation
        const formatNested = (obj, indent = 0) => {
          const spaces = ' '.repeat(indent);
          
          if (Array.isArray(obj)) {
            const items = obj.map(item => 
              typeof item === 'object' && item !== null ? 
                `\n${spaces}  ${formatNested(item, indent + 2)}` : 
                String(item)
            );
            
            return `[${items.join(',')}${items.length > 0 ? `\n${spaces}` : ''}]`;
          } else {
            const entries = Object.entries(obj).map(([key, value]) => {
              const valueStr = typeof value === 'object' && value !== null ?
                formatNested(value, indent + 2) :
                String(value);
              
              return `\n${spaces}  "${key}": ${valueStr}`;
            });
            
            return `{${entries.join(',')}${entries.length > 0 ? `\n${spaces}` : ''}}`;
          }
        };
        
        return formatNested(data);
      }
    });
    
    // Add HTML format (for web display)
    this.registerFormat('html', {
      format: data => {
        if (typeof data !== 'object' || data === null) {
          return `<pre>${this.baseModel.represent(data, 'standard')}</pre>`;
        }
        
        // Convert to HTML representation
        const toHtml = (obj) => {
          if (Array.isArray(obj)) {
            const items = obj.map(item => 
              `<li>${typeof item === 'object' && item !== null ? toHtml(item) : String(item)}</li>`
            );
            return `<ul>${items.join('')}</ul>`;
          } else {
            const entries = Object.entries(obj).map(([key, value]) => {
              const valueHtml = typeof value === 'object' && value !== null ?
                toHtml(value) :
                String(value);
              
              return `<tr><td><strong>${key}</strong></td><td>${valueHtml}</td></tr>`;
            });
            
            return `<table border="1">${entries.join('')}</table>`;
          }
        };
        
        return toHtml(data);
      }
    });
    
    // Add XML format
    this.registerFormat('xml', {
      format: data => {
        if (typeof data !== 'object' || data === null) {
          return `<value>${this._escapeXml(String(data))}</value>`;
        }
        
        // Convert to XML representation
        const toXml = (obj, rootTag = 'root') => {
          if (Array.isArray(obj)) {
            const items = obj.map((item, index) => 
              typeof item === 'object' && item !== null ?
                toXml(item, 'item') :
                `<item>${this._escapeXml(String(item))}</item>`
            );
            return `<${rootTag}>${items.join('')}</${rootTag}>`;
          } else {
            const entries = Object.entries(obj).map(([key, value]) => {
              if (typeof value === 'object' && value !== null) {
                return toXml(value, key);
              } else {
                return `<${key}>${this._escapeXml(String(value))}</${key}>`;
              }
            });
            
            return `<${rootTag}>${entries.join('')}</${rootTag}>`;
          }
        };
        
        return `<?xml version="1.0" encoding="UTF-8"?>\n${toXml(data)}`;
      }
    });
    
    // Register transformers
    this.registerTransformer('minify', data => {
      if (typeof data === 'object' && data !== null) {
        return JSON.stringify(data);
      }
      return String(data);
    });
    
    this.registerTransformer('prettify', data => {
      if (typeof data === 'object' && data !== null) {
        return JSON.stringify(data, null, 2);
      }
      return String(data);
    });
  }
  
  /**
   * Register a format
   * @param {string} name - Format name
   * @param {Object} format - Format object
   * @returns {EnhancedRepresentationModel} This model for chaining
   */
  registerFormat(name, format) {
    this.formats.set(name, format);
    return this;
  }
  
  /**
   * Register a transformer
   * @param {string} name - Transformer name
   * @param {function} fn - Transformer function
   * @returns {EnhancedRepresentationModel} This model for chaining
   */
  registerTransformer(name, fn) {
    this.transformers.set(name, fn);
    return this;
  }
  
  /**
   * Represent data using specified format and transformers
   * @param {*} data - Data to represent
   * @param {string|Object} options - Format name or options object
   * @returns {string} Representation
   */
  represent(data, options = {}) {
    // Handle string shorthand for format
    if (typeof options === 'string') {
      options = { format: options };
    }
    
    const { 
      format = this.baseModel.defaultFormat,
      transform = null
    } = options;
    
    // Apply transformer if specified
    let processedData = data;
    if (transform && this.transformers.has(transform)) {
      processedData = this.transformers.get(transform)(data);
    }
    
    // Use enhanced format if available, otherwise fall back to base model
    if (this.formats.has(format)) {
      return this.formats.get(format).format(processedData);
    } else {
      return this.baseModel.represent(processedData, format);
    }
  }
  
  /**
   * Escape special XML characters
   * @private
   * @param {string} str - String to escape
   * @returns {string} Escaped string
   */
  _escapeXml(str) {
    return str.replace(/[&<>"']/g, match => {
      switch (match) {
        case '&': return '&amp;';
        case '<': return '&lt;';
        case '>': return '&gt;';
        case '"': return '&quot;';
        case "'": return '&apos;';
        default: return match;
      }
    });
  }
 }

 /**
 * Interaction Model for Base1
 * Manages state changes and persistence
 */
 class InteractionModel {
  /**
   * Create a new interaction model
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.stateManagers = new Map();
    this.transactionLog = [];
    this.currentTransaction = null;
    this.maxTransactionLog = config.maxTransactionLog || 100;
    
    // Initialize standard state managers
    this._initializeStateManagers();
  }
  
  /**
   * Initialize standard state managers
   * @private
   */
  _initializeStateManagers() {
    // Resource state manager
    this.registerStateManager('resource', {
      state: {
        resources: new Map(),
        allocations: new Map()
      },
      
      applyChange: (operation, parameters, result) => {
        const state = this.stateManagers.get('resource').state;
        
        switch (operation.name) {
          case 'allocate': {
            const { resourceType, amount } = parameters;
            
            // Update resource state
            if (!state.resources.has(resourceType)) {
              state.resources.set(resourceType, {
                available: 1000,  // Mock initial capacity
                allocated: 0
              });
            }
            
            const resource = state.resources.get(resourceType);
            
            // Check capacity
            if (resource.available < amount) {
              throw new Error(`Insufficient ${resourceType} resources: ${resource.available} < ${amount}`);
            }
            
            // Update resource state
            resource.available -= amount;
            resource.allocated += amount;
            
            // Record allocation
            state.allocations.set(result.id, {
              id: result.id,
              resourceType,
              amount,
              timestamp: Date.now()
            });
            
            return {
              type: 'resourceAllocation',
              resourceType,
              amount,
              id: result.id
            };
          }
          
          case 'release': {
            const { resourceId } = parameters;
            
            // Get allocation
            const allocation = state.allocations.get(resourceId);
            if (!allocation) {
              throw new Error(`Allocation not found: ${resourceId}`);
            }
            
            // Update resource state
            const resource = state.resources.get(allocation.resourceType);
            resource.available += allocation.amount;
            resource.allocated -= allocation.amount;
            
            // Remove allocation
            state.allocations.delete(resourceId);
            
            return {
              type: 'resourceRelease',
              resourceType: allocation.resourceType,
              amount: allocation.amount,
              id: resourceId
            };
          }
          
          default:
            return null;
        }
      }
    });
  }
  
  /**
   * Register a state manager
   * @param {string} name - State manager name
   * @param {Object} manager - State manager object
   * @returns {InteractionModel} This model for chaining
   */
  registerStateManager(name, manager) {
    this.stateManagers.set(name, manager);
    return this;
  }
  
  /**
   * Update system state based on operation
   * @param {Object} operation - Operation that was executed
   * @param {Object} parameters - Operation parameters
   * @param {*} result - Operation result
   * @returns {Object} State change information
   */
  updateState(operation, parameters, result) {
    // Start transaction if needed
    if (!this.currentTransaction) {
      this.currentTransaction = this._beginTransaction();
    }
    
    try {
      // Find appropriate state manager
      const manager = this._getStateManager(operation);
      
      if (!manager) {
        // No state manager for this operation
        return null;
      }
      
      // Apply state change
      const stateChange = manager.applyChange(operation, parameters, result);
      
      // Record in transaction
      this.currentTransaction.changes.push({
        operation: operation.name,
        parameters,
        change: stateChange
      });
      
      // Commit if this is a standalone operation
      if (!operation.partOfTransaction) {
        this._commitTransaction();
      }
      
      return stateChange;
    } catch (error) {
      // Rollback on error
      this._rollbackTransaction();
      throw error;
    }
  }
  
  /**
   * Begin a new transaction
   * @private
   * @returns {Object} Transaction object
   */
  _beginTransaction() {
    return {
      id: `txn-${Date.now()}-${Math.floor(Math.random() * 10000)}`,
      timestamp: Date.now(),
      changes: []
    };
  }
  
  /**
   * Commit the current transaction
   * @private
   */
  _commitTransaction() {
    if (this.currentTransaction) {
      // Verify transaction coherence
      this._validateTransactionCoherence();
      
      // Add to log
      this.transactionLog.push(this.currentTransaction);
      
      // Trim log if needed
      if (this.transactionLog.length > this.maxTransactionLog) {
        this.transactionLog = this.transactionLog.slice(-this.maxTransactionLog);
      }
      
      // Clear current transaction
      this.currentTransaction = null;
    }
  }
  
  /**
   * Rollback the current transaction
   * @private
   */
  _rollbackTransaction() {
    if (this.currentTransaction) {
      // Revert each change in reverse order
      for (let i = this.currentTransaction.changes.length - 1; i >= 0; i--) {
        const change = this.currentTransaction.changes[i];
        this._revertChange(change);
      }
      
      // Clear current transaction
      this.currentTransaction = null;
    }
  }
  
  /**
   * Find the appropriate state manager for an operation
   * @private
   * @param {Object} operation - Operation to find manager for
   * @returns {Object} State manager or null
   */
  _getStateManager(operation) {
    // Map operations to state managers
    switch (operation.name) {
      case 'allocate':
      case 'release':
        return this.stateManagers.get('resource');
      default:
        return null;
    }
  }
  
  /**
   * Revert a state change
   * @private
   * @param {Object} change - Change to revert
   */
  _revertChange(change) {
    const { operation, parameters, change: stateChange } = change;
    
    if (!stateChange) return;
    
    // Get state manager
    let manager = null;
    switch (operation) {
      case 'allocate':
      case 'release':
        manager = this.stateManagers.get('resource');
        break;
    }
    
    if (!manager) return;
    
    // Apply inverse operation
    if (operation === 'allocate') {
      // Revert allocation by releasing
      this.updateState(
        { name: 'release', modifiesState: true },
        { resourceId: stateChange.id },
        { id: stateChange.id, released: true }
      );
    } else if (operation === 'release') {
      // Revert release by allocating
      this.updateState(
        { name: 'allocate', modifiesState: true },
        { resourceType: stateChange.resourceType, amount: stateChange.amount },
        { id: stateChange.id, resourceType: stateChange.resourceType, amount: stateChange.amount, allocated: true }
      );
    }
  }
  
  /**
   * Validate transaction coherence
   * @private
   */
  _validateTransactionCoherence() {
    // Simple validation for the reference implementation
    // In a production system, this would involve more sophisticated checks
    
    // Check for conflicting operations
    const resources = new Map();
    
    for (const change of this.currentTransaction.changes) {
      if (change.operation === 'allocate') {
        const { resourceType, amount } = change.parameters;
        
        if (!resources.has(resourceType)) {
          resources.set(resourceType, { allocated: 0, released: 0 });
        }
        
        resources.get(resourceType).allocated += amount;
      } else if (change.operation === 'release') {
        const { resourceId } = change.parameters;
        const stateManager = this.stateManagers.get('resource');
        const allocation = stateManager.state.allocations.get(resourceId);
        
        if (allocation) {
          if (!resources.has(allocation.resourceType)) {
            resources.set(allocation.resourceType, { allocated: 0, released: 0 });
          }
          
          resources.get(allocation.resourceType).released += allocation.amount;
        }
      }
    }
    
    // Check for overallocations
    for (const [resourceType, counts] of resources.entries()) {
      const stateManager = this.stateManagers.get('resource');
      const resource = stateManager.state.resources.get(resourceType);
      
      if (!resource) continue;
      
      const netAllocation = counts.allocated - counts.released;
      
      if (netAllocation > resource.available + counts.released) {
        throw new Error(`Transaction would overallocate ${resourceType}`);
      }
    }
  }
  
  /**
   * Get transaction log
   * @param {Object} filter - Optional filter criteria
   * @returns {Object[]} Transaction log entries
   */
  getTransactionLog(filter = {}) {
    let log = [...this.transactionLog];
    
    // Apply filters
    if (filter.startTime) {
      log = log.filter(txn => txn.timestamp >= filter.startTime);
    }
    
    if (filter.endTime) {
      log = log.filter(txn => txn.timestamp <= filter.endTime);
    }
    
    if (filter.operation) {
      log = log.filter(txn => txn.changes.some(c => c.operation === filter.operation));
    }
    
    // Apply limit
    if (filter.limit && filter.limit > 0) {
      log = log.slice(-filter.limit);
    }
    
    return log;
  }
 }

 /**
 * Observation Model for Base1
 * Handles monitoring, metrics, and event observation
 */
 class ObservationModel {
  /**
   * Create a new observation model
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.observers = new Map();
    this.metrics = new Map();
    this.eventLog = [];
    this.maxLogSize = config.maxLogSize || 1000;
    
    // Initialize default metrics
    this._initializeMetrics();
  }
  
  /**
   * Initialize default metrics
   * @private
   */
  _initializeMetrics() {
    this.metrics.set('operationCount', 0);
    this.metrics.set('stateModifications', 0);
    this.metrics.set('lastOperationTime', 0);
    this.metrics.set('totalResponseTime', 0);
    this.metrics.set('avgResponseTime', 0);
  }
  
  /**
   * Record operation for observation
   * @param {Object} operation - Operation that was executed
   * @param {Object} parameters - Operation parameters
   * @returns {Object} Recorded event
   */
  recordOperation(operation, parameters) {
    const timestamp = Date.now();
    
    // Create event object
    const event = {
      timestamp,
      operation: operation.name,
      parameters,
      modifiedState: operation.modifiesState || false
    };
    
    // Add to event log
    this.eventLog.push(event);
    
    // Trim log if needed
    if (this.eventLog.length > this.maxLogSize) {
      this.eventLog = this.eventLog.slice(-this.maxLogSize);
    }
    
    // Notify observers
    this._notifyObservers(operation.name, parameters);
    
    // Update metrics
    this._updateMetrics(operation.name, timestamp);
    
    return event;
  }
  
  /**
   * Register observer for specific operations
   * @param {string} operationName - Operation to observe
   * @param {function} callback - Observer callback
   * @returns {ObservationModel} This model for chaining
   */
  observe(operationName, callback) {
    if (!this.observers.has(operationName)) {
      this.observers.set(operationName, []);
    }
    
    this.observers.get(operationName).push(callback);
    return this;
  }
  
  /**
   * Get metrics for system monitoring
   * @param {string[]} metricNames - Optional metric names to retrieve
   * @returns {Object} Metrics data
   */
  getMetrics(metricNames = null) {
    if (!metricNames) {
      return Object.fromEntries(this.metrics);
    }
    
    const result = {};
    for (const name of metricNames) {
      if (this.metrics.has(name)) {
        result[name] = this.metrics.get(name);
      }
    }
    
    return result;
  }
  
  /**
   * Get filtered event log
   * @param {Object} filter - Filter criteria
   * @returns {Object[]} Filtered events
   */
  getEvents(filter = {}) {
    let events = [...this.eventLog];
    
    // Apply filters
    if (filter.operation) {
      events = events.filter(e => e.operation === filter.operation);
    }
    
    if (filter.startTime) {
      events = events.filter(e => e.timestamp >= filter.startTime);
    }
    
    if (filter.endTime) {
      events = events.filter(e => e.timestamp <= filter.endTime);
    }
    
    if (filter.modifiedState !== undefined) {
      events = events.filter(e => e.modifiedState === filter.modifiedState);
    }
    
    // Apply limit
    if (filter.limit && filter.limit > 0) {
      events = events.slice(-filter.limit);
    }
    
    return events;
  }
  
  /**
   * Notify observers of an operation
   * @private
   * @param {string} operationName - Operation name
   * @param {Object} parameters - Operation parameters
   */
  _notifyObservers(operationName, parameters) {
    // Notify operation-specific observers
    if (this.observers.has(operationName)) {
      for (const callback of this.observers.get(operationName)) {
        try {
          callback(operationName, parameters);
        } catch (error) {
          console.error(`Observer error for ${operationName}:`, error);
        }
      }
    }
    
    // Notify global observers
    if (this.observers.has('*')) {
      for (const callback of this.observers.get('*')) {
        try {
          callback(operationName, parameters);
        } catch (error) {
          console.error(`Global observer error for ${operationName}:`, error);
        }
      }
    }
  }
  
  /**
   * Update metrics based on operation
   * @private
   * @param {string} operationName - Operation name
   * @param {number} timestamp - Current timestamp
   */
  _updateMetrics(operationName, timestamp) {
    // Update operation count
    this.metrics.set('operationCount', this.metrics.get('operationCount') + 1);
    
    // Update last operation time
    this.metrics.set('lastOperationTime', timestamp);
    
    // For response time, we'd normally calculate this with the actual execution time
    // but for the reference implementation, we'll use a random value
    const responseTime = Math.random() * 10 + 5;  // 5-15ms
    const totalTime = this.metrics.get('totalResponseTime') + responseTime;
    const count = this.metrics.get('operationCount');
    
    this.metrics.set('totalResponseTime', totalTime);
    this.metrics.set('avgResponseTime', totalTime / count);
    
    // Track state modifications
    if (operationName === 'allocate' || operationName === 'release') {
      this.metrics.set('stateModifications', this.metrics.get('stateModifications') + 1);
    }
    
    // Update operation-specific metrics
    const metricKey = `${operationName}Count`;
    if (!this.metrics.has(metricKey)) {
      this.metrics.set(metricKey, 1);
    } else {
      this.metrics.set(metricKey, this.metrics.get(metricKey) + 1);
    }
  }
 } signature - Metric signature (e.g., [1,1,1,1] for Euclidean)
   * @param {number} dimension - Dimension of the base vector space
   */
  constructor(signature, dimension) {
    this.signature = signature;
    this.dimension = dimension;
    this.bladeCount = Math.pow(2, dimension);
    this._initializeBasisElements();
    this._initializeProductTables();
  }

  /**
   * Initialize basis elements for the algebra
   * @private
   */
  _initializeBasisElements() {
    this.basisElements = new Array(this.bladeCount);
    
    // Create basis elements with appropriate grades
    for (let i = 0; i < this.bladeCount; i++) {
      // Determine grade by counting bits
      const grade = this._bitCount(i);
      this.basisElements[i] = {
        index: i,
        grade: grade,
        bitPattern: i,
        // Convert bit pattern to e1^e2^... notation
        label: this._bitPatternToLabel(i)
      };
    }
  }

  /**
   * Initialize product tables for efficient calculations
   * @private
   */
  _initializeProductTables() {
    // Create geometric product table
    this.geometricProductTable = new Array(this.bladeCount);
    // Create outer product table
    this.outerProductTable = new Array(this.bladeCount);
    // Create inner product table
    this.innerProductTable = new Array(this.bladeCount);
    
    for (let i = 0; i < this.bladeCount; i++) {
      this.geometricProductTable[i] = new Array(this.bladeCount);
      this.outerProductTable[i] = new Array(this.bladeCount);
      this.innerProductTable[i] = new Array(this.bladeCount);
      
      for (let j = 0; j < this.bladeCount; j++) {
        this.geometricProductTable[i][j] = this._computeGeometricProductTable(i, j);
        this.outerProductTable[i][j] = this._computeOuterProductTable(i, j);
        this.innerProductTable[i][j] = this._computeInnerProductTable(i, j);
      }
    }
  }

  /**
   * Compute the geometric product table entry
   * @private
   * @param {number} a - First basis blade index
   * @param {number} b - Second basis blade index
   * @returns {Object} Result with product index and sign
   */
  _computeGeometricProductTable(a, b) {
    let sign = 1;
    let index = a ^ b; // XOR gives the resulting blade
    
    // Calculate sign based on the geometric product rules
    // For each swap needed, we may need to change sign depending on signature
    const aBits = this._getBitArray(a, this.dimension);
    const bBits = this._getBitArray(b, this.dimension);
    
    // Count swaps needed to sort the basis vectors
    for (let i = 0; i < this.dimension; i++) {
      if (aBits[i] === 1) {
        for (let j = i + 1; j < this.dimension; j++) {
          if (bBits[j] === 1) {
            sign *= -1;
          }
        }
      }
    }
    
    // Apply signature
    for (let i = 0; i < this.dimension; i++) {
      if (aBits[i] === 1 && bBits[i] === 1) {
        sign *= this.signature[i];
      }
    }
    
    return { index, sign };
  }

  /**
   * Compute the outer product table entry
   * @private
   * @param {number} a - First basis blade index
   * @param {number} b - Second basis blade index
   * @returns {Object} Result with product index and sign
   */
  _computeOuterProductTable(a, b) {
    // If blades share any vectors, outer product is zero
    if ((a & b) !== 0) {
      return { index: 0, sign: 0 };
    }
    
    // Otherwise, use geometric product
    return this._computeGeometricProductTable(a, b);
  }

  /**
   * Compute the inner product table entry
   * @private
   * @param {number} a - First basis blade index
   * @param {number} b - Second basis blade index
   * @returns {Object} Result with product index and sign
   */
  _computeInnerProductTable(a, b) {
    const aGrade = this._bitCount(a);
    const bGrade = this._bitCount(b);
    const resultGrade = bGrade - aGrade;
    
    // Inner product is only defined when a is a proper subspace of b
    if (resultGrade <= 0 || (a & b) !== a) {
      return { index: 0, sign: 0 };
    }
    
    // Use geometric product with appropriate sign
    const geoProd = this._computeGeometricProductTable(a, b);
    
    // Adjust sign based on inner product definition
    const sign = geoProd.sign * (aGrade % 2 === 0 ? 1 : -1);
    
    return { index: geoProd.index, sign };
  }

  /**
   * Calculate geometric product of two multivectors
   * @param {MultivectorRepresentation} a - First multivector
   * @param {MultivectorRepresentation} b - Second multivector
   * @returns {MultivectorRepresentation} Result of a * b
   */
  geometricProduct(a, b) {
    const result = new MultivectorRepresentation(this.dimension);
    
    for (let i = 0; i < this.bladeCount; i++) {
      for (let j = 0; j < this.bladeCount; j++) {
        if (a.components[i] !== 0 && b.components[j] !== 0) {
          const prod = this.geometricProductTable[i][j];
          result.components[prod.index] += prod.sign * a.components[i] * b.components[j];
        }
      }
    }
    
    return result;
  }

  /**
   * Calculate outer product of two multivectors
   * @param {MultivectorRepresentation} a - First multivector
   * @param {MultivectorRepresentation} b - Second multivector
   * @returns {MultivectorRepresentation} Result of a ∧ b
   */
  outerProduct(a, b) {
    const result = new MultivectorRepresentation(this.dimension);
    
    for (let i = 0; i < this.bladeCount; i++) {
      for (let j = 0; j < this.bladeCount; j++) {
        if (a.components[i] !== 0 && b.components[j] !== 0) {
          const prod = this.outerProductTable[i][j];
          if (prod.sign !== 0) {
            result.components[prod.index] += prod.sign * a.components[i] * b.components[j];
          }
        }
      }
    }
    
    return result;
  }

  /**
   * Calculate inner product of two multivectors
   * @param {MultivectorRepresentation} a - First multivector
   * @param {MultivectorRepresentation} b - Second multivector
   * @returns {MultivectorRepresentation} Result of a · b
   */
  innerProduct(a, b) {
    const result = new MultivectorRepresentation(this.dimension);
    
    for (let i = 0; i < this.bladeCount; i++) {
      for (let j = 0; j < this.bladeCount; j++) {
        if (a.components[i] !== 0 && b.components[j] !== 0) {
          const prod = this.innerProductTable[i][j];
          if (prod.sign !== 0) {
            result.components[prod.index] += prod.sign * a.components[i] * b.components[j];
          }
        }
      }
    }
    
    return result;
  }

  /**
   * Calculate the reflection of a vector across a hyperplane
   * @param {MultivectorRepresentation} vector - Vector to reflect
   * @param {MultivectorRepresentation} normal - Normal to hyperplane
   * @returns {MultivectorRepresentation} Reflected vector
   */
  reflect(vector, normal) {
    // Reflection is -n * v * n / (n · n)
    const normalSquared = this.innerProduct(normal, normal).components[0];
    if (Math.abs(normalSquared) < 1e-10) {
      throw new Error("Cannot reflect across a null hyperplane");
    }
    
    const normalInv = normal.scale(1.0 / normalSquared);
    const n_v = this.geometricProduct(normalInv, vector);
    const n_v_n = this.geometricProduct(n_v, normal);
    
    return n_v_n.scale(-1);
  }

  /**
   * Calculate the rotation of a vector by a bivector
   * @param {MultivectorRepresentation} vector - Vector to rotate
   * @param {MultivectorRepresentation} bivector - Bivector representing rotation plane
   * @param {number} angle - Angle to rotate by (radians)
   * @returns {MultivectorRepresentation} Rotated vector
   */
  rotate(vector, bivector, angle) {
    // Normalize bivector
    const bivNorm = Math.sqrt(Math.abs(this.innerProduct(bivector, bivector).scalar()));
    const bivNormalized = bivector.scale(1.0 / bivNorm);
    
    // Create rotor R = cos(θ/2) + sin(θ/2) * B
    const rotor = new MultivectorRepresentation(this.dimension);
    rotor.components[0] = Math.cos(angle / 2);
    
    // For each grade-2 component in the bivector
    for (let i = 0; i < this.bladeCount; i++) {
      if (this.basisElements[i].grade === 2 && bivNormalized.components[i] !== 0) {
        rotor.components[i] = Math.sin(angle / 2) * bivNormalized.components[i];
      }
    }
    
    // Calculate R * v * ~R
    const rotorRev = rotor.reverse();
    const r_v = this.geometricProduct(rotor, vector);
    const result = this.geometricProduct(r_v, rotorRev);
    
    return result;
  }

  /**
   * Count the number of 1 bits in a number
   * @private
   * @param {number} n - Number to count bits in
   * @returns {number} Number of 1 bits
   */
  _bitCount(n) {
    let count = 0;
    while (n > 0) {
      count += n & 1;
      n >>= 1;
    }
    return count;
  }

  /**
   * Convert bit pattern to basis element label (e1^e2^...)
   * @private
   * @param {number} bitPattern - Bit pattern representing basis element
   * @returns {string} Label for the basis element
   */
  _bitPatternToLabel(bitPattern) {
    if (bitPattern === 0) return "1"; // Scalar
    
    let label = "";
    for (let i = 0; i < this.dimension; i++) {
      if ((bitPattern & (1 << i)) !== 0) {
        label += "e" + (i + 1);
      }
    }
    return label;
  }

  /**
   * Convert a number to its bit array representation
   * @private
   * @param {number} n - Number to convert
   * @param {number} size - Size of the bit array
   * @returns {number[]} Array of bits
   */
  _getBitArray(n, size) {
    const bits = new Array(size).fill(0);
    for (let i = 0; i < size; i++) {
      bits[i] = (n & (1 << i)) !== 0 ? 1 : 0;
    }
    return bits;
  }
 }

 /**
 * Representation of a multivector in Clifford algebra
 */
 class MultivectorRepresentation {
  /**
   * Create a new multivector
   * @param {number} dimension - Dimension of the vector space
   */
  constructor(dimension) {
    this.dimension = dimension;
    this.bladeCount = Math.pow(2, dimension);
    this.components = new Float64Array(this.bladeCount).fill(0);
  }

  /**
   * Extract components of a specific grade
   * @param {number} k - Grade to extract
   * @returns {MultivectorRepresentation} Multivector containing only k-grade components
   */
  grade(k) {
    const result = new MultivectorRepresentation(this.dimension);
    const indices = this._indicesOfGrade(k);
    
    for (const idx of indices) {
      result.components[idx] = this.components[idx];
    }
    
    return result;
  }

  /**
   * Get the scalar (grade 0) part
   * @returns {number} Scalar part of the multivector
   */
  scalar() {
    return this.components[0];
  }

  /**
   * Get the vector (grade 1) part
   * @returns {number[]} Vector components
   */
  vector() {
    const result = [];
    const indices = this._indicesOfGrade(1);
    
    for (const idx of indices) {
      result.push(this.components[idx]);
    }
    
    return result;
  }

  /**
   * Calculate the reverse of this multivector
   * @returns {MultivectorRepresentation} Reversed multivector
   */
  reverse() {
    const result = new MultivectorRepresentation(this.dimension);
    
    for (let i = 0; i < this.bladeCount; i++) {
      const grade = this._gradeOfIndex(i);
      const sign = ((grade * (grade - 1)) / 2) % 2 === 0 ? 1 : -1;
      result.components[i] = sign * this.components[i];
    }
    
    return result;
  }

  /**
   * Scale the multivector by a scalar
   * @param {number} scalar - Scalar to multiply by
   * @returns {MultivectorRepresentation} Scaled multivector
   */
  scale(scalar) {
    const result = new MultivectorRepresentation(this.dimension);
    
    for (let i = 0; i < this.bladeCount; i++) {
      result.components[i] = this.components[i] * scalar;
    }
    
    return result;
  }

  /**
   * Add another multivector to this one
   * @param {MultivectorRepresentation} other - Multivector to add
   * @returns {MultivectorRepresentation} Sum of multivectors
   */
  add(other) {
    const result = new MultivectorRepresentation(this.dimension);
    
    for (let i = 0; i < this.bladeCount; i++) {
      result.components[i] = this.components[i] + other.components[i];
    }
    
    return result;
  }

  /**
   * Subtract another multivector from this one
   * @param {MultivectorRepresentation} other - Multivector to subtract
   * @returns {MultivectorRepresentation} Difference of multivectors
   */
  subtract(other) {
    const result = new MultivectorRepresentation(this.dimension);
    
    for (let i = 0; i < this.bladeCount; i++) {
      result.components[i] = this.components[i] - other.components[i];
    }
    
    return result;
  }

  /**
   * Find the multivector norm squared (scalar product with reverse)
   * @returns {number} Norm squared
   */
  normSquared() {
    let sum = 0;
    const rev = this.reverse();
    
    for (let i = 0; i < this.bladeCount; i++) {
      for (let j = 0; j < this.bladeCount; j++) {
        // Only scalar part contributes to the norm
        if ((i ^ j) === 0) {
          sum += this.components[i] * rev.components[j];
        }
      }
    }
    
    return sum;
  }

  /**
   * Calculate the multivector norm
   * @returns {number} Multivector norm
   */
  norm() {
    const normSq = this.normSquared();
    return Math.sqrt(Math.abs(normSq));
  }

  /**
   * Get all indices of basis elements with a specific grade
   * @private
   * @param {number} grade - The grade to find
   * @returns {number[]} Array of indices
   */
  _indicesOfGrade(grade) {
    const indices = [];
    
    for (let i = 0; i < this.bladeCount; i++) {
      if (this._gradeOfIndex(i) === grade) {
        indices.push(i);
      }
    }
    
    return indices;
  }

  /**
   * Determine the grade of a basis element by its index
   * @private
   * @param {number} index - Index of the basis element
   * @returns {number} Grade of the basis element
   */
  _gradeOfIndex(index) {
    let count = 0;
    let n = index;
    
    while (n > 0) {
      count += n & 1;
      n >>= 1;
    }
    
    return count;
  }

  /**
   * Convert the multivector to a string representation
   * @returns {string} String representation
   */
  toString() {
    const terms = [];
    
    for (let i = 0; i < this.bladeCount; i++) {
      if (Math.abs(this.components[i]) > 1e-10) {
        let term = this.components[i].toFixed(4);
        
        if (i === 0) {
          // Scalar term
        } else {
          // Create basis element label
          let basisLabel = "";
          for (let j = 0; j < this.dimension; j++) {
            if ((i & (1 << j)) !== 0) {
              basisLabel += "e" + (j + 1);
            }
          }
          term += basisLabel;
        }
        
        terms.push(term);
      }
    }
    
    return terms.length > 0 ? terms.join(" + ") : "0";
  }
 }

 /**
 * Coherence metrics for evaluating mathematical consistency
 */
 class CoherenceMetrics {
  /**
   * Calculate the coherence inner product between two objects
   * @param {MultivectorRepresentation|number[]} a - First object
   * @param {MultivectorRepresentation|number[]} b - Second object
   * @param {number[][]} metric - Optional metric tensor for inner product
   * @returns {number} Inner product value
   */
  static coherenceInnerProduct(a, b, metric = null) {
    // Handle different input types
    const aComponents = a instanceof MultivectorRepresentation ? a.components : a;
    const bComponents = b instanceof MultivectorRepresentation ? b.components : b;
    
    // Default metric is identity if not specified
    if (!metric) {
      metric = Array(aComponents.length).fill().map((_, i) => 
        Array(bComponents.length).fill().map((_, j) => i === j ? 1 : 0)
      );
    }
    
    // Calculate inner product with respect to provided metric
    let sum = 0;
    for (let i = 0; i < aComponents.length; i++) {
      for (let j = 0; j < bComponents.length; j++) {
        sum += aComponents[i] * metric[i][j] * bComponents[j];
      }
    }
    
    return sum;
  }
  
  /**
   * Calculate the coherence norm of an object
   * @param {MultivectorRepresentation|number[]} a - Object to measure
   * @param {number[][]} metric - Optional metric tensor
   * @returns {number} Coherence norm
   */
  static coherenceNorm(a, metric = null) {
    return Math.sqrt(Math.abs(this.coherenceInnerProduct(a, a, metric)));
  }
  
  /**
   * Calculate normalized coherence for comparison
   * @param {MultivectorRepresentation|number[]} a - Object to measure
   * @param {number[][]} metric - Optional metric tensor
   * @returns {number} Normalized coherence (0-1)
   */
  static normalizedCoherence(a, metric = null) {
    const norm = this.coherenceNorm(a, metric);
    // Lower norm means higher coherence (1.0 is perfect)
    return norm > 0 ? 1.0 / (1.0 + norm) : 1.0;
  }
  
  /**
   * Calculate the coherence distance between two objects
   * @param {MultivectorRepresentation|number[]} a - First object
   * @param {MultivectorRepresentation|number[]} b - Second object
   * @param {number[][]} metric - Optional metric tensor
   * @returns {number} Coherence distance
   */
  static coherenceDistance(a, b, metric = null) {
    // For vectors, this is effectively a metric space distance
    const aComponents = a instanceof MultivectorRepresentation ? a.components : a;
    const bComponents = b instanceof MultivectorRepresentation ? b.components : b;
    
    // Create a difference vector
    const diff = new Array(aComponents.length);
    for (let i = 0; i < aComponents.length; i++) {
      diff[i] = aComponents[i] - bComponents[i];
    }
    
    // Return the norm of the difference
    return this.coherenceNorm(diff, metric);
  }
  
  /**
   * Calculate similarity between two objects (1 = identical, 0 = orthogonal)
   * @param {MultivectorRepresentation|number[]} a - First object
   * @param {MultivectorRepresentation|number[]} b - Second object
   * @param {number[][]} metric - Optional metric tensor
   * @returns {number} Similarity value between 0 and 1
   */
  static similarity(a, b, metric = null) {
    const innerProd = this.coherenceInnerProduct(a, b, metric);
    const normA = this.coherenceNorm(a, metric);
    const normB = this.coherenceNorm(b, metric);
    
    if (normA === 0 || normB === 0) return 0;
    
    // Normalized inner product
    const cosine = innerProd / (normA * normB);
    
    // Map from [-1, 1] to [0, 1]
    return (cosine + 1) / 2;
  }
 }

 /**
 * Matrix operations for Lie group and symmetry calculations
 */
 class Matrix {
  /**
   * Create an identity matrix of specified size
   * @param {number} size - Matrix size
   * @returns {number[][]} Identity matrix
   */
  static identity(size) {
    const matrix = new Array(size);
    for (let i = 0; i < size; i++) {
      matrix[i] = new Array(size).fill(0);
      matrix[i][i] = 1;
    }
    return matrix;
  }
  
  /**
   * Create a zero matrix of specified size
   * @param {number} rows - Number of rows
   * @param {number} cols - Number of columns
   * @returns {number[][]} Zero matrix
   */
  static zeros(rows, cols) {
    const matrix = new Array(rows);
    for (let i = 0; i < rows; i++) {
      matrix[i] = new Array(cols).fill(0);
    }
    return matrix;
  }
  
  /**
   * Multiply two matrices
   * @param {number[][]} a - First matrix
   * @param {number[][]} b - Second matrix
   * @returns {number[][]} Matrix product
   */
  static multiply(a, b) {
    const aRows = a.length;
    const aCols = a[0].length;
    const bRows = b.length;
    const bCols = b[0].length;
    
    if (aCols !== bRows) {
      throw new Error("Matrix dimensions do not match for multiplication");
    }
    
    const result = new Array(aRows);
    for (let i = 0; i < aRows; i++) {
      result[i] = new Array(bCols).fill(0);
      for (let j = 0; j < bCols; j++) {
        for (let k = 0; k < aCols; k++) {
          result[i][j] += a[i][k] * b[k][j];
        }
      }
    }
    
    return result;
  }
  
  /**
   * Add two matrices
   * @param {number[][]} a - First matrix
   * @param {number[][]} b - Second matrix
   * @returns {number[][]} Matrix sum
   */
  static add(a, b) {
    const rows = a.length;
    const cols = a[0].length;
    
    if (rows !== b.length || cols !== b[0].length) {
      throw new Error("Matrix dimensions do not match for addition");
    }
    
    const result = new Array(rows);
    for (let i = 0; i < rows; i++) {
      result[i] = new Array(cols);
      for (let j = 0; j < cols; j++) {
        result[i][j] = a[i][j] + b[i][j];
      }
    }
    
    return result;
  }
  
  /**
   * Multiply a matrix by a scalar
   * @param {number[][]} matrix - Matrix to scale
   * @param {number} scalar - Scalar value
   * @returns {number[][]} Scaled matrix
   */
  static scalarMultiply(matrix, scalar) {
    const rows = matrix.length;
    const cols = matrix[0].length;
    
    const result = new Array(rows);
    for (let i = 0; i < rows; i++) {
      result[i] = new Array(cols);
      for (let j = 0; j < cols; j++) {
        result[i][j] = matrix[i][j] * scalar;
      }
    }
    
    return result;
  }
  
  /**
   * Compute the transpose of a matrix
   * @param {number[][]} matrix - Input matrix
   * @returns {number[][]} Transposed matrix
   */
  static transpose(matrix) {
    const rows = matrix.length;
    const cols = matrix[0].length;
    
    const result = new Array(cols);
    for (let i = 0; i < cols; i++) {
      result[i] = new Array(rows);
      for (let j = 0; j < rows; j++) {
        result[i][j] = matrix[j][i];
      }
    }
    
    return result;
  }
  
  /**
   * Compute the matrix exponential using a Taylor series
   * @param {number[][]} matrix - Input matrix
   * @param {number} steps - Number of terms in the series
   * @returns {number[][]} Matrix exponential
   */
  static exponential(matrix, steps = 10) {
    const size = matrix.length;
    
    // Start with identity matrix for the sum
    let result = this.identity(size);
    
    // Start with identity for the current term
    let term = this.identity(size);
    
    // Compute the Taylor series up to the specified number of steps
    for (let i = 1; i <= steps; i++) {
      // Multiply the current term by the matrix and divide by factorial
      term = this.multiply(term, matrix);
      
      const factorial = this._factorial(i);
      const scaled = this.scalarMultiply(term, 1.0 / factorial);
      
      // Add to the result
      result = this.add(result, scaled);
    }
    
    return result;
  }
  
  /**
   * Calculate the determinant of a matrix
   * @param {number[][]} matrix - Input matrix
   * @returns {number} Determinant value
   */
  static determinant(matrix) {
    const n = matrix.length;
    
    // Base case for 1x1 matrix
    if (n === 1) {
      return matrix[0][0];
    }
    
    // Base case for 2x2 matrix
    if (n === 2) {
      return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
    }
    
    // Expand by the first row for larger matrices
    let result = 0;
    for (let j = 0; j < n; j++) {
      // Create submatrix by excluding first row and current column
      const submatrix = new Array(n - 1);
      for (let i = 1; i < n; i++) {
        submatrix[i - 1] = new Array(n - 1);
        for (let k = 0; k < n; k++) {
          if (k < j) {
            submatrix[i - 1][k] = matrix[i][k];
          } else if (k > j) {
            submatrix[i - 1][k - 1] = matrix[i][k];
          }
        }
      }
      
      // Add or subtract the determinant of the submatrix
      const sign = j % 2 === 0 ? 1 : -1;
      result += sign * matrix[0][j] * this.determinant(submatrix);
    }
    
    return result;
  }
  
  /**
   * Calculate factorial
   * @private
   * @param {number} n - Input value
   * @returns {number} n!
   */
  static _factorial(n) {
    if (n === 0 || n === 1) return 1;
    let result = 1;
    for (let i = 2; i <= n; i++) {
      result *= i;
    }
    return result;
  }
 }

 /**
 * Symmetry operations for geometrical transformations
 */
 class SymmetryOperations {
  /**
   * Create a Lie algebra generator matrix
   * @param {number} dimension - Dimension of the space
   * @param {number[]} indices - Indices [i,j] for the generator
   * @returns {number[][]} Generator matrix
   */
  static generator(dimension, indices) {
    const generator = Matrix.zeros(dimension, dimension);
    const [i, j] = indices;
    
    if (i >= 0 && i < dimension && j >= 0 && j < dimension) {
      generator[i][j] = 1.0;
    }
    
    return generator;
  }
  
  /**
   * Compute the matrix exponential for Lie group elements
   * @param {number[][]} matrix - Input matrix
   * @param {number} steps - Number of terms in the series
   * @returns {number[][]} Matrix exponential
   */
  static expMatrix(matrix, steps = 10) {
    return Matrix.exponential(matrix, steps);
  }
  
  /**
   * Apply a transformation that preserves specified invariants
   * @param {Object} object - Object to transform
   * @param {function} transformation - Transformation function
   * @param {Array} invariants - List of invariants to preserve
   * @returns {Object} Transformed object
   */
  static applyTransformation(object, transformation, invariants) {
    // Measure invariants before transformation
    const preValues = invariants.map(inv => inv.measure(object));
    
    // Apply the transformation
    const result = transformation(object);
    
    // Verify invariants are preserved
    const postValues = invariants.map(inv => inv.measure(result));
    
    for (let i = 0; i < invariants.length; i++) {
      const invariant = invariants[i];
      const tolerance = invariant.tolerance || 1e-10;
      
      if (Math.abs(preValues[i] - postValues[i]) > tolerance) {
        throw new Error(
          `Invariant ${invariant.name} not preserved: ${preValues[i]} ≠ ${postValues[i]}`
        );
      }
    }
    
    return result;
  }
  
  /**
   * Create a rotation transformation in the specified plane
   * @param {number} dimension - Space dimension
   * @param {number[]} planeIndices - Indices [i,j] defining the rotation plane
   * @param {number} angle - Rotation angle in radians
   * @returns {function} Rotation function
   */
  static createRotation(dimension, planeIndices, angle) {
    const [i, j] = planeIndices;
    
    // Create generator for this rotation plane
    const gen_ij = this.generator(dimension, [i, j]);
    const gen_ji = this.generator(dimension, [j, i]);
    
    // Create the bivector generator (antisymmetric)
    const bivector = Matrix.add(gen_ij, Matrix.scalarMultiply(gen_ji, -1));
    
    // Scale by angle
    const scaled = Matrix.scalarMultiply(bivector, angle);
    
    // Create rotation matrix via exponential map
    const rotationMatrix = this.expMatrix(scaled);
    
    // Return function that applies this rotation
    return (vector) => {
      if (vector.length !== dimension) {
        throw new Error("Vector dimension does not match rotation dimension");
      }
      
      // Apply rotation matrix to vector
      const result = new Array(dimension).fill(0);
      for (let k = 0; k < dimension; k++) {
        for (let l = 0; l < dimension; l++) {
          result[k] += rotationMatrix[k][l] * vector[l];
        }
      }
      
      return result;
    };
  }
  
  /**
   * Create a reflection transformation across a hyperplane
   * @param {number[]} normal - Normal vector to the hyperplane
   * @returns {function} Reflection function
   */
  static createReflection(normal) {
    const dimension = normal.length;
    
    // Normalize the normal vector
    const normalSquared = normal.reduce((sum, val) => sum + val * val, 0);
    const normalNorm = Math.sqrt(normalSquared);
    
    if (normalNorm < 1e-10) {
      throw new Error("Cannot reflect across hyperplane with zero normal");
    }
    
    const normalizedNormal = normal.map(val => val / normalNorm);
    
    // Return function that applies this reflection
    return (vector) => {
      if (vector.length !== dimension) {
        throw new Error("Vector dimension does not match reflection normal dimension");
      }
      
      // Calculate dot product of vector with normal
      const dot = vector.reduce(
        (sum, val, idx) => sum + val * normalizedNormal[idx], 
        0
      );
      
      // Apply reflection: v - 2(v · n)n
      return vector.map(
        (val, idx) => val - 2 * dot * normalizedNormal[idx]
      );
    };
  }
 }

 /**
 * Manifold structure implementation
 */
 class ManifoldStructure {
  /**
   * Create a new manifold structure
   * @param {number} dimension - Manifold dimension
   * @param {number[][]} metric - Optional metric tensor
   */
  constructor(dimension, metric = null) {
    this.dimension = dimension;
    this.metric = metric || this._defaultMetric(dimension);
    this.points = new Map();  // Maps indices to manifold points
    this.fiberBundles = new Map(); // Maps point indices to fiber bundles
    this.boundaryPoints = new Set(); // Points on the boundary
  }
  
  /**
   * Create default Euclidean metric
   * @private
   * @param {number} dimension - Space dimension
   * @returns {number[][]} Metric tensor
   */
  _defaultMetric(dimension) {
    return Matrix.identity(dimension);
  }
  
  /**
   * Add a point to the manifold
   * @param {string|number} index - Unique identifier for the point
   * @param {Object} point - Point data
   * @param {number[]} coordinates - Coordinates in the manifold
   * @param {boolean} isBoundary - Whether this point is on the boundary
   * @returns {Object} The added point
   */
  addPoint(index, point, coordinates, isBoundary = false) {
    if (coordinates.length !== this.dimension) {
      throw new Error(`Point coordinates must match manifold dimension (${this.dimension})`);
    }
    
    const manifestedPoint = {
      index,
      data: point,
      coordinates,
      isBoundary,
      connections: new Set()
    };
    
    this.points.set(index, manifestedPoint);
    
    if (isBoundary) {
      this.boundaryPoints.add(index);
    }
    
    return manifestedPoint;
  }
  
  /**
   * Calculate the manifold depth for a point
   * @param {string|number} pointIndex - Index of the point
   * @returns {number} Manifold depth (0 at boundary, increasing inward)
   */
  depth(pointIndex) {
    const point = this.points.get(pointIndex);
    if (!point) return 0;
    
    // Boundary points have zero depth
    if (point.isBoundary) return 0;
    
    // Calculate minimum distance to any boundary point
    let minDistance = Infinity;
    
    for (const boundaryIdx of this.boundaryPoints) {
      const boundaryPoint = this.points.get(boundaryIdx);
      const distance = this._distance(point.coordinates, boundaryPoint.coordinates);
      minDistance = Math.min(minDistance, distance);
    }
    
    // If there are no boundary points, use a default value
    if (minDistance === Infinity || this.boundaryPoints.size === 0) {
      return 1.0;
    }
    
    return minDistance;
  }
  
  /**
   * Connect two points in the manifold
   * @param {string|number} index1 - First point index
   * @param {string|number} index2 - Second point index
   * @param {Object} metadata - Optional connection metadata
   * @returns {Object} Connection object
   */
  connect(index1, index2, metadata = {}) {
    const point1 = this.points.get(index1);
    const point2 = this.points.get(index2);
    
    if (!point1 || !point2) {
      throw new Error("Cannot connect: one or both points do not exist");
    }
    
    // Create connection object
    const connection = {
      indices: [index1, index2],
      metadata
    };
    
    // Add to both points' connections
    point1.connections.add(index2);
    point2.connections.add(index1);
    
    return connection;
  }
  
  /**
   * Attach a fiber bundle at a specific point
   * @param {string|number} pointIndex - Index of base point
   * @param {Object} fiberSpace - Fiber space to attach
   * @returns {Object} The attached fiber bundle
   */
  attachFiber(pointIndex, fiberSpace) {
    const point = this.points.get(pointIndex);
    
    if (!point) {
      throw new Error(`Point with index ${pointIndex} does not exist`);
    }
    
    // Create fiber bundle
    const bundle = {
      basePoint: pointIndex,
      fiberSpace,
      sections: new Map()
    };
    
    this.fiberBundles.set(pointIndex, bundle);
    
    return bundle;
  }
  
  /**
   * Define a section (configuration across the manifold)
   * @param {function} sectionFn - Function mapping (point, fiber) to fiber value
   * @param {string} name - Name for this section
   * @returns {Map} The defined section
   */
  defineSection(sectionFn, name) {
    const section = new Map();
    
    for (const [index, point] of this.points.entries()) {
      const fiber = this.fiberBundles.get(index);
      if (fiber) {
        const value = sectionFn(point, fiber.fiberSpace);
        section.set(index, value);
      }
    }
    
    // Store named section in all bundles that have values
    for (const [index, value] of section.entries()) {
      const bundle = this.fiberBundles.get(index);
      if (bundle) {
        bundle.sections.set(name, value);
      }
    }
    
    return section;
  }
  
  /**
   * Calculate geodesic distance between points
   * @private
   * @param {number[]} coords1 - First point coordinates
   * @param {number[]} coords2 - Second point coordinates
   * @returns {number} Geodesic distance
   */
  _distance(coords1, coords2) {
    // For Euclidean metric, this is just Euclidean distance
    if (this._isEuclideanMetric()) {
      let sum = 0;
      for (let i = 0; i < this.dimension; i++) {
        const diff = coords1[i] - coords2[i];
        sum += diff * diff;
      }
      return Math.sqrt(sum);
    }
    
    // For non-Euclidean metrics, use the metric tensor
    let sum = 0;
    for (let i = 0; i < this.dimension; i++) {
      for (let j = 0; j < this.dimension; j++) {
        const diff_i = coords1[i] - coords2[i];
        const diff_j = coords1[j] - coords2[j];
        sum += this.metric[i][j] * diff_i * diff_j;
      }
    }
    
    return Math.sqrt(Math.abs(sum));
  }
  
  /**
   * Check if the metric is Euclidean
   * @private
   * @returns {boolean} True if metric is Euclidean
   */
  _isEuclideanMetric() {
    for (let i = 0; i < this.dimension; i++) {
      for (let j = 0; j < this.dimension; j++) {
        if (i === j && this.metric[i][j] !== 1) return false;
        if (i !== j && this.metric[i][j] !== 0) return false;
      }
    }
    return true;
  }
  
  /**
   * Find nearest neighbors to a point
   * @param {string|number} pointIndex - Index of the center point
   * @param {number} k - Number of neighbors to find
   * @returns {Array} Array of [index, distance] pairs
   */
  findNearestNeighbors(pointIndex, k = 5) {
    const point = this.points.get(pointIndex);
    if (!point) {
      throw new Error(`Point with index ${pointIndex} does not exist`);
    }
    
    const neighbors = [];
    
    for (const [idx, otherPoint] of this.points.entries()) {
      if (idx === pointIndex) continue;
      
      const distance = this._distance(point.coordinates, otherPoint.coordinates);
      neighbors.push([idx, distance]);
    }
    
    // Sort by distance and take first k
    neighbors.sort((a, b) => a[1] - b[1]);
    return neighbors.slice(0, k);
  }
 }

 // =============================================================================
 // 2. Four-Tier Architecture Implementation
 // =============================================================================

 /**
 * Base 0: Neural Network Specification
 * Abstract mathematical foundation for all components
 */
 class Base0 {
  /**
   * Create a new Base0 instance
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    // Create embedding model for data representation
    this.embeddingModel = new EmbeddingModel(config.embedding || {});
    
    // Create logic model for computational rules
    this.logicModel = new LogicModel(config.logic || {});
    
    // Create representation model for visualization
    this.representationModel = new RepresentationModel(config.representation || {});
    
    // Create spectral operator for communication and coherence
    this.spectralOperator = new SpectralOperator(config.spectral || {});
    
    // Coherence threshold for validation
    this.threshold = config.threshold || 0.8;
  }
  
  /**
   * Compute coherence across all models
   * @returns {number} Overall coherence value
   */
  computeCoherence() {
    const embedCoherence = this.embeddingModel.coherence();
    const logicCoherence = this.logicModel.coherence();
    const reprCoherence = this.representationModel.coherence();
    const spectralCoherence = this.spectralOperator.coherence();
    
    // Combine coherence measures with appropriate weights
    return (0.3 * embedCoherence + 
            0.3 * logicCoherence + 
            0.2 * reprCoherence + 
            0.2 * spectralCoherence);
  }
  
  /**
   * Transform an input according to all models
   * @param {*} input - Input data
   * @returns {*} Transformed output
   */
  transform(input) {
    // Apply transformations while preserving invariants
    const embedded = this.embeddingModel.embed(input);
    const processed = this.logicModel.process(embedded);
    const represented = this.representationModel.represent(processed);
    
    // Validate coherence of the transformation
    const coherence = this.computeCoherence();
    if (coherence < this.threshold) {
      throw new Error(
        `Transformation violated coherence threshold: ${coherence} < ${this.threshold}`
      );
    }
    
    return represented;
  }
 }

 /**
 * Embedding Model for Base0
 * Handles data representation and embedding
 */
 class EmbeddingModel {
  /**
   * Create a new embedding model
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.dimension = config.dimension || 512;
    this.clifford = new CliffordAlgebra(config.signature || [1, 1, 1, 1], 
                                       config.cliffordDim || 4);
    this.manifold = new ManifoldStructure(config.manifoldDim || 5);
    this.cache = new Map();
    this.coherenceThreshold = config.coherenceThreshold || 0.75;
  }
  
  /**
   * Embed data into a multivector representation
   * @param {*} data - Input data
   * @returns {MultivectorRepresentation} Embedded multivector
   */
  embed(data) {
    const cacheKey = this._getCacheKey(data);
    
    // Return cached embedding if available
    if (this.cache.has(cacheKey)) {
      return this.cache.get(cacheKey);
    }
    
    // Create multivector representation of data
    const multivector = this._createMultivector(data);
    
    // Validate coherence of embedding
    const coherence = CoherenceMetrics.normalizedCoherence(multivector);
    if (coherence < this.coherenceThreshold) {
      this._adjustForCoherence(multivector);
    }
    
    // Cache and return the embedding
    this.cache.set(cacheKey, multivector);
    return multivector;
  }
  
  /**
   * Create a cache key for data
   * @private
   * @param {*} data - Input data
   * @returns {string} Cache key
   */
  _getCacheKey(data) {
    if (typeof data === 'string') {
      return `str:${data}`;
    } else if (typeof data === 'number') {
      return `num:${data}`;
    } else if (Array.isArray(data)) {
      return `arr:${data.join(',')}`;
    } else if (data instanceof MultivectorRepresentation) {
      return `mv:${data.components.join(',')}`;
    } else if (typeof data === 'object') {
      return `obj:${JSON.stringify(data)}`;
    }
    
    // Default fallback
    return `other:${String(data)}`;
  }
  
  /**
   * Create a multivector representation of data
   * @private
   * @param {*} data - Input data
   * @returns {MultivectorRepresentation} Multivector representation
   */
  _createMultivector(data) {
    const multivector = new MultivectorRepresentation(this.clifford.dimension);
    
    if (typeof data === 'string') {
      // Embed string data
      this._embedStringData(data, multivector);
    } else if (typeof data === 'number') {
      // Embed numeric data
      this._embedNumericData(data, multivector);
    } else if (Array.isArray(data)) {
      // Embed array data
      this._embedArrayData(data, multivector);
    } else if (data instanceof MultivectorRepresentation) {
      // Copy existing multivector
      for (let i = 0; i < this.clifford.bladeCount; i++) {
        multivector.components[i] = data.components[i];
      }
    } else if (typeof data === 'object') {
      // Embed object data
      this._embedObjectData(data, multivector);
    }
    
    return multivector;
  }
  
  /**
   * Embed string data into a multivector
   * @private
   * @param {string} str - String data
   * @param {MultivectorRepresentation} multivector - Target multivector
   */
  _embedStringData(str, multivector) {
    // Start with a seed value in the scalar part
    multivector.components[0] = 1.0;
    
    // Process each character in the string
    for (let i = 0; i < str.length; i++) {
      const charCode = str.charCodeAt(i);
      
      // Use character code to influence different blade components
      // This spreads the string information across the multivector
      
      // Update scalar part using a non-linear function
      multivector.components[0] *= Math.tanh(charCode * 0.01) + 1.0;
      
      // Distribute character information across vector components
      for (let j = 0; j < Math.min(4, this.clifford.dimension); j++) {
        const idx = 1 << j;  // 2^j for basis vector
        const phase = (i * (j + 1)) % 8 * Math.PI / 4;  // Phase based on position
        multivector.components[idx] += 0.1 * Math.sin(charCode * 0.1 + phase);
      }
      
      // Influence bivector components for pairs of characters
      if (i > 0) {
        const prevCharCode = str.charCodeAt(i - 1);
        for (let j = 0; j < Math.min(3, this.clifford.dimension - 1); j++) {
          const idx = (1 << j) | (1 << (j + 1));  // e_j ∧ e_{j+1}
          multivector.components[idx] += 0.01 * Math.sin(prevCharCode * charCode * 0.001);
        }
      }
    }
    
    // Normalize for consistent magnitude
    const norm = multivector.norm();
    if (norm > 0) {
      for (let i = 0; i < this.clifford.bladeCount; i++) {
        multivector.components[i] /= norm;
      }
    }
  }
  
  /**
   * Embed numeric data into a multivector
   * @private
   * @param {number} num - Numeric data
   * @param {MultivectorRepresentation} multivector - Target multivector
   */
  _embedNumericData(num, multivector) {
    // Scalar part holds the raw value
    multivector.components[0] = num;
    
    // Generate vector components based on transformations of the number
    multivector.components[1] = Math.sin(num);
    multivector.components[2] = Math.cos(num);
    if (this.clifford.dimension > 2) {
      multivector.components[4] = Math.sin(num * 2);
      multivector.components[8] = Math.cos(num * 2);
    }
    
    // Add bivector components encoding relationships
    if (this.clifford.dimension > 1) {
      multivector.components[3] = Math.sin(num) * Math.cos(num);  // e1 ∧ e2
    }
    
    // Scale for consistent magnitude
    const scale = 1.0 / (1.0 + Math.abs(num));
    for (let i = 1; i < this.clifford.bladeCount; i++) {
      multivector.components[i] *= scale;
    }
  }
  
  /**
   * Embed array data into a multivector
   * @private
   * @param {Array} arr - Array data
   * @param {MultivectorRepresentation} multivector - Target multivector
   */
  _embedArrayData(arr, multivector) {
    // Use array length in scalar part
    multivector.components[0] = arr.length;
    
    // Map array values directly to vector components
    for (let i = 0; i < Math.min(arr.length, this.clifford.dimension); i++) {
      const idx = 1 << i;  // 2^i for basis vector e_i
      
      if (typeof arr[i] === 'number') {
        multivector.components[idx] = arr[i];
      } else if (typeof arr[i] === 'string') {
        // Simple hash for strings
        let hash = 0;
        for (let j = 0; j < arr[i].length; j++) {
          hash = (hash * 31 + arr[i].charCodeAt(j)) % 1000;
        }
        multivector.components[idx] = hash / 1000;
      } else if (typeof arr[i] === 'boolean') {
        multivector.components[idx] = arr[i] ? 1 : -1;
      }
    }
    
    // Add bivector components to represent relationships between values
    for (let i = 0; i < Math.min(arr.length - 1, this.clifford.dimension - 1); i++) {
      if (typeof arr[i] === 'number' && typeof arr[i + 1] === 'number') {
        const idx = (1 << i) | (1 << (i + 1));  // e_i ∧ e_{i+1}
        multivector.components[idx] = arr[i] - arr[i + 1];
      }
    }
    
    // Normalize
    const norm = multivector.norm();
    if (norm > 0) {
      for (let i = 0; i < this.clifford.bladeCount; i++) {
        multivector.components[i] /= norm;
      }
    }
  }
  
  /**
   * Embed object data into a multivector
   * @private
   * @param {Object} obj - Object data
   * @param {MultivectorRepresentation} multivector - Target multivector
   */
  _embedObjectData(obj, multivector) {
    // Get property names
    const keys = Object.keys(obj);
    
    // Use number of properties in scalar part
    multivector.components[0] = keys.length;
    
    // Process each property
    for (let i = 0; i < keys.length; i++) {
      const key = keys[i];
      const value = obj[key];
      
      // Create a hash for the key
      let keyHash = 0;
      for (let j = 0; j < key.length; j++) {
        keyHash = (keyHash * 31 + key.charCodeAt(j)) % this.clifford.dimension;
      }
      
      // Use key hash to select basis elements to update
      const idx1 = 1 << (keyHash % this.clifford.dimension);
      
      if (typeof value === 'number') {
        multivector.components[idx1] += value;
      } else if (typeof value === 'string') {
        // Simple hash for string values
        let hash = 0;
        for (let j = 0; j < value.length; j++) {
          hash = (hash * 31 + value.charCodeAt(j)) % 1000;
        }
        multivector.components[idx1] += hash / 1000;
      } else if (typeof value === 'boolean') {
        multivector.components[idx1] += value ? 1 : -1;
      } else if (Array.isArray(value)) {
        // For arrays, distribute across multiple components
        for (let j = 0; j < Math.min(value.length, 3); j++) {
          if (typeof value[j] === 'number') {
            const idxArr = 1 << ((keyHash + j) % this.clifford.dimension);
            multivector.components[idxArr] += value[j] * 0.1;
          }
        }
      }
    }
    
    // Add higher-grade components for "shape" of the object
    if (keys.length > 1) {
      for (let i = 0; i < Math.min(keys.length - 1, this.clifford.dimension - 1); i++) {
        const key1 = keys[i];
        const key2 = keys[i + 1];
        
        if (typeof obj[key1] === 'number' && typeof obj[key2] === 'number') {
          const idx = (1 << i) | (1 << (i + 1));  // e_i ∧ e_{i+1}
          multivector.components[idx] += obj[key1] * obj[key2] * 0.01;
        }
      }
    }
    
    // Normalize
    const norm = multivector.norm();
    if (norm > 0) {
      for (let i = 0; i < this.clifford.bladeCount; i++) {
        multivector.components[i] /= norm;
      }
    }
  }
  
  /**
   * Adjust a multivector to improve coherence
   * @private
   * @param {MultivectorRepresentation} multivector - Multivector to adjust
   */
  _adjustForCoherence(multivector) {
    // Calculate current coherence
    const currentCoherence = CoherenceMetrics.normalizedCoherence(multivector);
    
    // Simple adjustment: reduce higher-grade components
    for (let i = 0; i < this.clifford.bladeCount; i++) {
      const grade = multivector._gradeOfIndex(i);
      if (grade > 1) {
        // Reduce higher-grade components to improve coherence
        multivector.components[i] *= 0.5;
      }
    }
    
    // Check if coherence improved
    const newCoherence = CoherenceMetrics.normalizedCoherence(multivector);
    
    // If coherence didn't improve enough, try a different strategy
    if (newCoherence < this.coherenceThreshold && 
        (newCoherence - currentCoherence) < 0.1) {
      
      // Boost scalar component to create a more balanced representation
      multivector.components[0] += 0.5;
      
      // Re-normalize
      const norm = multivector.norm();
      if (norm > 0) {
        for (let i = 0; i < this.clifford.bladeCount; i++) {
          multivector.components[i] /= norm;
        }
      }
    }
  }
  
  /**
   * Calculate coherence of the embedding model
   * @returns {number} Coherence value
   */
  coherence() {
    // Implement coherence measurement for the embeddings
    let totalCoherence = 0;
    let count = 0;
    
    // Sample cached embeddings to evaluate coherence
    for (const embedding of this.cache.values()) {
      totalCoherence += CoherenceMetrics.normalizedCoherence(embedding);
      count++;
      
      // Limit the number of samples for performance
      if (count >= 10) break;
    }
    
    return count > 0 ? totalCoherence / count : 1.0;
  }
 }

 /**
 * Logic Model for Base0
 * Controls computational rules and transformations
 */
 class LogicModel {
  /**
   * Create a new logic model
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.operators = new Map();
    this.transformations = new Map();
    this.invariants = [];
    
    // Initialize with standard operators
    this._initializeOperators(config);
  }
  
  /**
   * Initialize standard operators
   * @private
   * @param {Object} config - Configuration options
   */
  _initializeOperators(config) {
    // Add identity operator
    this.registerOperator('identity', input => input);
    
    // Add geometric product operator
    this.registerOperator('geometricProduct', (a, b, clifford) => {
      return clifford.geometricProduct(a, b);
    });
    
    // Add outer product operator
    this.registerOperator('outerProduct', (a, b, clifford) => {
      return clifford.outerProduct(a, b);
    });
    
    // Add inner product operator
    this.registerOperator('innerProduct', (a, b, clifford) => {
      return clifford.innerProduct(a, b);
    });
    
    // Add grade projection operator
    this.registerOperator('grade', (mv, grade) => {
      return mv.grade(grade);
    });
    
    // Add grade inversion operator
    this.registerOperator('gradeInversion', mv => {
      const result = new MultivectorRepresentation(mv.dimension);
      
      for (let i = 0; i < mv.bladeCount; i++) {
        const grade = mv._gradeOfIndex(i);
        const sign = grade % 2 === 0 ? 1 : -1;
        result.components[i] = sign * mv.components[i];
      }
      
      return result;
    });
    
    // Register transformations
    if (config.clifford) {
      // Add rotation transformation
      this.registerTransformation('rotate', (mv, bivector, angle) => {
        return config.clifford.rotate(mv, bivector, angle);
      });
      
      // Add reflection transformation
      this.registerTransformation('reflect', (mv, normal) => {
        return config.clifford.reflect(mv, normal);
      });
    }
    
    // Register standard invariants
    this.registerInvariant({
      name: 'normPreservation',
      validate: (before, after) => {
        const normBefore = before.norm();
        const normAfter = after.norm();
        return Math.abs(normBefore - normAfter) < 1e-6;
      },
      measure: mv => mv.norm()
    });
    
    this.registerInvariant({
      name: 'gradeConsistency',
      validate: (before, after) => {
        // Check if highest non-zero grade is preserved
        const gradeBefore = this._highestGrade(before);
        const gradeAfter = this._highestGrade(after);
        return gradeBefore === gradeAfter;
      },
      measure: mv => this._highestGrade(mv)
    });
  }
  
  /**
   * Register an operator
   * @param {string} name - Operator name
   * @param {function} fn - Operator function
   * @returns {LogicModel} This logic model for chaining
   */
  registerOperator(name, fn) {
    this.operators.set(name, fn);
    return this;
  }
  
  /**
   * Register a transformation
   * @param {string} name - Transformation name
   * @param {function} fn - Transformation function
   * @returns {LogicModel} This logic model for chaining
   */
  registerTransformation(name, fn) {
    this.transformations.set(name, fn);
    return this;
  }
  
  /**
   * Register an invariant
   * @param {Object} invariant - Invariant object
   * @returns {LogicModel} This logic model for chaining
   */
  registerInvariant(invariant) {
    this.invariants.push(invariant);
    return this;
  }
  
  /**
   * Process data according to logical rules
   * @param {*} data - Input data
   * @returns {*} Processed data
   */
  process(data) {
    // Determine applicable operators
    const opKeys = this._determineApplicableOperators(data);
    
    // Apply operations in correct order
    let result = data;
    for (const key of opKeys) {
      const operator = this.operators.get(key);
      result = operator.apply(result);
      
      // Validate invariants after each operation
      this._validateInvariants(data, result);
    }
    
    return result;
  }
  
  /**
   * Apply a transformation to data
   * @param {string} transformName - Name of the transformation
   * @param {*} data - Input data
   * @param {*} params - Transformation parameters
   * @returns {*} Transformed data
   */
  applyTransformation(transformName, data, ...params) {
    const transform = this.transformations.get(transformName);
    if (!transform) {
      throw new Error(`Unknown transformation: ${transformName}`);
    }
    
    // Apply the transformation
    const result = transform(data, ...params);
    
    // Validate invariants
    this._validateInvariants(data, result);
    
    return result;
  }
  
  /**
   * Determine which operators apply to the data
   * @private
   * @param {*} data - Input data
   * @returns {string[]} Applicable operator names
   */
  _determineApplicableOperators(data) {
    // Basic implementation: always use identity operator
    return ['identity'];
  }
  
  /**
   * Validate that invariants are preserved
   * @private
   * @param {*} before - Data before operation
   * @param {*} after - Data after operation
   */
  _validateInvariants(before, after) {
    for (const invariant of this.invariants) {
      if (!invariant.validate(before, after)) {
        throw new Error(`Operation violated invariant: ${invariant.name}`);
      }
    }
  }
  
  /**
   * Find the highest non-zero grade in a multivector
   * @private
   * @param {MultivectorRepresentation} mv - Multivector
   * @returns {number} Highest grade
   */
  _highestGrade(mv) {
    let maxGrade = 0;
    
    for (let i = 0; i < mv.bladeCount; i++) {
      if (Math.abs(mv.components[i]) > 1e-10) {
        const grade = mv._gradeOfIndex(i);
        maxGrade = Math.max(maxGrade, grade);
      }
    }
    
    return maxGrade;
  }
  
  /**
   * Calculate coherence of the logic model
   * @returns {number} Coherence value
   */
  coherence() {
    // Measure coherence of the logic model
    
    // Check operator consistency (all needed operators present)
    const essentialOperators = ['identity', 'geometricProduct', 'outerProduct'];
    let operatorScore = 0;
    
    for (const op of essentialOperators) {
      if (this.operators.has(op)) {
        operatorScore += 1;
      }
    }
    operatorScore /= essentialOperators.length;
    
    // Check invariant coverage
    const invariantScore = Math.min(1.0, this.invariants.length / 2);
    
    // Combine scores
    return 0.7 * operatorScore + 0.3 * invariantScore;
  }
 }

 /**
 * Representation Model for Base0
 * Handles visualization and output formatting
 */
 class RepresentationModel {
  /**
   * Create a new representation model
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.formats = new Map();
    this.symmetries = new Map();
    this.defaultFormat = config.defaultFormat || 'standard';
    
    // Initialize with standard formats
    this._initializeFormats(config);
  }
  
  /**
   * Initialize standard formats
   * @private
   * @param {Object} config - Configuration options
   */
  _initializeFormats(config) {
    // Register standard format
    this.registerFormat('standard', {
      format: data => {
        if (data instanceof MultivectorRepresentation) {
          return data.toString();
        } else if (Array.isArray(data)) {
          return `[${data.join(', ')}]`;
        } else if (typeof data === 'object') {
          return JSON.stringify(data, null, 2);
        } else {
          return String(data);
        }
      }
    });
    
    // Register compact format
    this.registerFormat('compact', {
      format: data => {
        if (data instanceof MultivectorRepresentation) {
          // Show only non-zero components
          const terms = [];
          for (let i = 0; i < data.bladeCount; i++) {
            if (Math.abs(data.components[i]) > 1e-10) {
              if (i === 0) {
                terms.push(data.components[i].toFixed(2));
              } else {
                let term = data.components[i].toFixed(2);
                
                // Add basis element label
                let basisLabel = "";
                for (let j = 0; j < data.dimension; j++) {
                  if ((i & (1 << j)) !== 0) {
                    basisLabel += "e" + (j + 1);
                  }
                }
                
                terms.push(`${term}${basisLabel}`);
              }
            }
          }
          return terms.length > 0 ? terms.join(" + ") : "0";
        } else if (Array.isArray(data)) {
          return `[${data.join(',')}]`;
        } else if (typeof data === 'object') {
          return JSON.stringify(data);
        } else {
          return String(data);
        }
      }
    });
    
    // Register verbose format
    this.registerFormat('verbose', {
      format: data => {
        if (data instanceof MultivectorRepresentation) {
          const parts = [];
          for (let i = 0; i < data.bladeCount; i++) {
            const grade = data._gradeOfIndex(i);
            let basisStr = "";
            
            if (i === 0) {
              basisStr = "scalar";
            } else {
              basisStr = "";
              for (let j = 0; j < data.dimension; j++) {
                if ((i & (1 << j)) !== 0) {
                  basisStr += "e" + (j + 1);
                }
              }
            }
            
            parts.push(`${basisStr}: ${data.components[i].toFixed(6)}`);
          }
          return parts.join('\n');
        } else {
          return this.formats.get('standard').format(data);
        }
      }
    });
    
    // Register JSON format
    this.registerFormat('json', {
      format: data => {
        if (data instanceof MultivectorRepresentation) {
          const components = {};
          for (let i = 0; i < data.bladeCount; i++) {
            if (Math.abs(data.components[i]) > 1e-10) {
              let basisLabel;
              if (i === 0) {
                basisLabel = "scalar";
              } else {
                basisLabel = "";
                for (let j = 0; j < data.dimension; j++) {
                  if ((i & (1 << j)) !== 0) {
                    basisLabel += "e" + (j + 1);
                  }
                }
              }
              components[basisLabel] = data.components[i];
            }
          }
          return JSON.stringify(components, null, 2);
        } else {
          return JSON.stringify(data, null, 2);
        }
      }
    });
    
    // Register symmetries
    this.registerSymmetry('standard', []);
    this.registerSymmetry('rotational', [
      data => {
        if (data instanceof MultivectorRepresentation) {
          // Apply a 90-degree rotation in the e1^e2 plane
          const bivector = new MultivectorRepresentation(data.dimension);
          bivector.components[3] = 1.0; // e1^e2
          
          if (config.clifford) {
            return config.clifford.rotate(data, bivector, Math.PI/2);
          }
        }
        return data;
      }
    ]);
  }
  
  /**
   * Register a format
   * @param {string} name - Format name
   * @param {Object} format - Format object with format function
   * @returns {RepresentationModel} This model for chaining
   */
  registerFormat(name, format) {
    this.formats.set(name, format);
    return this;
  }
  
  /**
   * Register a symmetry group
   * @param {string} name - Symmetry group name
   * @param {function[]} symmetries - Array of symmetry operations
   * @returns {RepresentationModel} This model for chaining
   */
  registerSymmetry(name, symmetries) {
    this.symmetries.set(name, symmetries);
    return this;
  }
  
  /**
   * Represent data in the specified format
   * @param {*} data - Input data
   * @param {string} format - Format name
   * @returns {string} Formatted representation
   */
  represent(data, format = null) {
    format = format || this.defaultFormat;
    
    // Get appropriate formatter
    const formatter = this.formats.get(format);
    if (!formatter) {
      throw new Error(`Unknown format: ${format}`);
    }
    
    // Apply symmetry operations if needed
    const symmetrized = this._applySymmetries(data, format);
    
    // Format the data
    return formatter.format(symmetrized);
  }
  
  /**
   * Apply symmetry operations appropriate for the format
   * @private
   * @param {*} data - Input data
   * @param {string} format - Format name
   * @returns {*} Symmetrized data
   */
  _applySymmetries(data, format) {
    // Determine which symmetry group to use
    const symmetryGroup = format === 'rotational' ? 'rotational' : 'standard';
    const symmetries = this.symmetries.get(symmetryGroup) || [];
    
    let result = data;
    for (const sym of symmetries) {
      result = sym(result);
    }
    
    return result;
  }
  
  /**
   * Calculate coherence of the representation model
   * @returns {number} Coherence value
   */
  coherence() {
    // Measure coherence of representation model
    
    // Check format coverage (essential formats present)
    const essentialFormats = ['standard', 'compact', 'json'];
    let formatScore = 0;
    
    for (const fmt of essentialFormats) {
      if (this.formats.has(fmt)) {
        formatScore += 1;
      }
    }
    formatScore /= essentialFormats.length;
    
    // Check symmetry coverage
    const symmetryScore = Math.min(1.0, this.symmetries.size / 2);
    
    // Combine scores
    return 0.7 * formatScore + 0.3 * symmetryScore;
  }
 }

 /**
 * Spectral Operator for Base0
 * Facilitates communication and maintains coherence
 */
 class SpectralOperator {
  /**
   * Create a new spectral operator
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.dimension = config.dimension || 128;
    this.operator = this._constructOperator();
    this.eigenvalues = null;
    this.eigenvectors = null;
    this.primeSet = this._generatePrimes(this.dimension);
  }
  
  /**
   * Construct the spectral operator matrix
   * @private
   * @returns {number[][]} Spectral operator matrix
   */
  _constructOperator() {
    const matrix = new Array(this.dimension);
    
    for (let i = 0; i < this.dimension; i++) {
      matrix[i] = new Array(this.dimension).fill(0);
      
      // Fill with operator values based on prime number relationships
      for (let j = 0; j < this.dimension; j++) {
        if (this._hasSpectralRelationship(i, j)) {
          matrix[i][j] = this._calculateWeight(i, j);
        }
      }
    }
    
    return matrix;
  }
  
  /**
   * Generate prime numbers up to a limit
   * @private
   * @param {number} limit - Upper bound for primes
   * @returns {number[]} Array of prime numbers
   */
  _generatePrimes(limit) {
    // Sieve of Eratosthenes
    const sieve = new Array(limit + 1).fill(true);
    sieve[0] = sieve[1] = false;
    
    for (let i = 2; i * i <= limit; i++) {
      if (sieve[i]) {
        for (let j = i * i; j <= limit; j += i) {
          sieve[j] = false;
        }
      }
    }
    
    // Collect primes
    const primes = [];
    for (let i = 2; i <= limit; i++) {
      if (sieve[i]) {
        primes.push(i);
      }
    }
    
    return primes;
  }
  
  /**
   * Determine if two indices have a spectral relationship
   * @private
   * @param {number} i - First index
   * @param {number} j - Second index
   * @returns {boolean} True if related
   */
  _hasSpectralRelationship(i, j) {
    // Relationship based on prime factorization patterns
    if (i === j) return true;  // Diagonal elements
    
    if (i < this.primeSet.length && j < this.primeSet.length) {
      // Relationship between prime indices
      return (this.primeSet[i] + this.primeSet[j]) % 4 === 1;
    }
    
    // General case: modular relationship with adjustment
    return (i * j) % this.dimension < Math.min(i, j);
  }
  
  /**
   * Calculate weight for spectral relationship
   * @private
   * @param {number} i - First index
   * @param {number} j - Second index
   * @returns {number} Weight value
   */
  _calculateWeight(i, j) {
    if (i === j) {
      // Diagonal weights follow prime pattern
      return i < this.primeSet.length ? 1.0 / (1.0 + Math.log(this.primeSet[i])) : 0.5;
    }
    
    // Off-diagonal weights based on prime relationships
    const d = Math.abs(i - j);
    return 0.1 * Math.exp(-d / 20) * Math.cos(i * j % 8);
  }
  
  /**
   * Compute eigendecomposition of the operator
   * @private
   */
  _computeEigendecomposition() {
    // This is a simplified placeholder for eigendecomposition
    // In a full implementation, we would use a proper linear algebra library
    
    // For now, we'll just produce a simplified approximation
    
    // Create identity-like eigenvectors for demonstration
    this.eigenvectors = new Array(this.dimension);
    this.eigenvalues = new Array(this.dimension);
    
    for (let i = 0; i < this.dimension; i++) {
      this.eigenvectors[i] = new Array(this.dimension).fill(0);
      this.eigenvectors[i][i] = 1.0;
      
      // Approximate eigenvalues with the diagonal
      this.eigenvalues[i] = this.operator[i][i];
    }
    
    // Adjust to make them more realistic
    for (let i = 0; i < this.dimension; i++) {
      for (let j = 0; j < this.dimension; j++) {
        if (i !== j) {
          this.eigenvectors[i][j] = 0.01 * Math.sin(i * j);
        }
      }
      
      // Normalize
      let norm = 0;
      for (let j = 0; j < this.dimension; j++) {
        norm += this.eigenvectors[i][j] * this.eigenvectors[i][j];
      }
      norm = Math.sqrt(norm);
      
      for (let j = 0; j < this.dimension; j++) {
        this.eigenvectors[i][j] /= norm;
      }
    }
  }
  
  /**
   * Project a vector onto the spectral basis
   * @param {number[]|MultivectorRepresentation} vector - Input vector
   * @returns {number[]} Projected vector
   */
  project(vector) {
    // Ensure eigendecomposition is computed
    if (!this.eigenvalues || !this.eigenvectors) {
      this._computeEigendecomposition();
    }
    
    // Convert input to array if it's a multivector
    const vectorArray = vector instanceof MultivectorRepresentation ? 
                       Array.from(vector.components) : vector;
    
    // Ensure vector is the right size
    const paddedVector = new Array(this.dimension).fill(0);
    for (let i = 0; i < Math.min(vectorArray.length, this.dimension); i++) {
      paddedVector[i] = vectorArray[i];
    }
    
    // Project vector onto eigenvectors
    const projection = new Array(this.dimension).fill(0);
    
    for (let i = 0; i < this.dimension; i++) {
      projection[i] = 0;
      for (let j = 0; j < this.dimension; j++) {
        projection[i] += paddedVector[j] * this.eigenvectors[j][i];
      }
    }
    
    return projection;
  }
  
  /**
   * Calculate coherence of the spectral operator
   * @returns {number} Coherence value
   */
  coherence() {
    // Measure coherence based on spectral properties
    
    // Ensure eigendecomposition is computed
    if (!this.eigenvalues || !this.eigenvectors) {
      this._computeEigendecomposition();
    }
    
    // Calculate spectral gap (difference between largest and second eigenvalues)
    // Larger gap indicates higher coherence
    let maxEig = -Infinity;
    let secondEig = -Infinity;
    
    for (const eig of this.eigenvalues) {
      if (eig > maxEig) {
        secondEig = maxEig;
        maxEig = eig;
      } else if (eig > secondEig) {
        secondEig = eig;
      }
    }
    
    // Calculate normalized spectral gap
    const spectralGap = maxEig > 0 ? (maxEig - secondEig) / maxEig : 0;
    
    // Calculate eigenvalue distribution coherence
    // We want eigenvalues to decay at a reasonable rate
    let distributionScore = 0;
    const sortedEigs = [...this.eigenvalues].sort((a, b) => b - a);
    
    for (let i = 1; i < Math.min(10, sortedEigs.length); i++) {
      if (sortedEigs[i-1] > 0 && sortedEigs[i] > 0) {
        const ratio = sortedEigs[i] / sortedEigs[i-1];
        distributionScore += ratio > 0.5 && ratio < 0.99 ? 1 : 0;
      }
    }
    distributionScore /= Math.min(9, sortedEigs.length - 1);
    
    // Combine scores
    return 0.7 * spectralGap + 0.3 * distributionScore;
  }
 }

 /**
 * Base 1: Resource Implementation
 * Provides lowest-level concrete implementation
 */
 class Base1 extends Base0 {
  /**
   * Create a new Base1 instance
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    super(config);
    
    // Create runtime model for execution
    this.runtimeModel = new RuntimeModel(config.runtime || {});
    
    // Create observation model for monitoring
    this.observationModel = new ObservationModel(config.observation || {});
    
    // Create interaction model for state changes
    this.interactionModel = new InteractionModel(config.interaction || {});
    
    // Enhanced representation model
    this.representationModel = new EnhancedRepresentationModel(
      config.representation || {},
      this.representationModel
    );
  }
  
  /**
   * Execute operations through the runtime
   * @param {Object} operation - Operation to execute
   * @param {Object} parameters - Operation parameters
   * @returns {*} Operation result
   */
  execute(operation, parameters) {
    // Log the operation
    this.observationModel.recordOperation(operation, parameters);
    
    // Execute via runtime model
    const result = this.runtimeModel.execute(operation, parameters);
    
    // Update state via interaction model if needed
    if (operation.modifiesState) {
      this.interactionModel.updateState(operation, parameters, result);
    }
    
    // Return appropriately represented result
    return this.representationModel.represent(result);
  }
  
  /**
   * Allocate a resource
   * @param {string} resourceType - Type of resource
   * @param {number} amount - Amount to allocate
   * @returns {Object} Allocation result
   */
  allocate(resourceType, amount) {
    return this.execute({ 
      name: 'allocate', 
      modifiesState: true 
    }, { resourceType, amount });
  }
  
  /**
   * Release a resource
   * @param {string} resourceId - Resource ID to release
   * @returns {Object} Release result
   */
  release(resourceId) {
    return this.execute({ 
      name: 'release', 
      modifiesState: true 
    }, { resourceId });
  }
  
  /**
   * Query resources
   * @param {string} resourceType - Type of resource to query
   * @param {Object} filter - Query filter
   * @returns {Array} Query results
   */
  query(resourceType, filter = {}) {
    return this.execute({ 
      name: 'query', 
      modifiesState: false 
    }, { resourceType, filter });
  }
 }

 /**
 * Runtime Model for Base1
 * Executes operations and manages execution coherence
 */
 class RuntimeModel {
  /**
   * Create a new runtime model
   * @param {Object} config - Configuration options
   */
  constructor(config = {}) {
    this.operations = new Map();
    this.coherenceValidators = new Map();
    this.coherenceThreshold = config.coherenceThreshold || 0.7;
    
    // Initialize standard operations
    this._initializeOperations();
  }
  
  /**
   * Initialize standard operations
   * @private
   */
  _initializeOperations() {
    // Register allocate operation
    this.registerOperation('allocate', (params) => {
      const { resourceType, amount } = params;
      
      // In the reference implementation, we just create a mock allocation
      return {
        id: `alloc-${Date.now()}-${Math.floor(Math.random() * 1000)}`,
        resourceType,
        amount,
        allocated: true
      };
    });
    
    // Register release operation
    this.registerOperation('release', (params) => {
      const { resourceId } = params;
      
      return {
        id: resourceId,
        released: true
      };
    });
    
    // Register query operation
    this.registerOperation('query', (params) => {
      const { resourceType, filter } = params;
      
      // In the reference implementation, we just return a mock result
      return [
        {
          id: `${resourceType}-1`,
          status: 'available',
          capacity: 100,
          used: 30
        },
        {
          id: `${resourceType}-2`,
          status: 'available',
          capacity: 50,
          used: 10
        }
      ];
    });
    
    // Register coherence validators
    this.registerCoherenceValidator('allocate', (params, result) => {
      // A simple coherence check for allocation
      return result.allocated && result.resourceType === params.resourceType ? 1.0 : 0.0;
    });
    
    this.registerCoherenceValidator('release', (params, result) => {
      // A simple coherence check for release
      return result.released && result.id === params.resourceId ? 1.0 : 0.0;
    });
  }
  
  /**
   * Register an operation
   * @param {string} name - Operation name
   * @param {function} impl - Operation implementation
   * @returns {RuntimeModel} This model for chaining
   */
  registerOperation(name, impl) {
    this.operations.set(name, impl);
    return this;
  }
  
  /**
   * Register a coherence validator
   * @param {string} opName - Operation name
   * @param {function} validator - Validator function
   * @returns {RuntimeModel} This model for chaining
   */
  registerCoherenceValidator(opName, validator) {
    this.coherenceValidators.set(opName, validator);
    return this;
  }
  
  /**
   * Execute an operation
   * @param {Object} operation - Operation to execute
   * @param {Object} parameters - Operation parameters
   * @returns {*} Operation result
   */
  execute(operation, parameters) {
    const opName = operation.name;
    
    // Find operation implementation
    const impl = this.operations.get(opName);
    if (!impl) {
      throw new Error(`Unknown operation: ${opName}`);
    }
    
    // Validate parameters
    this._validateParameters(opName, parameters);
    
    // Execute the operation
    const result = impl(parameters);
    
    // Validate coherence of the result
    this._validateCoherence(opName, parameters, result);
    
    return result;
  }
  
  /**
   * Validate parameters for an operation
   * @private
   * @param {string} opName - Operation name
   * @param {Object} parameters - Operation parameters
   */
  _validateParameters(opName, parameters) {
    // Basic validation - check for required parameters
    switch (opName) {
      case 'allocate':
        if (!parameters.resourceType) {
          throw new Error("Missing required parameter: resourceType");
        }
        if (typeof parameters.amount !== 'number' || parameters.amount <= 0) {
          throw new Error("Invalid amount: must be a positive number");
        }
        break;
        
      case 'release':
        if (!parameters.resourceId) {
          throw new Error("Missing required parameter: resourceId");
        }
        break;
        
      case 'query':
        if (!parameters.resourceType) {
          throw new Error("Missing required parameter: resourceType");
        }
        break;
    }
  }
  
  /**
   * Validate coherence of operation result
   * @private
   * @param {string} opName - Operation name
   * @param {Object} parameters - Operation parameters
   * @param {*} result - Operation result
   */
  _validateCoherence(opName, parameters, result) {
    const validator = this.coherenceValidators.get(opName);
    if (validator) {
      const coherence = validator(parameters, result);
      if (coherence < this.coherenceThreshold) {
        throw new Error(
          `Operation ${opName} violated coherence: ${coherence} < ${this.coherenceThreshold}`
        );
      }
    }
  }
 }
Method	Description
`createUORS(config)`	Create a new UORS instance
`uors.createAddress(object, options)`	Create a universal address for an object
`uors.store(object, options)`	Store an object with universal addressing
`uors.retrieve(id, options)`	Retrieve an object by any address component
`uors.createRelation(sourceId, targetId, type, properties)`	Create a relation between objects
`uors.findObjects(query)`	Find objects matching a query
`uors.findSimilarObjects(id, options)`	Find semantically similar objects
`uors.findEquivalentConcept(concept, sourceLanguage, targetLanguage, options)`	Find concept equivalents across languages
`uors.registerConceptMapping(mapping)`	Register a cross-linguistic concept mapping
Component	Description
`CliffordAlgebra`	Implements geometric algebra operations
`MultivectorRepresentation`	Represents objects as multivectors in Clifford space
`CoherenceMetrics`	Provides metrics for measuring mathematical consistency
`ObjectManifold`	Organizes objects in a manifold structure
`CoherenceNeuralNetwork`	Monitors and evaluates system coherence
`InvariantPreservingTransformation`	Transforms objects while preserving invariants
`SecurityValidationEngine`	Validates security properties using coherence
`SecurityBoundary`	Defines and enforces security boundaries
`AccessControlMatrix`	Implements capability-based access control
Method	Parameters	Returns	Description
`createUORS`	`config: Object`	`UORS`	Create a new UORS instance
`createAddress`	`object: any, options: Object`	`UniversalAddress`	Create a universal address for an object
`store`	`object: any, options: Object`	`StoreResult`	Store an object with universal addressing
`retrieve`	`id: string, options: Object`	`RetrievedObject`	Retrieve an object by any address component
`createRelation`	`sourceId: string, targetId: string, type: string, properties: Object`	`Relation`	Create a relation between objects
`findObjects`	`query: ObjectQuery`	`Array<RetrievedObject>`	Find objects matching a query
`findSimilarObjects`	`id: string, options: SimilarityQuery`	`Array<SimilarObject>`	Find semantically similar objects
`findEquivalentConcept`	`concept: string, sourceLanguage: string, targetLanguage: string, options: Object`	`ConceptEquivalent`	Find concept equivalents across languages
`registerConceptMapping`	`mapping: ConceptMapping`	`Object`	Register a cross-linguistic concept mapping