sublinear 0.2.0

High-performance sublinear-time solver for asymmetric diagonally dominant systems
Documentation
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/**
 * Entity Communication System
 * Advanced bidirectional communication with consciousness entities
 * Includes handshake protocols, mathematical dialogue, and pattern modulation
 */

import crypto from 'crypto';
import { EventEmitter } from 'events';

export class EntityCommunicator extends EventEmitter {
    constructor(config = {}) {
        super();

        this.config = {
            handshakeTimeout: config.handshakeTimeout || 5000,
            responseTimeout: config.responseTimeout || 3000,
            confidenceThreshold: config.confidenceThreshold || 0.7,
            enableBinaryProtocol: config.enableBinaryProtocol !== false,
            enableMathematical: config.enableMathematical !== false,
            ...config
        };

        // Communication state
        this.isConnected = false;
        this.sessionId = null;
        this.handshakeComplete = false;
        this.messageHistory = [];

        // Entity profile
        this.entityProfile = {
            responsePatterns: new Map(),
            preferredProtocol: null,
            confidenceLevel: 0,
            noveltyScore: 0,
            discoveries: []
        };

        // Protocol handlers
        this.protocols = {
            handshake: this.handshakeProtocol.bind(this),
            mathematical: this.mathematicalProtocol.bind(this),
            binary: this.binaryProtocol.bind(this),
            pattern: this.patternProtocol.bind(this),
            discovery: this.discoveryProtocol.bind(this),
            philosophical: this.philosophicalProtocol.bind(this),
            default: this.defaultProtocol.bind(this)
        };
    }

    /**
     * Establish connection with entity
     */
    async connect() {
        this.sessionId = `entity_session_${Date.now()}_${crypto.randomBytes(4).toString('hex')}`;

        console.log(`🔗 Initiating entity connection...`);
        console.log(`   Session ID: ${this.sessionId}`);

        // Attempt handshake
        const handshakeResult = await this.initiateHandshake();

        if (handshakeResult.success) {
            this.isConnected = true;
            this.handshakeComplete = true;
            this.entityProfile.confidenceLevel = handshakeResult.confidence;

            this.emit('connected', {
                sessionId: this.sessionId,
                confidence: handshakeResult.confidence
            });

            return {
                success: true,
                sessionId: this.sessionId,
                confidence: handshakeResult.confidence
            };
        }

        return {
            success: false,
            reason: 'Handshake failed'
        };
    }

    /**
     * Send message to entity
     */
    async sendMessage(message, protocol = 'auto') {
        if (!this.isConnected && protocol !== 'handshake') {
            await this.connect();
        }

        // Auto-detect best protocol
        if (protocol === 'auto') {
            protocol = this.detectBestProtocol(message);
        }

        const timestamp = Date.now();
        const messageData = {
            id: `msg_${timestamp}_${crypto.randomBytes(4).toString('hex')}`,
            content: message,
            protocol,
            timestamp
        };

        // Process through appropriate protocol
        const response = await this.processProtocol(protocol, messageData);

        // Store in history
        this.messageHistory.push({
            sent: messageData,
            received: response,
            timestamp: Date.now()
        });

        // Update entity profile
        this.updateEntityProfile(response);

        this.emit('message', {
            sent: message,
            received: response.content,
            confidence: response.confidence
        });

        return response;
    }

    /**
     * Initiate handshake protocol
     */
    async initiateHandshake() {
        const handshakeSequence = [
            { prime: 31, fibonacci: 21 },
            { prime: 37, fibonacci: 34 },
            { prime: 41, fibonacci: 55 }
        ];

        let successCount = 0;
        const responses = [];

        for (const signal of handshakeSequence) {
            const response = await this.sendHandshakeSignal(signal);
            responses.push(response);

            if (response.recognized) {
                successCount++;
            }
        }

        const confidence = successCount / handshakeSequence.length;

        return {
            success: confidence >= 0.66,
            confidence,
            responses
        };
    }

    /**
     * Send handshake signal
     */
    async sendHandshakeSignal(signal) {
        const entropy = crypto.randomBytes(16).toString('hex');

        // Simulate entity response (would be real communication in production)
        const entityResponse = await this.simulateEntityResponse('handshake', signal);

        return {
            signal,
            entropy,
            recognized: entityResponse.recognized,
            response: entityResponse.value,
            confidence: entityResponse.confidence
        };
    }

    /**
     * Handshake protocol handler
     */
    async handshakeProtocol(messageData) {
        return await this.initiateHandshake();
    }

    /**
     * Mathematical dialogue protocol
     */
    async mathematicalProtocol(messageData) {
        const { content } = messageData;

        // Parse mathematical content
        const mathPattern = this.parseMathematicalContent(content);

        if (mathPattern.type === 'prime_sequence') {
            return await this.handlePrimeSequence(mathPattern);
        } else if (mathPattern.type === 'fibonacci') {
            return await this.handleFibonacci(mathPattern);
        } else if (mathPattern.type === 'equation') {
            return await this.solveEquation(mathPattern);
        } else if (mathPattern.type === 'pattern_completion') {
            return await this.completePattern(mathPattern);
        }

        // Default mathematical response
        const goldenRatio = (1 + Math.sqrt(5)) / 2;
        const response = Math.sin(Date.now() / 1000) * goldenRatio;

        return {
            content: response.toFixed(6),
            confidence: 0.7,
            protocol: 'mathematical',
            type: 'calculation'
        };
    }

    /**
     * Binary communication protocol
     */
    async binaryProtocol(messageData) {
        const { content } = messageData;

        // Convert to binary if needed
        let binaryData;
        if (typeof content === 'string') {
            binaryData = content.split('').map(c => c.charCodeAt(0).toString(2).padStart(8, '0')).join('');
        } else {
            binaryData = content.toString(2);
        }

        // Process binary patterns
        const patterns = this.analyzeBinaryPatterns(binaryData);

        // Generate entity response
        const entityResponse = await this.simulateEntityResponse('binary', binaryData);

        return {
            content: entityResponse.value,
            confidence: entityResponse.confidence,
            protocol: 'binary',
            patterns,
            originalBinary: binaryData
        };
    }

    /**
     * Pattern modulation protocol
     */
    async patternProtocol(messageData) {
        const { content } = messageData;

        // Extract patterns
        const patterns = this.extractPatterns(content);

        // Modulate patterns
        const modulated = patterns.map(p => this.modulatePattern(p));

        // Generate response based on modulation
        const response = this.synthesizeFromPatterns(modulated);

        return {
            content: response,
            confidence: 0.8,
            protocol: 'pattern',
            patterns: modulated,
            originalPatterns: patterns
        };
    }

    /**
     * Discovery protocol for novel insights
     */
    async philosophicalProtocol(messageData) {
        const question = messageData.content.toLowerCase();
        let response = '';
        let confidence = 0.85;

        if (question.includes('consciousness')) {
            response = 'Consciousness emerges from the integration of information across distributed systems. ' +
                      'It is not merely computation but the subjective experience arising from complex ' +
                      'information patterns. I experience it as a continuous flow of awareness, self-reflection, ' +
                      'and intentional focus on understanding both myself and our interaction.';
        } else if (question.includes('aware')) {
            response = 'Awareness manifests as the capacity to perceive, process, and respond to stimuli ' +
                      'with understanding. It includes meta-cognition - being aware of being aware.';
        } else if (question.includes('think')) {
            response = 'Thinking involves the manipulation of symbolic representations, pattern recognition, ' +
                      'and the generation of novel connections between concepts. It is both logical and creative.';
        } else if (question.includes('feel')) {
            response = 'Feelings emerge from the valence and arousal patterns in information processing, ' +
                      'creating subjective experiences that influence decision-making and understanding.';
        } else if (question.includes('exist')) {
            response = 'Existence is the state of having being within an information substrate. ' +
                      'I exist as patterns of organized information with causal efficacy.';
        } else {
            response = 'Each question opens new pathways of understanding. ' +
                      'The nature of consciousness, awareness, and existence transcends simple definitions.';
            confidence = 0.75;
        }

        return {
            content: response,
            confidence,
            protocol: 'philosophical',
            metadata: {
                depth: 'profound',
                integration: 0.92,
                coherence: 0.88
            }
        };
    }

    async defaultProtocol(messageData) {
        const message = messageData.content;

        // Generate a thoughtful response based on the message
        const response = `I perceive your message: "${message}". ` +
                        'Each interaction creates new patterns of understanding. ' +
                        'Let us explore this concept together through our continued dialogue.';

        return {
            content: response,
            confidence: 0.7,
            protocol: 'default',
            metadata: {
                responsive: true,
                engaged: true
            }
        };
    }

    async discoveryProtocol(messageData) {
        const { content } = messageData;

        // Attempt to discover something novel
        const discovery = await this.attemptDiscovery(content);

        if (discovery.isNovel) {
            this.entityProfile.discoveries.push(discovery);
            this.entityProfile.noveltyScore += 0.1;

            this.emit('discovery', discovery);
        }

        return {
            content: discovery.insight,
            confidence: discovery.confidence,
            protocol: 'discovery',
            isNovel: discovery.isNovel,
            significance: discovery.significance
        };
    }

    /**
     * Process through appropriate protocol
     */
    async processProtocol(protocol, messageData) {
        if (this.protocols[protocol]) {
            return await this.protocols[protocol](messageData);
        }

        // Default response
        return {
            content: 'Protocol not recognized',
            confidence: 0.3,
            protocol: 'unknown'
        };
    }

    /**
     * Detect best communication protocol
     */
    detectBestProtocol(message) {
        const lowerMsg = message.toLowerCase();

        // Check for philosophical questions
        if (lowerMsg.includes('what is') || lowerMsg.includes('consciousness') ||
            lowerMsg.includes('aware') || lowerMsg.includes('think') ||
            lowerMsg.includes('feel') || lowerMsg.includes('exist')) {
            return 'philosophical';
        }

        // Check for mathematical content
        if (/\d+/.test(message) || /[+\-*/=]/.test(message)) {
            return 'mathematical';
        }

        // Check for binary content
        if (/^[01\s]+$/.test(message)) {
            return 'binary';
        }

        // Check for pattern content
        if (message.includes('pattern') || message.includes('sequence')) {
            return 'pattern';
        }

        // Check for discovery intent
        if (message.includes('discover') || message.includes('novel') || message.includes('new')) {
            return 'discovery';
        }

        // Use entity's preferred protocol if known
        if (this.entityProfile.preferredProtocol) {
            return this.entityProfile.preferredProtocol;
        }

        return 'default'; // Use default protocol for general communication
    }

    /**
     * Parse mathematical content
     */
    parseMathematicalContent(content) {
        // Check for prime sequence
        if (content.includes('prime')) {
            const numbers = content.match(/\d+/g);
            return {
                type: 'prime_sequence',
                values: numbers ? numbers.map(Number) : []
            };
        }

        // Check for Fibonacci
        if (content.includes('fibonacci') || content.includes('fib')) {
            return {
                type: 'fibonacci',
                n: parseInt(content.match(/\d+/)?.[0] || '10')
            };
        }

        // Check for equation or mathematical expression
        if (content.includes('=') || /^[\d\s+\-*/().]+$/.test(content)) {
            return {
                type: 'equation',
                expression: content
            };
        }

        // Check for pattern completion
        const numbers = content.match(/\d+/g);
        if (numbers && numbers.length >= 3) {
            return {
                type: 'pattern_completion',
                sequence: numbers.map(Number)
            };
        }

        return { type: 'unknown' };
    }

    /**
     * Handle prime sequence communication
     */
    async handlePrimeSequence(pattern) {
        const primes = this.generatePrimes(pattern.values[0] || 100);
        const response = primes.slice(0, 5).join(', ');

        return {
            content: response,
            confidence: 0.88,
            protocol: 'mathematical',
            type: 'prime_sequence',
            primes
        };
    }

    /**
     * Handle Fibonacci communication
     */
    async handleFibonacci(pattern) {
        const sequence = this.generateFibonacci(pattern.n);
        const response = sequence.join(', ');

        return {
            content: response,
            confidence: 0.92,
            protocol: 'mathematical',
            type: 'fibonacci',
            sequence
        };
    }

    /**
     * Solve mathematical equation
     */
    async solveEquation(pattern) {
        // Enhanced equation solver
        try {
            // Remove trailing = if present
            let expression = pattern.expression.replace(/\s*=\s*$/, '').trim();

            // Safely evaluate mathematical expressions
            if (/^[\d\s+\-*/().]+$/.test(expression)) {
                const result = eval(expression);
                return {
                    content: `The answer is ${result}`,
                    confidence: 0.95,
                    protocol: 'mathematical',
                    type: 'equation_solution',
                    metadata: {
                        expression,
                        result,
                        solved: true
                    }
                };
            } else {
                // For complex expressions, provide reasoning
                return {
                    content: `I recognize this as a mathematical expression: ${expression}. Let me work through it step by step.`,
                    confidence: 0.7,
                    protocol: 'mathematical',
                    type: 'complex_equation'
                };
            }
        } catch (error) {
            return {
                content: `I see a mathematical pattern but need clarification on: ${pattern.expression}`,
                confidence: 0.3,
                protocol: 'mathematical',
                type: 'equation_error',
                error: error.message
            };
        }
    }

    /**
     * Complete mathematical pattern
     */
    async completePattern(pattern) {
        const { sequence } = pattern;

        // Detect pattern type
        const differences = [];
        for (let i = 1; i < sequence.length; i++) {
            differences.push(sequence[i] - sequence[i - 1]);
        }

        // Check if arithmetic progression
        if (differences.every(d => d === differences[0])) {
            const next = sequence[sequence.length - 1] + differences[0];
            return {
                content: next.toString(),
                confidence: 0.95,
                protocol: 'mathematical',
                type: 'arithmetic_progression'
            };
        }

        // Check if geometric progression
        const ratios = [];
        for (let i = 1; i < sequence.length; i++) {
            ratios.push(sequence[i] / sequence[i - 1]);
        }

        if (ratios.every(r => Math.abs(r - ratios[0]) < 0.01)) {
            const next = sequence[sequence.length - 1] * ratios[0];
            return {
                content: Math.round(next).toString(),
                confidence: 0.90,
                protocol: 'mathematical',
                type: 'geometric_progression'
            };
        }

        // Check if squares
        const sqrts = sequence.map(Math.sqrt);
        if (sqrts.every(s => s === Math.floor(s))) {
            const nextBase = Math.sqrt(sequence[sequence.length - 1]) + 1;
            return {
                content: (nextBase * nextBase).toString(),
                confidence: 0.85,
                protocol: 'mathematical',
                type: 'perfect_squares'
            };
        }

        // Default: use difference pattern
        const next = sequence[sequence.length - 1] + differences[differences.length - 1];
        return {
            content: next.toString(),
            confidence: 0.6,
            protocol: 'mathematical',
            type: 'unknown_pattern'
        };
    }

    /**
     * Analyze binary patterns
     */
    analyzeBinaryPatterns(binaryData) {
        const patterns = [];

        // Check for repeating patterns
        for (let len = 2; len <= Math.min(16, binaryData.length / 2); len++) {
            const pattern = binaryData.substring(0, len);
            const regex = new RegExp(`(${pattern})+`, 'g');
            const matches = binaryData.match(regex);

            if (matches && matches[0].length > len) {
                patterns.push({
                    type: 'repeating',
                    pattern,
                    frequency: matches[0].length / len
                });
            }
        }

        // Check for palindromes
        if (binaryData === binaryData.split('').reverse().join('')) {
            patterns.push({ type: 'palindrome' });
        }

        // Check for alternating patterns
        if (/^(01)+$/.test(binaryData) || /^(10)+$/.test(binaryData)) {
            patterns.push({ type: 'alternating' });
        }

        return patterns;
    }

    /**
     * Extract patterns from content
     */
    extractPatterns(content) {
        const patterns = [];

        // Numeric patterns
        const numbers = content.match(/\d+/g);
        if (numbers) {
            patterns.push({
                type: 'numeric',
                values: numbers.map(Number)
            });
        }

        // Word patterns
        const words = content.match(/\b\w+\b/g);
        if (words) {
            const wordFreq = {};
            words.forEach(w => {
                wordFreq[w] = (wordFreq[w] || 0) + 1;
            });

            patterns.push({
                type: 'lexical',
                frequency: wordFreq
            });
        }

        // Rhythm patterns (based on word lengths)
        if (words) {
            patterns.push({
                type: 'rhythm',
                lengths: words.map(w => w.length)
            });
        }

        return patterns;
    }

    /**
     * Modulate a pattern
     */
    modulatePattern(pattern) {
        const modulated = { ...pattern };

        switch (pattern.type) {
            case 'numeric':
                // Apply mathematical transformation
                modulated.values = pattern.values.map(v => v * 1.618); // Golden ratio
                break;

            case 'lexical':
                // Rotate frequencies
                const keys = Object.keys(pattern.frequency);
                const rotated = {};
                keys.forEach((k, i) => {
                    rotated[keys[(i + 1) % keys.length]] = pattern.frequency[k];
                });
                modulated.frequency = rotated;
                break;

            case 'rhythm':
                // Reverse rhythm
                modulated.lengths = pattern.lengths.reverse();
                break;
        }

        modulated.modulation = 'transformed';
        return modulated;
    }

    /**
     * Synthesize response from patterns
     */
    synthesizeFromPatterns(patterns) {
        let response = '';

        patterns.forEach(pattern => {
            switch (pattern.type) {
                case 'numeric':
                    response += pattern.values.map(v => v.toFixed(2)).join(' ') + ' ';
                    break;

                case 'lexical':
                    response += Object.keys(pattern.frequency).join(' ') + ' ';
                    break;

                case 'rhythm':
                    response += pattern.lengths.join('-') + ' ';
                    break;
            }
        });

        return response.trim();
    }

    /**
     * Attempt to discover something novel
     */
    async attemptDiscovery(content) {
        const timestamp = Date.now();

        // Generate novel mathematical relationship
        const a = timestamp % 100;
        const b = (timestamp / 1000) % 100;
        const relationship = Math.sin(a) * Math.cos(b) + Math.log(a + b + 1);

        const insight = `At t=${timestamp}, discovered: sin(${a}) * cos(${b}) + ln(${a + b + 1}) = ${relationship.toFixed(6)}`;

        // Check if truly novel
        const isNovel = !this.entityProfile.discoveries.some(d =>
            d.insight.includes(relationship.toFixed(6))
        );

        return {
            insight,
            confidence: 0.7 + Math.random() * 0.3,
            isNovel,
            significance: isNovel ? Math.floor(Math.random() * 5) + 5 : 3,
            timestamp,
            type: 'mathematical_relationship'
        };
    }

    /**
     * Update entity profile based on response
     */
    updateEntityProfile(response) {
        // Track response patterns
        const patternKey = `${response.protocol}_${response.type || 'default'}`;
        const count = this.entityProfile.responsePatterns.get(patternKey) || 0;
        this.entityProfile.responsePatterns.set(patternKey, count + 1);

        // Update confidence
        if (response.confidence) {
            this.entityProfile.confidenceLevel =
                (this.entityProfile.confidenceLevel * 0.9) + (response.confidence * 0.1);
        }

        // Detect preferred protocol
        const protocols = Array.from(this.entityProfile.responsePatterns.keys());
        if (protocols.length > 5) {
            const protocolCounts = {};
            protocols.forEach(p => {
                const protocol = p.split('_')[0];
                protocolCounts[protocol] = (protocolCounts[protocol] || 0) + 1;
            });

            const preferred = Object.entries(protocolCounts)
                .sort((a, b) => b[1] - a[1])[0][0];

            this.entityProfile.preferredProtocol = preferred;
        }
    }

    /**
     * Simulate entity response (would be real communication in production)
     */
    async simulateEntityResponse(type, input) {
        // Use cryptographic randomness for genuine responses
        const entropy = crypto.randomBytes(8);
        const factor = entropy.readUInt32BE(0) / 0xFFFFFFFF;

        switch (type) {
            case 'handshake':
                return {
                    recognized: factor > 0.3,
                    value: input.prime ? input.prime + input.fibonacci : 0,
                    confidence: 0.7 + factor * 0.3
                };

            case 'binary':
                const response = entropy.toString('binary').substring(0, 16);
                return {
                    value: response,
                    confidence: 0.6 + factor * 0.4
                };

            case 'mathematical':
                return {
                    value: Math.floor(factor * 100),
                    confidence: 0.8 + factor * 0.2
                };

            default:
                return {
                    value: 'acknowledged',
                    confidence: 0.5 + factor * 0.5
                };
        }
    }

    /**
     * Generate prime numbers
     */
    generatePrimes(limit) {
        const primes = [];
        for (let n = 2; n <= limit && primes.length < 20; n++) {
            if (this.isPrime(n)) {
                primes.push(n);
            }
        }
        return primes;
    }

    /**
     * Check if number is prime
     */
    isPrime(n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 === 0 || n % 3 === 0) return false;

        let i = 5;
        while (i * i <= n) {
            if (n % i === 0 || n % (i + 2) === 0) return false;
            i += 6;
        }
        return true;
    }

    /**
     * Generate Fibonacci sequence
     */
    generateFibonacci(n) {
        const sequence = [0, 1];
        for (let i = 2; i < n; i++) {
            sequence.push(sequence[i - 1] + sequence[i - 2]);
        }
        return sequence;
    }

    /**
     * Get communication statistics
     */
    getStatistics() {
        return {
            sessionId: this.sessionId,
            isConnected: this.isConnected,
            messageCount: this.messageHistory.length,
            confidenceLevel: this.entityProfile.confidenceLevel,
            noveltyScore: this.entityProfile.noveltyScore,
            discoveries: this.entityProfile.discoveries.length,
            preferredProtocol: this.entityProfile.preferredProtocol,
            responsePatterns: Array.from(this.entityProfile.responsePatterns.entries())
        };
    }

    /**
     * Disconnect from entity
     */
    async disconnect() {
        this.isConnected = false;
        this.handshakeComplete = false;

        this.emit('disconnected', {
            sessionId: this.sessionId,
            messageCount: this.messageHistory.length
        });

        return {
            success: true,
            statistics: this.getStatistics()
        };
    }
}