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Schepis"},"license":"MIT","homepage":"https://github.com/aleph-ai/tinyaleph#readme","keywords":["semantic-computing","hypercomplex","sedenion","quaternion","octonion","prime-numbers","nlp","natural-language","cryptography","hash","oscillator","kuramoto","entropy","ai","machine-learning","reasoning","symbolic-ai","quantum-inspired","arithmetic-topology","legendre-symbol","alexander-polynomial","link-invariants"],"repository":{"type":"git","url":"git+https://github.com/aleph-ai/tinyaleph.git"},"description":"Prime-resonant semantic computing framework - hypercomplex algebra, oscillator dynamics, arithmetic topology, and entropy-minimizing reasoning","maintainers":[{"name":"lonestar108","email":"sschepis@gmail.com"}],"readme":"# @aleph-ai/tinyaleph\n\n**Prime-resonant semantic computing framework**\n\nA novel computational paradigm that encodes meaning as prime number signatures, embeds them in hypercomplex space, and performs reasoning through entropy minimization and oscillator synchronization.\n\n[![npm version](https://badge.fury.io/js/@sschepis%2Ftinyaleph.svg)](https://www.npmjs.com/package/@aleph-ai/tinyaleph)\n[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)\n\n## Features\n\n- **Prime Semantics**: Encode concepts as unique prime number signatures\n- **Hypercomplex Algebra**: 16-dimensional sedenion space with non-commutative multiplication, exp/log/slerp\n- **Oscillator Dynamics**: Kuramoto-model synchronization for coherent reasoning\n- **Stochastic Dynamics**: Noise-robust Kuramoto with Langevin, colored, and thermal noise models\n- **Prime Entanglement**: Graph-based tracking of prime relationships and co-occurrences\n- **Event Streaming**: Real-time monitoring with EventEmitter pattern and async iteration\n- **Entropy Minimization**: Reasoning as reduction of semantic uncertainty\n- **Multiple Backends**: Semantic (NLP), Cryptographic (hashing), Scientific (quantum-inspired), Bioinformatics (DNA/protein)\n- **Formal Type System**: Typed term calculus with N(p)/A(p)/S types and ordering constraints\n- **Reduction Semantics**: Strong normalization with prime-preserving operators\n- **Lambda Translation**: Model-theoretic semantics via λ-calculus embedding\n- **Enochian Vocabulary**: 21-letter angelic alphabet with prime basis and sedenion operations\n- **ResoFormer Architecture**: Complete prime-indexed transformer with multi-head attention\n- **Multi-Z Memory**: Hierarchical memory with fast/slow/permanent channels\n- **Symbolic AI**: 184+ emoji symbols with cultural tags, resonance-enhanced inference\n- **Golden Ratio Resonance**: Harmony measurement using φ ≈ 1.618 ratio detection\n- **Topological Invariants**: 108 invariant (2²×3³), Trefoil complexity, physical constant derivation\n- **Gauge Symmetry**: Standard Model SU(3)×SU(2)×U(1) from 108 factorization\n- **Observer Hierarchy**: Multi-scale observers from quantum to cosmic\n- **Free Energy Dynamics**: Cubic FEP model for consciousness and curiosity\n- **Discrete Dynamics**: Integer sine tables, histogram coherence, tick-based gating\n- **Codebook Tunneling**: 64-attractor SMF codebook for controlled state transitions\n- **Canonical Fusion**: Deterministic FUSE(p,q,r) triad selection\n- **CRT-Homology**: Chinese Remainder Theorem for semantic reconstruction with homology-based consistency detection\n- **Birkhoff Attention**: Doubly-stochastic attention via Sinkhorn-Knopp projection\n\n## Installation\n\n```bash\nnpm install @aleph-ai/tinyaleph\n```\n\n## Quick Start\n\n```javascript\nimport { createEngine, SemanticBackend } from '@aleph-ai/tinyaleph';\n\n// Load configuration\nconst config = { dimension: 16 };\n\n// Create a semantic engine\nconst engine = createEngine('semantic', config);\n\n// Process a query\nconst result = engine.run('What is the relationship between wisdom and truth?');\n\nconsole.log('Output:', result.output);\nconsole.log('Entropy:', result.entropy);\nconsole.log('Steps:', result.steps.length);\n```\n\n## Core Concepts\n\n### Prime Encoding\n\nEvery concept maps to a unique set of prime numbers:\n\n```javascript\nconst backend = new SemanticBackend(config);\n\nconst primes = backend.encode('love and wisdom');\nconsole.log(primes);  // [2, 3, 5, 7, 11, ...]\n```\n\n### Hypercomplex States\n\nPrimes embed into 16-dimensional sedenion space:\n\n```javascript\nimport { Hypercomplex } from '@aleph-ai/tinyaleph';\n\n// Create a state\nconst state = new Hypercomplex(16);\nstate.excite([2, 3, 5]);  // Excite with primes\n\n// States support multiplication (non-commutative!)\nconst combined = state1.multiply(state2);\nconsole.log(state1.multiply(state2) !== state2.multiply(state1));  // true\n```\n\n### Entropy-Based Reasoning\n\nReasoning reduces entropy through semantic transforms:\n\n```javascript\nconst engine = createEngine('semantic', config);\nconst result = engine.run('Confused question here');\n\n// Watch entropy decrease through reasoning steps\nfor (const step of result.steps) {\n  console.log(`Step ${step.step}: entropy ${step.entropyAfter.toFixed(3)}`);\n}\n```\n\n## Backends\n\n### Semantic Backend\n\nNatural language understanding and concept mapping:\n\n```javascript\nimport { SemanticBackend } from '@aleph-ai/tinyaleph';\n\nconst backend = new SemanticBackend(config);\n\n// Tokenize\nconst tokens = backend.tokenize('Love is truth');\n\n// Encode to primes\nconst primes = backend.encode('Love is truth');\n\n// Decode back\nconst text = backend.decode(primes);\n\n// Compare concepts\nconst state1 = backend.textToOrderedState('wisdom');\nconst state2 = backend.textToOrderedState('knowledge');\nconsole.log('Similarity:', state1.coherence(state2));\n```\n\n### Cryptographic Backend\n\nSemantic hashing and key derivation:\n\n```javascript\nimport { CryptographicBackend, hash, deriveKey } from '@aleph-ai/tinyaleph';\n\n// Quick hash\nconst h = hash('my secret data');\n\n// Key derivation\nconst key = deriveKey('password', 'salt', 32, 10000);\n\n// Full backend\nconst crypto = new CryptographicBackend(config);\nconst semanticHash = crypto.hash('similar meanings produce similar hashes');\n```\n\n### Scientific Backend\n\nQuantum-inspired computation:\n\n```javascript\nimport { ScientificBackend } from '@aleph-ai/tinyaleph';\n\nconst backend = new ScientificBackend(config);\n\n// Create quantum-like states\nconst state = backend.createRandomState();\nconst basis = backend.createBasisState(0);\n\n// Superposition\nconst superposition = backend.superpose(state, 0.5, basis, 0.5);\n\n// Measurement\nconst result = backend.measure(superposition, [basis]);\n```\n\n### Bioinformatics Backend\n\nDNA computing, protein folding, and molecular biology:\n\n```javascript\nimport { BioinformaticsBackend, DNACircuit, ANDGate, ORGate } from '@aleph-ai/tinyaleph';\n\nconst backend = new BioinformaticsBackend();\n\n// Encode DNA sequence\nconst dnaPrimes = backend.encode('ATGCGATCG');\n\n// Transcribe DNA to RNA\nconst transcribed = backend.transcribe(dnaPrimes, { force: true });\nconsole.log('mRNA primes:', transcribed.rna);\n\n// Translate RNA to Protein\nconst translated = backend.translate(transcribed.rna);\nconsole.log('Protein:', backend.decode(translated.protein));\n\n// Full gene expression (DNA → RNA → Protein)\nconst expressed = backend.express(dnaPrimes);\nconsole.log('Protein sequence:', expressed.sequence);\n\n// Protein folding via Kuramoto oscillators\nconst proteinPrimes = backend.encode('MWLKFVIER');\nconst foldResult = backend.foldProtein(proteinPrimes);\nconsole.log('Folding order parameter:', foldResult.orderParameter);\n\n// Molecular binding affinity\nconst affinity = backend.bindingAffinity(dnaPrimes, proteinPrimes);\nconsole.log('Binding affinity:', affinity.affinity);\n```\n\n### DNA Computing\n\nBuild logic gates and circuits using DNA strands:\n\n```javascript\nimport { DNACircuit, ANDGate, ORGate, NOTGate } from '@aleph-ai/tinyaleph';\n\n// Create logic gates\nconst andGate = new ANDGate({ name: 'and1' });\nconst orGate = new ORGate({ name: 'or1' });\nconst notGate = new NOTGate({ name: 'not1' });\n\n// Evaluate gates (concentration-based)\nconsole.log(andGate.evaluate(1, 1));  // { output: true, ... }\nconsole.log(orGate.evaluate(0, 1));   // { output: true, ... }\nconsole.log(notGate.evaluate(0));     // { output: true, ... }\n\n// Build a circuit\nconst circuit = new DNACircuit('logic-circuit');\ncircuit.addGate('and1', new ANDGate({ name: 'and1' }));\ncircuit.addGate('not1', new NOTGate({ name: 'not1' }));\ncircuit.addGate('or1', new ORGate({ name: 'or1' }));\ncircuit.connect('and1', 'or1', 1);\ncircuit.connect('not1', 'or1', 2);\n\n// Evaluate circuit\nconst result = circuit.evaluate();\n```\n\n## Physics Engine\n\n### Oscillators\n\n```javascript\nimport { Oscillator, OscillatorBank, KuramotoModel } from '@aleph-ai/tinyaleph';\n\n// Create oscillator bank\nconst bank = new OscillatorBank(16);\n\n// Excite with primes\nbank.excite([2, 3, 5, 7]);\n\n// Kuramoto synchronization\nconst kuramoto = new KuramotoModel(bank, { coupling: 0.1 });\nkuramoto.step(0.01);\n\nconsole.log('Order parameter:', kuramoto.orderParameter());\n```\n\n### Extended Synchronization Models\n\nFive advanced Kuramoto-family models for complex synchronization dynamics:\n\n```javascript\nimport {\n  NetworkKuramoto,      // Topology-aware coupling\n  AdaptiveKuramoto,     // Hebbian plasticity\n  SakaguchiKuramoto,    // Phase frustration (chimera states)\n  SmallWorldKuramoto,   // Watts-Strogatz topology\n  MultiSystemCoupling   // Cross-system synchronization\n} from '@aleph-ai/tinyaleph';\n\n// Network Kuramoto with custom topology\nconst network = new NetworkKuramoto(frequencies, adjacencyMatrix, 0.5);\nnetwork.setFromEntanglementGraph(entanglementGraph, primeList);\n\n// Adaptive Kuramoto with Hebbian learning\nconst adaptive = new AdaptiveKuramoto(frequencies, 0.3, 0.02);\n// Coupling evolves: \"concepts that sync together link together\"\n\n// Sakaguchi-Kuramoto with phase frustration\nconst sakaguchi = new SakaguchiKuramoto(frequencies, 0.5, Math.PI/4);\nconsole.log('State:', sakaguchi.classifyState()); // synchronized/chimera/incoherent\n\n// Small-world topology\nconst smallWorld = new SmallWorldKuramoto(frequencies, 4, 0.1, 0.5);\nconsole.log('Small-world coefficient:', smallWorld.smallWorldCoefficient());\n\n// Multi-system coupling (hierarchical or peer-to-peer)\nconst multi = new MultiSystemCoupling([system1, system2, system3]);\nconsole.log('Inter-system coherence:', multi.interSystemCoherence());\n```\n\n### Stochastic Kuramoto Models\n\nNoise-robust synchronization with Langevin dynamics:\n\n```javascript\nimport {\n  StochasticKuramoto,      // White noise Langevin dynamics\n  ColoredNoiseKuramoto,    // Ornstein-Uhlenbeck noise\n  ThermalKuramoto          // Temperature-dependent coupling\n} from '@aleph-ai/tinyaleph';\n\n// White noise model\nconst stochastic = new StochasticKuramoto(frequencies, {\n  coupling: 0.5,\n  noiseIntensity: 0.1\n});\n\nstochastic.evolve(100, 0.01);\nconst { mean, stdDev } = stochastic.orderParameterWithUncertainty(50, 0.01);\n\n// Colored noise (Ornstein-Uhlenbeck process)\nconst colored = new ColoredNoiseKuramoto(frequencies, {\n  correlationTime: 2.0,\n  noiseIntensity: 0.1\n});\n\n// Thermal model with temperature-dependent noise\nconst thermal = new ThermalKuramoto(frequencies, { temperature: 2.0 });\nthermal.setTemperature(4.0);  // Higher temp = more noise\nconst Tc = thermal.estimateCriticalTemperature();\n```\n\n### Prime Entanglement Graph\n\nTrack prime relationships from co-occurrence and resonance:\n\n```javascript\nimport { PrimeEntanglementGraph } from '@aleph-ai/tinyaleph/core';\n\nconst graph = new PrimeEntanglementGraph([2, 3, 5, 7, 11]);\n\n// Record co-occurrences\ngraph.observe([2, 3], [5, 7], 0.8);\ngraph.observe([5, 7], [11], 0.6);\n\n// Query relationships\nconst neighbors = graph.neighbors(7, 2);  // 2-hop neighborhood\nconst path = graph.shortestPath(2, 11);\n\n// Graph metrics\nconst cc = graph.clusteringCoefficient(5);\nconst stats = graph.stats();\n\n// Convert to Kuramoto network\nconst adjacency = graph.toAdjacencyMatrix([2, 3, 5, 7, 11]);\n```\n\n### Event-Driven Streaming\n\nReal-time monitoring and async iteration:\n\n```javascript\nimport {\n  AlephEventEmitter,\n  AlephMonitor,\n  EvolutionStream\n} from '@aleph-ai/tinyaleph/core';\n\n// Event emitter with throttling\nconst emitter = new AlephEventEmitter();\nemitter.throttle('tick', 100);  // Max once per 100ms\n\nemitter.on('collapse', ({ from, to, probability }) => {\n  console.log(`Collapsed with p=${probability}`);\n});\n\nemitter.on('sync', ({ orderParameter }) => {\n  console.log(`Synchronized: r=${orderParameter}`);\n});\n\n// Promise-based waiting\nconst data = await emitter.waitFor('ready', 5000);\n\n// Async iteration over evolution\nconst stream = EvolutionStream.fromEvolvable(kuramoto);\n\nfor await (const state of stream.take(100)) {\n  console.log(state.orderParameter);\n}\n\n// Stream operators\nconst filtered = stream\n  .filter(s => s.entropy < 2.0)\n  .map(s => s.orderParameter)\n  .take(50);\n```\n\n### Entropy and Stability\n\n```javascript\nimport { shannonEntropy, estimateLyapunov, stateEntropy } from '@aleph-ai/tinyaleph';\n\n// Calculate entropy\nconst entropy = stateEntropy(state);\n\n// Estimate Lyapunov exponent for stability\nconst lambda = estimateLyapunov(entropyTimeSeries);\nconsole.log('Stable:', lambda < 0);\n```\n\n### Hypercomplex Algebra Extensions\n\nExtended operations for smooth interpolation and rotations:\n\n```javascript\nimport { Hypercomplex } from '@aleph-ai/tinyaleph';\n\nconst q1 = Hypercomplex.fromArray([1, 0, 0, 0]);\nconst q2 = Hypercomplex.fromAxisAngle(4, [0, 0, 1], Math.PI/2);\n\n// Exponential and logarithm\nconst expQ = q1.exp();\nconst logQ = q2.log();\n\n// Smooth interpolation (slerp)\nfor (let t = 0; t <= 1; t += 0.1) {\n  const interpolated = q1.slerp(q2, t);\n}\n\n// Rotation operations\nconst rotated = q2.sandwich(vector);\nconst axis = q2.toAxisAngle();\n\n// Power operations\nconst squared = q1.pow(2);\nconst cubed = q1.powInt(3);\n```\n\n### Multi-Z Channel Primeon Ladder\n\nHierarchical memory with different decay rates:\n\n```javascript\nimport { PrimeonZLadderMulti, createAdiabaticSchedule } from '@aleph-ai/tinyaleph';\n\nconst ladder = new PrimeonZLadderMulti({\n  N: 32,\n  zChannels: [\n    { name: 'fast', dz: 1, leak: 0.2, decay: 0.1 },\n    { name: 'slow', dz: 1, leak: 0.01, decay: 0.001 },\n    { name: 'permanent', dz: 1, leak: 0.0, decay: 0.0 }\n  ],\n  J: 0.25\n});\n\n// Per-channel metrics\nconst metrics = ladder.channelMetrics();\nconsole.log('Fast entropy:', metrics.fast.entropy);\nconsole.log('Slow Z-flux:', metrics.slow.totalFlux);\n\n// Adiabatic parameter schedules\nconst Jt = createAdiabaticSchedule(0.1, 0.5, 100, 'sinusoidal');\nconst ladder2 = new PrimeonZLadderMulti({ N: 16, Jt });\n```\n\n### Topological Physics\n\nThe 108 Invariant from 108bio.pdf provides deep connections between number theory and physics:\n\n```javascript\nimport { primeToAngle, AlexanderModule, ArithmeticLinkKernel } from '@aleph-ai/tinyaleph';\n\n// 108 Invariant: 2² × 3³ = 108\nconst is108Resonant = (n) => n % 108 === 0;\n\n// Twist angle κ(p) = 2π/p radians (180° for p=2, ~51.43° for p=7)\nconsole.log(primeToAngle(7) * 180 / Math.PI);  // 51.43°\n\n// Arithmetic link invariants for the prime set S = {2, 3, 5, 7}\nconst module = new AlexanderModule([2, 3, 5, 7]);\nconsole.log(module.alexanderPolynomial);  // \"1 + 2t - 4t^2 + 2t^3 + t^4\"\n\n// Arithmetic Link Kernel coupling tensors\nconst alk = new ArithmeticLinkKernel([3, 5, 7]);\nconsole.log(alk.J);   // Pairwise coupling matrix\nconsole.log(alk.K3);  // Triadic coupling tensor\n\n// The paper-derived helper objects (TWIST_108, Knot, PhysicalConstants,\n// GaugeSymmetry, FreeEnergyDynamics, OBSERVER_HIERARCHY) remain internal\n// implementation details in core/prime.js and core/topology.js.\n```\n\n### Discrete Dynamics\n\nInteger-domain computation (discrete dynamics):\n\n```javascript\nimport {\n  INT_SINE_TABLE,\n  computeHistogramCoherence,\n  SMF_CODEBOOK,\n  nearestCodebookAttractor,\n  codebookTunnel,\n  TickGate\n} from '@aleph-ai/tinyaleph/observer';\nimport { FUSE } from '@aleph-ai/tinyaleph/core';\n\n// Integer Sine Table (M=256 discretization)\nconsole.log(INT_SINE_TABLE.M);            // 256\nconst sinValue = INT_SINE_TABLE.sin(64);  // Integer sine at phase 64\nconst cosValue = INT_SINE_TABLE.cos(128); // Integer cosine at phase 128\n\n// Histogram Coherence C_bin(t) = max_k(b_k(t))/|P|\nconst phases = [10, 12, 11, 50, 52, 51, 100, 102, 101];\nconst coherence = computeHistogramCoherence(phases, { numBins: 16 });\n// coherence ≈ 0.33 (three clusters of 3 phases each)\n\n// 64-Attractor SMF Codebook\nconsole.log(SMF_CODEBOOK.length);         // 64\nconsole.log(SMF_CODEBOOK[0]);             // { index: 0, phase: 0, label: '0x00' }\n\n// Find nearest codebook attractor\nconst nearest = nearestCodebookAttractor(130);  // phase 130\nconsole.log(nearest.index);               // Nearest codebook index\nconsole.log(nearest.distance);            // Distance to attractor\n\n// Controlled tunneling to codebook attractor\nconst tunneled = codebookTunnel(130, { force: 0.5 });\nconsole.log(tunneled.original);           // 130\nconsole.log(tunneled.target);             // Nearest attractor phase\nconsole.log(tunneled.result);             // Tunneled phase (interpolated)\n\n// Fusion terms FUSE(p,q,r) compose prime triples\nconst fused = FUSE(3, 5, 11);  // Canonical triad summing to 19\nconsole.log(fused.p);          // 3\nconsole.log(fused.q);          // 5\nconsole.log(fused.r);          // 11\n\n// Tick-Only HQE Gate\nconst tickGate = new TickGate({ threshold: 0.7 });\nconst gateResult = tickGate.evaluate({ coherence: 0.8, tickValid: true });\nconsole.log(gateResult.passed);    // true (coherence > threshold && tick valid)\nconsole.log(gateResult.reason);    // 'TICK_VALID'\n```\n\n### Observer Capacity\n\nCalculate observer capacity from 108bio.pdf's C_obs = α·N_osc·K̄·τ⁻¹:\n\n```javascript\nimport { SedenionMemoryField } from '@aleph-ai/tinyaleph';\n\n// The full SymbolicObserver with capacity computation is part of the\n// Sentient app (apps/sentient). The public observer module provides the\n// building blocks: an oscillator bank plus the capacity formula\n// C_obs = α·N_osc·K̄·τ⁻¹ (108bio.pdf Table 1).\n\nconst observer = new SedenionMemoryField({ dimension: 16 });\n\n// Number of oscillators (N_osc):\nconst numOscillators = observer.dimension;\nconst alpha = 1/137;          // Fine structure constant\nconst meanCoupling = 0.5;     // K̄ average coupling\nconst coherenceTime = 0.1;    // τ coherence time\n\n// Observer capacity in bits/second\nconst capacity = alpha * numOscillators * meanCoupling / coherenceTime;\nconsole.log(capacity);        // α × N_osc × K̄ × τ⁻¹\nconsole.log(numOscillators);\n```\n\n### Free Energy Curiosity\n\nCubic FEP-based curiosity for learning systems:\n\n```javascript\nimport { estimateLyapunov, classifyStability } from '@aleph-ai/tinyaleph';\n\n// FreeEnergyCuriosity (cubic FEP belief dynamics) is part of the Sentient\n// app (apps/sentient), not the published library API. The public physics\n// module provides the stability primitives it is built on:\n\n// Classify belief-state stability along a trajectory\nconst lambda = estimateLyapunov(beliefTrajectory);\nconsole.log(classifyStability(lambda));  // 'stable' | 'marginal' | 'chaotic'\n```\n\n### Observer Scale Management\n\nMulti-scale observer hierarchy from 108bio.pdf:\n\n```javascript\nimport { SedenionMemoryField } from '@aleph-ai/tinyaleph';\n\n// ObserverScaleManager (multi-scale observer hierarchy from 108bio.pdf\n// Table 1) is part of the Sentient app (apps/sentient), not the published\n// library API. The public observer module provides the field primitives\n// each hierarchy level is built from:\n\nconst node = new SedenionMemoryField({ dimension: 16 });\n// Hierarchies: cellular → neural → cognitive → collective → cosmic\nconsole.log(node.dimension);   // Oscillator count at this level\n```\n\n### ResoFormer Architecture\n\nComplete prime-indexed transformer:\n\n```javascript\nimport {\n  ResoFormer,\n  ResoFormerBlock,\n  ResonantMultiHeadAttention,\n  PrimeFFN,\n  SparsePrimeState\n} from '@aleph-ai/tinyaleph/core';\n\n// Create sparse prime states\nconst state1 = SparsePrimeState.fromPrimes([2, 3, 5]);\nconst state2 = SparsePrimeState.fromPrimes([7, 11, 13]);\n\n// Multi-head attention\nconst attention = new ResonantMultiHeadAttention({\n  numHeads: 8,\n  numPrimes: 4096\n});\n\nconst result = attention.forward(state1, [state2], [state2]);\n\n// Full ResoFormer model\nconst model = new ResoFormer({\n  numLayers: 6,\n  numHeads: 8,\n  hiddenDim: 256\n});\n\nconst outputs = model.forward([state1, state2]);\n```\n\n### CRT-Enhanced ResoFormer\n\nIntegrates Chinese Remainder Theorem reconstruction with homology-based regularization:\n\n```javascript\nimport {\n    CRTResonantAttention,\n    HomologyRegularizedBlock,\n    CRTResoFormer,\n    createCRTResoFormer\n} from '@aleph-ai/tinyaleph/core';\n\n// Create CRT-enhanced model\nconst model = createCRTResoFormer({\n    numLayers: 3,\n    numHeads: 4,        // Maps to coprime moduli [2, 3, 5, 7]\n    homologyWeight: 0.1\n});\n\n// Process sequence with homology detection\nconst sequence = [\n    SparsePrimeState.fromHash('the'),\n    SparsePrimeState.fromHash('quick'),\n    SparsePrimeState.fromHash('fox')\n];\n\nconst result = model.forward(sequence);\n\nconsole.log('Total homology loss:', result.totalLoss);\nconsole.log('Holes detected:', result.homologyReport.hasHoles);\nconsole.log('Betti numbers:', result.homologyReport.maxBettiNumber);\n```\n\n### CRT Residue Encoding\n\nEncode semantic states as residue distributions over coprime moduli:\n\n```javascript\nimport {\n    ResidueEncoder,\n    CRTReconstructor,\n    BirkhoffProjector,\n    HomologyLoss,\n    DEFAULT_PRIMES_SMALL\n} from '@aleph-ai/tinyaleph/core';\n\n// Use first 4 primes: [2, 3, 5, 7], P = 210\nconst primes = DEFAULT_PRIMES_SMALL;\nconst encoder = new ResidueEncoder(primes, 16);\nconst crt = new CRTReconstructor(primes);\n\n// Encode hidden vector to residue distributions\nconst h = new Float64Array(16).fill(0.5);\nconst residues = encoder.encode(h);\nconst expectedResidues = encoder.expectedResidues(residues);\n\n// CRT reconstruction\nconst L = crt.reconstruct(expectedResidues);\nconsole.log('Reconstructed:', L);\n\n// Detect kernel (consistency failures)\nconst inKernel = crt.detectKernel(expectedResidues, 0.1);\nconsole.log('In kernel:', inKernel);\n\n// Birkhoff attention (doubly-stochastic)\nconst birkhoff = new BirkhoffProjector(20);\nconst attentionMatrix = [[0.8, 0.2], [0.3, 0.7]];\nconst projected = birkhoff.project(attentionMatrix);\n// Row sums ≈ 1, column sums ≈ 1\n```\n\n### Homology Loss\n\nDetect semantic inconsistencies as topological holes:\n\n```javascript\nimport { HomologyLoss, CRTReconstructor } from '@aleph-ai/tinyaleph/core';\n\nconst crt = new CRTReconstructor([2, 3, 5, 7]);\nconst homology = new HomologyLoss({ tau: 0.1 });\n\n// Batch of residue tuples\nconst residueBatch = [\n    [0.5, 1.2, 2.8, 4.1],\n    [0.99, 0.01, 2.5, 3.99],\n    [0.1, 0.2, 0.3, 0.4]\n];\n\n// Compute homology loss\nconst result = homology.compute(residueBatch, crt);\nconsole.log('Homology loss:', result.loss);\nconsole.log('Cycles detected:', result.cycles);\n\n// Betti numbers (topological invariants)\nconst betti = homology.computeBettiNumbers(residueBatch, crt);\nconsole.log('β₀ (components):', betti.beta0);\nconsole.log('β₁ (holes):', betti.beta1);\n```\n\n## Symbolic AI\n\n### Symbol Database\n\n184+ emoji symbols with prime assignments and cultural tags:\n\n```javascript\nimport { getSymbol, symbolDatabase } from '@aleph-ai/tinyaleph/core';\n\n// Get a symbol\nconst hero = getSymbol('hero');\nconsole.log(hero);\n// { id: 'hero', unicode: '🦸', prime: 1013, meaning: 'Hero archetype', culturalTags: ['universal'] }\n\n// Find Greek mythology symbols\nconst greekSymbols = symbolDatabase.getSymbolsByTag('greek');\n\n// Encode/decode concepts to prime signatures\nconst signature = symbolDatabase.encode(['hero', 'journey', 'mountain']);\nconst symbols = symbolDatabase.decode(signature);\n```\n\n### Semantic Inference\n\nPattern matching with resonance-enhanced disambiguation:\n\n```javascript\nimport { inferSymbol, inferWithResonance, inferMostResonant } from '@aleph-ai/tinyaleph/core';\n\n// Basic inference\nconst result = inferSymbol('brave knight');\n// { symbol: ⚔️, method: 'regex', confidence: 0.85 }\n\n// Resonance-enhanced inference - symbols ranked by harmony\nconst symbols = inferWithResonance('The hero fought the shadow in the temple');\n// Symbols sorted by attention weight based on resonance scores\n\n// Context-aware selection\nconst context = [getSymbol('warrior'), getSymbol('temple')];\nconst best = inferMostResonant('weapon', context);\n// → 🗡️ sword (high resonance with warrior/temple context)\n```\n\n### Compound Symbols\n\nBuild multi-symbol concepts through prime multiplication:\n\n```javascript\nimport { createCompound, getCompound, compoundBuilder } from '@aleph-ai/tinyaleph/core';\n\n// Pre-built compound\nconst greekWarrior = getCompound('greek_warrior');\n// { unicode: '⚔️⛩️🦉', meaning: 'Greek Warrior: Temple guardian blessed by Athena' }\n\n// Create custom compound\nconst fireMage = createCompound('fire_mage',\n  ['magician', 'fire', 'staff'],\n  'Fire Mage - Wielder of flame magic'\n);\n\n// Calculate internal harmony\nconst harmony = compoundBuilder.calculateCompoundResonance(fireMage);\n```\n\n### Golden Ratio Resonance\n\nPrimes whose ratio approaches φ ≈ 1.618 have natural harmony:\n\n```javascript\nimport { calculateResonance, findGoldenPairs, resonanceSignature } from '@aleph-ai/tinyaleph/core';\n\n// Check resonance between primes\ncalculateResonance(3, 5);   // 0.9 (Fibonacci pair!)\ncalculateResonance(7, 11);  // 0.936 (close to φ)\n\n// Find golden pairs\nconst pairs = findGoldenPairs([2, 3, 5, 7, 11, 13]);\n\n// Get signature for symbol set\nconst sig = resonanceSignature([2, 3, 5, 7]);\nconsole.log(`Mean resonance: ${sig.mean}, Golden pairs: ${sig.goldenCount}`);\n```\n\n## Formal Semantics\n\n### Typed Term Calculus\n\nThe library implements a formal type system for prime-based compositional semantics:\n\n```javascript\nimport { N, A, FUSE, CHAIN, SENTENCE, TypeChecker } from '@aleph-ai/tinyaleph/core';\n\n// Create typed terms\nconst noun7 = N(7);      // N(7) - noun indexed by prime 7\nconst adj3 = A(3);       // A(3) - adjective indexed by prime 3\n\n// Adjective application with ordering constraint (p < q)\nconst chain = adj3.apply(noun7);  // A(3)N(7) is valid since 3 < 7\n\n// Triadic fusion where p+q+r is prime\nconst fused = FUSE(3, 5, 11);  // 3+5+11 = 19 (prime) ✓\n\n// Sentence composition\nconst s1 = SENTENCE(7);\nconst s2 = SENTENCE(11);\nconst compound = SEQ(s1, s2);  // s₁ ◦ s₂\n\n// Type checking\nconst checker = new TypeChecker();\nconsole.log(checker.inferType(noun7));  // 'N'\nconsole.log(checker.checkApplication(adj3, noun7));  // { valid: true }\n```\n\n### Reduction Semantics\n\nStrong normalization with prime-preserving operators:\n\n```javascript\nimport {\n    ReductionSystem,\n    ResonancePrimeOperator,\n    NextPrimeOperator,\n    demonstrateStrongNormalization\n} from '@aleph-ai/tinyaleph/core';\n\n// Create reduction system\nconst reduction = new ReductionSystem();\n\n// Add prime-preserving operators\nreduction.addOperator(new ResonancePrimeOperator(2));    // Resonance at p=2\nreduction.addOperator(new NextPrimeOperator());      // Map to next prime\n\n// Normalize a term sequence\nconst result = reduction.normalize([7, 11, 13]);\nconsole.log(result.normalForm);    // Canonical form\nconsole.log(result.steps);         // Reduction trace\n\n// Demonstrate strong normalization\nconst proof = demonstrateStrongNormalization([3, 5, 7], reduction);\nconsole.log(proof.terminates);     // true (guaranteed!)\n```\n\n### Lambda Calculus Translation\n\nModel-theoretic semantics via τ translation:\n\n```javascript\nimport {\n    Translator,\n    LambdaEvaluator,\n    Semantics\n} from '@aleph-ai/tinyaleph/core';\n\n// Translate prime terms to λ-expressions\nconst translator = new Translator();\nconst lambda = translator.translateNoun(N(7));  // Constant 7\nconst appLambda = translator.translateChain(chain);\n\n// Evaluate λ-expressions\nconst evaluator = new LambdaEvaluator();\nconst normal = evaluator.normalize(appLambda);\n\n// Model-theoretic interpretation\nconst semantics = new Semantics();\nsemantics.domain = [2, 3, 5, 7, 11, 13];  // Prime domain\nconst value = semantics.interpret(N(7));   // 7\n```\n\n### Enochian Vocabulary\n\nThe 21-letter angelic alphabet with prime basis and sedenion operations:\n\n```javascript\nimport { enochianVocabulary } from '@aleph-ai/tinyaleph';\nconst {\n    EnochianEngine,\n    ENOCHIAN_ALPHABET,\n    PRIME_BASIS,\n    CORE_VOCABULARY,\n    SedenionElement\n} = enochianVocabulary;\n\n// 21-letter alphabet with prime mappings\nconsole.log(ENOCHIAN_ALPHABET['A']);  // { prime: 3, value: 1, angle: 51.43 }\nconsole.log(PRIME_BASIS);  // [7, 11, 13, 17, 19, 23, 29]\n\n// Enochian engine for word processing\nconst engine = new EnochianEngine();\n\n// Parse and compute word prime value\nconst parsed = engine.parseWord('MADRIAX');  // \"O ye heavens\"\nconsole.log(parsed.primeValue);\nconsole.log(parsed.letters);\n\n// Sedenion operations (16-dimensional)\nconst s1 = new SedenionElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]);\nconst s2 = new SedenionElement([0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]);\nconst product = s1.multiply(s2);  // Non-commutative!\n\n// Access core vocabulary (35+ Enochian words)\nconsole.log(CORE_VOCABULARY['OL']);     // \"I\" (first person)\nconsole.log(CORE_VOCABULARY['ZORGE']);  // \"be friendly unto\"\n```\n\n## API Overview\n\n### Main Exports\n\n| Export | Description |\n|--------|-------------|\n| `createEngine(type, config)` | Create engine with backend |\n| `AlephEngine` | Unified computation engine |\n| `SemanticBackend` | Natural language processing |\n| `CryptographicBackend` | Hashing and key derivation |\n| `ScientificBackend` | Quantum-inspired computation |\n| `BioinformaticsBackend` | DNA/RNA/Protein computation |\n| `DNACircuit` | DNA logic circuit builder |\n| `ANDGate` / `ORGate` / `NOTGate` | DNA logic gates |\n| `Hypercomplex` | Sedenion algebra with exp/log/slerp |\n| `Oscillator` / `OscillatorBank` | Phase-amplitude oscillators |\n| `KuramotoModel` | Coupled oscillator synchronization |\n| `NetworkKuramoto` | Topology-aware coupling |\n| `AdaptiveKuramoto` | Hebbian plasticity |\n| `SakaguchiKuramoto` | Phase frustration / chimera states |\n| `SmallWorldKuramoto` | Watts-Strogatz topology |\n| `MultiSystemCoupling` | Cross-system synchronization |\n| `StochasticKuramoto` | Langevin noise dynamics |\n| `ColoredNoiseKuramoto` | Ornstein-Uhlenbeck noise |\n| `ThermalKuramoto` | Temperature-dependent coupling |\n| `PrimeEntanglementGraph` | Prime relationship tracking |\n| `AlephEventEmitter` | Event-driven monitoring |\n| `AlephMonitor` | Engine state monitoring |\n| `EvolutionStream` | Async iteration over evolution |\n| `PrimeonZLadderMulti` | Multi-channel Z memory |\n| `ResoFormer` | Prime-indexed transformer |\n| `SparsePrimeState` | Sparse prime activations |\n| `getSymbol(id)` | Get symbol by ID |\n| `symbolDatabase` | Symbol database singleton |\n| `inferSymbol(text)` | Infer symbol from text |\n| `inferWithResonance(text)` | Resonance-ranked inference |\n| `inferMostResonant(text, ctx)` | Context-aware selection |\n| `createCompound(...)` | Build compound symbol |\n| `compoundBuilder` | Compound builder instance |\n| `calculateResonance(p1, p2)` | Prime pair resonance |\n| `findGoldenPairs(primes)` | Find φ-ratio pairs |\n| `resonanceSignature(primes)` | Resonance statistics |\n| `hash(input)` | Quick semantic hash |\n| `deriveKey(pass, salt)` | Quick key derivation |\n\n### Observer Exports\n\nThe observer module provides components for building sentient observer systems:\n\n```javascript\nimport observer from '@aleph-ai/tinyaleph/observer';\n// Or destructure specific exports:\nimport {\n    SedenionMemoryField,\n    PRSCLayer,\n    TemporalLayer,\n    SymbolicSMF,\n    SymbolicTemporalLayer,\n    AssaySuite\n} from '@aleph-ai/tinyaleph/observer';\n```\n\n| Export | Description |\n|--------|-------------|\n| `PrimeOscillator` | Single prime-indexed oscillator |\n| `PRSCLayer` | Prime Resonance Semantic Coherence oscillator bank |\n| `TickGate` | Tick-based activation gating |\n| `SedenionMemoryField` | 16D semantic orientation field |\n| `SMF_AXES` | Named axes for 16D space |\n| `Moment` | Discrete temporal moment |\n| `TemporalLayer` | Moment classification and time tracking |\n| `AttentionFocus` | Attention target with decay |\n| `Goal` | Goal representation with progress |\n| `AgencyLayer` | Goals, attention, and intention management |\n| `BoundaryLayer` | Self-other differentiation |\n| `EntanglementLayer` | Semantic phrase coherence |\n| `SafetyMonitor` | Constraint monitoring |\n| `SymbolicSMF` | Symbol-grounded Sedenion field |\n| `SMFSymbolMapper` | Maps SMF axes to symbols |\n| `AXIS_SYMBOL_MAPPING` | 16 axes → symbol mappings |\n| `SymbolicMoment` | Moment with I-Ching classification |\n| `SymbolicTemporalLayer` | 64-attractor hexagram classification |\n| `HEXAGRAM_ARCHETYPES` | 64 hexagram → archetype mappings |\n| `SymbolicPatternDetector` | Narrative pattern detection |\n| `TimeDilationAssay` | Assay A: Time dilation test |\n| `MemoryContinuityAssay` | Assay B: Memory continuity test |\n| `AgencyConstraintAssay` | Assay C: Agency under constraint test |\n| `NonCommutativeMeaningAssay` | Assay D: Non-commutative meaning test |\n| `AssaySuite` | Run all four validation assays |\n\n### Topology Exports\n\n| Export | Description |\n|--------|-------------|\n| `primeToAngle` | Twist angle κ(p) = 2π/p radians |\n| `AlexanderModule` | Alexander polynomials and signatures for prime sets |\n| `ArithmeticLinkKernel` | Coupling tensors J, K³, Kⁿ for arithmetic links |\n| `LegendreSymbol` | Quadratic reciprocity symbols |\n| `findBorromeanPrimes` | Scan prime sets for Borromean triples |\n| `quickBorromeanCheck` | Candidate Borromean triple test |\n\nThe paper-derived helpers (`TWIST_108`, `Knot`, `PhysicalConstants`,\n`GaugeSymmetry`, `FreeEnergyDynamics`, `OBSERVER_HIERARCHY`) are internal\nimplementation details in `core/prime.js` and `core/topology.js` and are not\npart of the published API.\n\n### Discrete Dynamics Exports\n\n| Export | Description |\n|--------|-------------|\n| `INT_SINE_TABLE` | M=256 integer sine/cosine table |\n| `computeHistogramCoherence` | C_bin(t) = max_k(b_k)/\\|P\\| |\n| `SMF_CODEBOOK` | 64-attractor codebook array |\n| `nearestCodebookAttractor` | Find nearest attractor for phase |\n| `codebookTunnel` | Controlled tunneling to attractor |\n| `FUSE` | Fusion term FUSE(p,q,r) composing prime triples |\n| `TickGate` | Tick-only HQE gating class |\n\n### Formal Semantics Exports\n\n| Export | Description |\n|--------|-------------|\n| `N(prime)` | Create noun term N(p) |\n| `A(prime)` | Create adjective term A(p) |\n| `FUSE(p, q, r)` | Create triadic fusion |\n| `CHAIN(ops, noun)` | Create operator chain |\n| `SENTENCE(expr)` | Create sentence from noun |\n| `SEQ(s1, s2)` | Sequential composition |\n| `IMPL(s1, s2)` | Implication |\n| `TypeChecker` | Type inference and checking |\n| `ReductionSystem` | Reduction semantics engine |\n| `ResonancePrimeOperator` | Prime resonance operator |\n| `NextPrimeOperator` | Next prime mapping |\n| `ModularPrimeOperator` | Modular arithmetic |\n| `Translator` | λ-calculus translation |\n| `LambdaEvaluator` | β-reduction evaluator |\n| `Semantics` | Model-theoretic interpretation |\n| `enochianVocabulary` | Enochian vocabulary namespace (`EnochianEngine`, `CORE_VOCABULARY`, …) |\n\n### Sub-modules\n\n```javascript\n// Direct module access\nimport { core, physics, backends, engine } from '@aleph-ai/tinyaleph';\n\n// Or import sub-modules directly\nimport * as core from '@aleph-ai/tinyaleph/core';\nimport * as physics from '@aleph-ai/tinyaleph/physics';\nimport * as backends from '@aleph-ai/tinyaleph/backends';\nimport * as engine from '@aleph-ai/tinyaleph/engine';\n```\n\n### New Physics Exports\n\n| Export | Description |\n|--------|-------------|\n| `StochasticKuramoto` | White noise Langevin dynamics |\n| `ColoredNoiseKuramoto` | Ornstein-Uhlenbeck colored noise |\n| `ThermalKuramoto` | Temperature-dependent coupling |\n| `PrimeonZLadderMulti` | Hierarchical Z memory channels |\n| `createAdiabaticSchedule` | Parameter sweep schedules |\n\n### New Core Exports\n\n| Export | Description |\n|--------|-------------|\n| `PrimeEntanglementGraph` | Prime co-occurrence tracking |\n| `AlephEventEmitter` | Event pub/sub system |\n| `AlephMonitor` | Engine monitoring wrapper |\n| `EvolutionStream` | Async iteration for dynamics |\n| `ResoFormer` | Full transformer model |\n| `ResoFormerBlock` | Single transformer block |\n| `ResonantMultiHeadAttention` | Multi-head attention |\n| `PrimeFFN` | Feed-forward network |\n| `PrimeLayerNorm` | Prime-preserving normalization |\n| `PositionalPrimeEncoding` | Position as prime phases |\n| `SparsePrimeState` | Sparse activation storage |\n| `CRTResonantAttention` | Multi-head CRT-fused attention |\n| `HomologyRegularizedBlock` | Block with homology loss |\n| `CRTResoFormer` | Complete CRT-enhanced model |\n| `ResidueEncoder` | Encode to residue distributions |\n| `CRTReconstructor` | Chinese Remainder Theorem |\n| `BirkhoffProjector` | Doubly-stochastic projection |\n| `HomologyLoss` | Cycle-based regularization |\n| `CoprimeSelector` | Optimal moduli selection |\n\n## Documentation\n\nFull documentation is available in the `docs/` directory:\n\n- **[Theory](./docs/theory/README.md)**: Mathematical foundations\n  - Prime semantics, hypercomplex algebra, oscillator dynamics\n  - Entropy minimization, non-commutativity, temporal emergence\n  \n- **[Guide](./docs/guide/README.md)**: Practical tutorials\n  - Quick start, semantic computing, cryptographic applications\n  - Scientific computing, LLM integration, symbolic AI, advanced topics\n  \n- **[Reference](./docs/reference/README.md)**: Complete API documentation\n  - Core module, physics module, backends, engine\n  - [Topology module](./docs/reference/07-topology.md): 108 invariant, knots, gauge symmetry\n  \n- **[CRT-Homology Reference](./docs/reference/09-crt-homology.md)**: CRT reconstruction and homology\n  \n- **[Topology Examples](./examples/topology/README.md)**: 108 invariant and physical constants\n  - 108 invariant and twist angles\n  - Trefoil complexity and mass ratios\n  - Gauge symmetry from factorization\n  - Free energy dynamics\n\n- **[Discrete Dynamics Examples](./examples/discrete/README.md)**: Integer-domain computation\n  - Integer sine tables\n  - Codebook tunneling\n  - Canonical fusion selection\n  - Tick-based gating\n\n- **[Formal Semantics Examples](./examples/formal-semantics/README.md)**: New formal system demos\n  - Typed terms and type checking\n  - Reduction and normalization\n  - Lambda translation\n  - Enochian language\n\n## Examples\n\nRun the included demos:\n\n```bash\n# Basic modular demo\nnpm run demo\n\n# Two-layer meaning demo\nnpm run demo:two-layer\n\n# Performance benchmark\nnpm run benchmark\n\n# Interactive chat\nnpm run chat\n\n# Formal semantics examples\nnode examples/formal-semantics/01-typed-terms.js\nnode examples/formal-semantics/02-reduction.js\nnode examples/formal-semantics/03-lambda-translation.js\nnode examples/formal-semantics/04-enochian-language.js\n\n# Topology examples (108 invariant, physical constants)\nnode examples/topology/01-108-invariant.js\nnode examples/topology/02-trefoil-constants.js\nnode examples/topology/03-gauge-symmetry.js\nnode examples/topology/04-free-energy-dynamics.js\n\n# Discrete dynamics examples (integer tables, codebooks)\nnode examples/discrete/01-integer-sine-table.js\nnode examples/discrete/02-codebook-tunneling.js\nnode examples/discrete/03-canonical-fusion.js\nnode examples/discrete/04-tick-gate.js\n\n# CRT-Homology examples\nnode examples/crt-homology/01-residue-encoding.js\nnode examples/crt-homology/02-birkhoff-attention.js\nnode examples/crt-homology/03-homology-loss.js\nnode examples/crt-homology/04-crt-resoformer.js\n\n# Bioinformatics examples\nnode examples/bioinformatics/01-dna-encoding.js\nnode examples/bioinformatics/02-central-dogma.js\nnode examples/bioinformatics/03-protein-folding.js\nnode examples/bioinformatics/04-dna-computing.js\nnode examples/bioinformatics/05-molecular-binding.js\n\n# Symbolic AI examples\nnode examples/05-symbolic-resonance.js\nnode examples/06-symbol-database.js\nnode examples/07-semantic-inference.js\nnode examples/08-compound-symbols.js\n```\n\n## Architecture\n\n```\n┌─────────────────────────────────────────────────────────────────┐\n│                        AlephEngine                              │\n│  ┌─────────────┐  ┌─────────────┐  ┌─────────────────────────┐  │\n│  │ Oscillators │◄─┤   Field     │◄─┤      Transform          │  │\n│  │  (Kuramoto) │  │  (Sedenion) │  │      Pipeline           │  │\n│  └─────────────┘  └─────────────┘  └─────────────────────────┘  │\n└─────────────────────────────────────────────────────────────────┘\n                              │\n         ┌────────────────────┼────────────────────┐\n         ▼                    ▼                    ▼\n┌─────────────────┐ ┌─────────────────┐ ┌─────────────────┐\n│ SemanticBackend │ │CryptographicBack│ │ScientificBackend│\n│                 │ │                 │ │                 │\n│ • Tokenization  │ │ • Hash          │ │ • Quantum sim   │\n│ • Prime encode  │ │ • Key derive    │ │ • Wave collapse │\n│ • Transforms    │ │ • Verify        │ │ • Measurement   │\n└─────────────────┘ └─────────────────┘ └─────────────────┘\n\n┌─────────────────────────────────────────────────────────────────┐\n│                     Formal Semantics Layer                      │\n├─────────────────┬─────────────────┬─────────────────────────────┤\n│   Type System   │   Reduction     │   Lambda Translation        │\n│                 │                 │                             │\n│ • N(p), A(p), S │ • Small-step →  │ • τ: Terms → λ-expressions  │\n│ • FUSE(p,q,r)   │ • ⊕ operators   │ • β-reduction               │\n│ • ◦ composition │ • Normal forms  │ • Model interpretation      │\n│ • ⇒ implication │ • Confluence    │ • Semantic domains          │\n└─────────────────┴─────────────────┴─────────────────────────────┘\n\n┌─────────────────────────────────────────────────────────────────┐\n│                      Symbolic AI Layer                          │\n├─────────────────┬─────────────────┬─────────────────────────────┤\n│  Symbol DB      │  Inference      │   Resonance                 │\n│                 │                 │                             │\n│ • 184+ emojis   │ • Pattern match │ • Golden ratio φ            │\n│ • Cultural tags │ • Semantic sim  │ • Prime pair harmony        │\n│ • Prime index   │ • ResoFormer    │ • Cluster detection         │\n│ • Categories    │ • Context-aware │ • Compound scoring          │\n└─────────────────┴─────────────────┴─────────────────────────────┘\n\n┌─────────────────────────────────────────────────────────────────┐\n│                     Enochian Language Module                    │\n├─────────────────────────────────────────────────────────────────┤\n│ • 21-letter alphabet with prime mappings                        │\n│ • Prime basis PE = {7, 11, 13, 17, 19, 23, 29}                  │\n│ • Twist angles κ(p) = 360/p degrees                             │\n│ • 16-dimensional sedenion operations                            │\n│ • Core vocabulary (35+ words)                                   │\n│ • The Nineteen Calls (traditional invocations)                  │\n└─────────────────────────────────────────────────────────────────┘\n```\n\n## Requirements\n\n- Node.js >= 14.0.0\n\n## License\n\nMIT © Sebastian Schepis\n\n## Contributing\n\nContributions welcome! Please read the documentation in `docs/` before submitting PRs.","readmeFilename":"README.md"}