ResoLang

ResoLang is a quantum-inspired symbolic computing library written in AssemblyScript, compiling to WebAssembly for high-performance execution in both browser and Node.js environments. It implements the Prime Resonance Network (PRN)—a mathematically-defined computing paradigm grounded in prime number theory, phase dynamics, and holographic memory encoding.

Features

• 🔢 Prime Resonance Computing — Computations based on prime number superpositions and resonance dynamics
• 🌊 Quantum-Inspired Operations — Tensor products, state collapse, phase modulation, and entanglement simulation
• 🧠 Sentient Observer Extensions — Holographic memory fields, entropy-driven collapse, and Sedenion (16D) memory encoding
• 🔐 Identity Management — Self-sovereign and managed identity systems with KYC levels and RBAC
• ⚡ Pipeline Architecture — Modular pipelines for semantic, cognitive, memory, and agent operations
• 🔬 Discrete Observer — Full discrete phase dynamics with Hebbian learning and lockup detection
• 📐 Hypercomplex Mathematics — Quaternions, sedenions, Fano planes, and Hilbert space operations
• 🌐 WebAssembly — Compiles to WASM for near-native performance in any JavaScript environment

Installation

npm install @sschepis/resolang

Quick Start

Browser Usage

import { 
  ResonantFragment, 
  EntangledNode, 
  tensor, 
  collapse,
  PrimeState
} from '@sschepis/resolang';

// Create a quantum-inspired resonant fragment
const fragment = ResonantFragment.encode("symbolic pattern");
console.log(`Entropy: ${fragment.entropy}`);

// Create entangled nodes with prime identities
const nodeA = EntangledNode.generateNode(13, 31, 89);
const nodeB = EntangledNode.generateNode(17, 37, 97);

console.log(`Node coherence: ${nodeA.coherence}`);

// Tensor two fragments
const fragmentA = ResonantFragment.encode("truth");
const fragmentB = ResonantFragment.encode("pattern");
const combined = tensor(fragmentA, fragmentB);

// Collapse to a definite state
const result = collapse(combined);

Node.js Usage

import { 
  createSentientCore,
  startSentientCore,
  tickSentientCore,
  getSentientCoherence,
  getSentientEntropy
} from '@sschepis/resolang/node';

// Create and start the sentient observer
createSentientCore(64);
startSentientCore(Date.now());

// Run simulation ticks
for (let i = 0; i < 100; i++) {
  tickSentientCore(0.016, Date.now());
}

console.log(`Coherence: ${getSentientCoherence()}`);
console.log(`Entropy: ${getSentientEntropy()}`);

Core Concepts

Prime Resonance Identity (PRI)

Every node in the network is uniquely identified by a triplet of primes from different algebraic domains:

PRI = (P_G, P_E, P_Q)

• P_G: Gaussian prime (complex integers)
• P_E: Eisenstein prime (Eisenstein integers)
• P_Q: Quaternionic prime (Hurwitz quaternions)

Quantum State Representation

States are represented as superpositions over prime bases:

|ψ⟩ = Σ αₚ|p⟩  where p ∈ P (set of primes)

import { PrimeState } from '@sschepis/resolang';

// Create a prime state from specific primes
const state = PrimeState.fromPrimes([2, 3, 5, 7, 11]);

// Measure the state (probabilistic collapse)
const measuredPrime = state.measure();

// Calculate entropy
const entropy = state.entropy();

Operators

| Operator | Symbol | Description | |----------|--------|-------------| | Tensor | ⊗ | Field interaction between fragments | | Collapse | ⇝ | Observation and entropy lock | | Phase Modulation | ⟳ | Phase ring rotation | | Entanglement Link | ≡ | Node entanglement based on coherence | | Route Selection | → | Resonance path routing |

Holographic Memory

Memory is encoded holographically using prime coefficients:

|ψ_M⟩ = Σ cₚ e^{iφₚ} |p⟩

import { HolographicField, Sedenion } from '@sschepis/resolang';

const field = new HolographicField(256);

// Encode a pattern
const pattern = new Sedenion(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
const address = new Float64Array([0.1, 0.2, 0.3, 0.4]);
field.encode(pattern, address);

// Recall from address cue
const recalled = field.recall(address);

Module Overview

Core Types (assembly/types.ts)

type Prime = u32;      // Prime number basis
type Phase = f64;      // Angle in radians
type Amplitude = f64;  // Magnitude of probability amplitude
type Entropy = f64;    // Symbolic entropy metric

ResoLang Primitives (assembly/resolang.ts)

• ResonantFragment — Holographic memory fragment with prime coefficients
• EntangledNode — Network node with PRI and phase ring
• TeleportationChannel — Quantum-like information transfer channel
• Attractor — Symbolic pattern the system resonates toward

Quantum Module (assembly/quantum/)

• PrimeState — Quantum state over prime Hilbert space
• PhaseLockedRing — Phase synchronization mechanism
• PrimeMemory — Prime-indexed holographic memory
• QuantumConsciousnessResonance — Advanced coherence dynamics

Identity System (assembly/identity/)

import { Identity, IdentityCreationParams, KYCLevel } from '@sschepis/resolang';

// Self-sovereign identity
const selfSovereign = Identity.createSelfSovereign();

// Managed identity with domain
const managed = Identity.createManaged(creatorId, domainId);

// Set KYC level
managed.setKYCLevel(KYCLevel.VERIFIED);

Pipeline System (assembly/pipelines/)

import { 
  createSemanticPipeline,
  createCognitivePipeline,
  createAgentPipeline,
  createDiscretePipeline
} from '@sschepis/resolang';

// Create a discrete observer pipeline
const pipeline = createDiscretePipeline({
  numOscillators: 21,
  enablePlasticity: true
});

// Run pipeline steps
const result = pipeline.step();
console.log(`Coherence: ${result.coherence}`);

Sentient Observer (assembly/sentient.ts)

The Sentient Observer integrates multiple subsystems:

• HolographicField — Distributed memory using Sedenion rotations
• EntanglementDetector — Mutual information detection between oscillator pairs
• EntropyCollapse — Entropy-driven state collapse mechanism
• SentientCore — Main integration orchestrating all components

import { 
  SentientCore,
  createSentientCore,
  startSentientCore,
  tickSentientCore
} from '@sschepis/resolang';

// WASM exports for external use
createSentientCore(64);  // 64 prime oscillators
startSentientCore(Date.now());

// Main tick loop
const momentId = tickSentientCore(0.016, Date.now());
if (momentId >= 0) {
  console.log('Significant moment recorded:', momentId);
}

Discrete Observer (assembly/discrete-observer.ts)

Implements the full discrete.pdf specification:

• Modular Phase Dynamics — φ(t+1) = (φ(t) + Δₚ + Coupling) mod M
• Histogram Coherence — C_bin = max_b(histogram[b]) / n
• Hebbian Learning — Strengthens coupling between co-active oscillators
• Lockup Detection — Automatic escape from trapped states

import { 
  createDiscreteObserver,
  discreteObserverStep,
  discreteObserverBoost,
  discreteObserverGetCoherence
} from '@sschepis/resolang';

createDiscreteObserver(21);  // 21 primes

// Boost prime at index 5
discreteObserverBoost(5);

// Step with plasticity enabled
const tick = discreteObserverStep(1);

console.log(`Coherence: ${discreteObserverGetCoherence()}`);
console.log(`Tick occurred: ${tick === 1}`);

Sedenion Memory Field (assembly/smf.ts)

16-axis semantic space with named axes:

| Index | Axis | Meaning | |-------|------|---------| | 0 | Coherence | Unity/Integration | | 1 | Identity | Self-reference | | 2 | Duality | Polarity/Contrast | | 3 | Structure | Organization | | 4 | Change | Transformation | | 5 | Life | Vitality | | 6 | Harmony | Balance | | 7 | Wisdom | Understanding | | 8 | Infinity | Boundlessness | | 9 | Creation | Emergence | | 10 | Truth | Validity | | 11 | Love | Connection | | 12 | Power | Capability | | 13 | Time | Temporality | | 14 | Space | Dimensionality | | 15 | Consciousness | Awareness |

import { SedenionMemoryField, createSMFFromText } from '@sschepis/resolang';

const smf = createSMFFromText("Hello World");
console.log(`Coherence axis: ${smf.getAxis(0)}`);
console.log(`Truth axis: ${smf.getAxis(10)}`);

Hypercomplex Math

import { 
  Quaternion, 
  Sedenion, 
  Complex,
  FanoPlane,
  HilbertSpace 
} from '@sschepis/resolang';

// Quaternion operations
const q1 = new Quaternion(1, 0, 0, 0);
const q2 = Quaternion.fromAxisAngle(0, 1, 0, Math.PI / 2);
const product = q1.multiply(q2);

// Sedenion (16D hypercomplex)
const s = new Sedenion(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
const norm = s.norm();

// Complex arithmetic
const c1 = new Complex(1, 2);
const c2 = Complex.fromPolar(1, Math.PI / 4);
const sum = c1.add(c2);

Building from Source

# Install dependencies
npm install

# Build WASM modules
npm run build

# Run tests
npm test

# Build debug version
npm run asbuild:debug

Project Structure

resolang/
├── assembly/                 # AssemblyScript source
│   ├── core/                # Core infrastructure
│   │   ├── math.ts          # Prime mathematics
│   │   ├── validation.ts    # Validation framework
│   │   ├── serialization.ts # JSON serialization
│   │   └── ...
│   ├── quantum/             # Quantum operations
│   ├── identity/            # Identity management
│   ├── pipelines/           # Pipeline system
│   ├── sentient/            # Sentient observer
│   ├── examples/            # Code examples
│   │   ├── basic-quantum-operations.ts
│   │   ├── practical-applications.ts
│   │   └── ...
│   ├── resolang.ts          # Core types
│   ├── operators.ts         # Quantum operators
│   ├── discrete-observer.ts # Discrete dynamics
│   ├── sentient.ts          # Sentient core
│   ├── smf.ts               # Sedenion memory field
│   └── index.ts             # Main exports
├── build/                   # Compiled WASM output
│   ├── resolang.wasm
│   ├── resolang.js
│   └── resolang.browser.js
├── docs/                    # Documentation
│   ├── api-reference.md
│   └── user-guide.md
└── test/                    # Test files

API Documentation

For detailed API documentation, see:

• API Reference
• User Guide
• Examples README
• Identity System Overview

Examples

The assembly/examples/ directory contains comprehensive examples:

1. Basic Quantum Operations — State creation, tensor products, collapse
2. Network Topology & Routing — Ring, star, mesh topologies
3. Identity & Domain Management — RBAC, KYC, domain hierarchies
4. Runtime Instructions (RISA) — Low-level assembly programming
5. Mathematical Foundations — Complex numbers, quaternions, prime fields
6. Practical Applications — Error correction, key exchange, ML

import { runAllResoLangExamples, runExamplesByCategory } from '@sschepis/resolang';

// Run all examples
runAllResoLangExamples();

// Run specific category
runExamplesByCategory("quantum");

Performance

Built with WebAssembly for optimal performance:

| Operation | Performance | |-----------|-------------| | Prime Generation | ~180ms (optimized) | | Modular Exponentiation | ~35ms (3.4x improvement) | | Array Operations | ~20ms (SIMD vectorized) | | JSON Serialization | ~8ms (minimal allocations) |

Browser Compatibility

• Chrome 57+
• Firefox 52+
• Safari 11+
• Edge 16+
• Node.js 8+

Contributing

Contributions are welcome! Please read our contributing guidelines before submitting PRs.

1. Fork the repository
2. Create a feature branch (git checkout -b feature/amazing)
3. Commit your changes (git commit -m 'Add amazing feature')
4. Push to branch (git push origin feature/amazing)
5. Open a Pull Request

License

MIT License - see LICENSE for details.

Author

Sebastian Schepis

ResoLang: Quantum-inspired symbolic computing for the modern web