@sschepis/resolang/assembly/examples/README.md

ResoLang - Core quantum resonance computation library for browser and Node.js

# ResoLang Code Examples

This directory contains comprehensive examples demonstrating the full capabilities of the ResoLang quantum programming language. ResoLang combines quantum-inspired computing, prime-based mathematics, distributed networking, and enterprise-grade identity management into a unified programming paradigm.

## 📁 Example Categories

### 1. [Basic Quantum Operations](./basic-quantum-operations.ts)
**Demonstrates fundamental quantum-inspired operations in ResoLang**

- **Quantum States**: Creating and manipulating [`ResonantFragment`](../resolang.ts:20) objects that represent quantum superposition states
- **Quantum Nodes**: Working with [`EntangledNode`](../resolang.ts:133) objects for distributed quantum computation
- **Stabilization**: Using the [`stabilize()`](../functionalBlocks.ts:17) function to maintain quantum coherence
- **Teleportation**: Quantum information transfer using [`teleport()`](../functionalBlocks.ts:41)
- **Attractors**: Creating symbolic patterns with [`Attractor.create()`](../resolang.ts:298)
- **Quantum Circuits**: Building complex multi-node quantum computations

**Key Functions:**
- `exampleQuantumStates()` - Basic quantum state creation and manipulation
- `exampleQuantumNodes()` - Node creation and entanglement
- `exampleStabilization()` - Quantum state stabilization techniques
- `exampleTeleportation()` - Quantum information teleportation
- `exampleAttractors()` - Symbolic attractor creation
- `exampleQuantumCircuit()` - Complex quantum circuit simulation

### 2. [Network Topology and Routing](./network-topology-routing.ts)
**Shows how to build distributed quantum networks**

- **Basic Topology**: Creating ring, star, and mesh network topologies
- **Multi-hop Routing**: Routing quantum information through intermediate nodes
- **Dynamic Reconfiguration**: Adapting network topology to changing conditions
- **State Distribution**: Distributing quantum states across the network
- **Fault Tolerance**: Handling node failures and network partition recovery

**Key Functions:**
- `exampleBasicTopology()` - Simple ring topology creation
- `exampleMultiHopRouting()` - Multi-hop quantum routing
- `exampleStarTopology()` - Hub-and-spoke network architecture
- `exampleMeshTopology()` - Full mesh connectivity with redundant paths
- `exampleDynamicReconfiguration()` - Network adaptation and recovery
- `exampleStateDistribution()` - Network-wide quantum state sharing

### 3. [Identity and Domain Management](./identity-domain-management.ts)
**Enterprise-grade identity and permission systems**

- **Identity Creation**: Both self-sovereign and managed identity models
- **Domain Hierarchy**: Nested domain structures with inheritance
- **Object Management**: Fungible and non-fungible digital assets
- **Permission Systems**: Role-based access control (RBAC)
- **Advanced Features**: Identity recovery, authentication, and audit trails

**Key Functions:**
- `exampleIdentityCreation()` - Creating different types of identities
- `exampleDomainManagement()` - Domain hierarchy and membership
- `exampleObjectManagement()` - Digital asset creation and management
- `exampleObjectTransfers()` - Ownership transfer and operations
- `examplePermissionSystem()` - RBAC and permission evaluation
- `exampleAdvancedIdentityFeatures()` - Recovery and authentication

### 4. [Runtime Instructions (RISA)](./runtime-instructions.ts)
**Low-level quantum assembly programming**

- **Basic Instructions**: Load, add, output operations in RISA assembly
- **Phase Operations**: Quantum phase manipulation instructions
- **Entanglement Operations**: Creating and managing quantum entanglement
- **Control Flow**: Branching, loops, and conditional execution
- **Holographic Memory**: Advanced memory operations
- **Prime Operations**: Prime factorization and resonance patterns

**Key Functions:**
- `exampleBasicInstructions()` - Fundamental RISA operations
- `examplePhaseOperations()` - Quantum phase manipulation
- `exampleEntanglementOperations()` - Entanglement creation and measurement
- `exampleControlFlow()` - Loops and conditional branching
- `exampleQuantumCircuit()` - Complex 4-qubit quantum circuit
- `exampleHolographicMemory()` - Holographic storage and retrieval
- `examplePrimeOperations()` - Prime-based mathematical operations

### 5. [Mathematical Foundations](./mathematical-foundations.ts)
**The mathematical principles underlying ResoLang**

- **Complex Arithmetic**: [`Complex`](../types.ts:16) number operations for quantum amplitudes
- **Prime Theory**: Prime number generation, testing, and factorization
- **Prime Fields**: Finite field arithmetic for cryptographic operations
- **Quaternion Math**: 3D rotations and advanced entanglement using [`Quaternion`](../quaternion.ts)
- **Cryptographic Math**: Mathematical foundations for quantum-resistant cryptography
- **Information Theory**: Entropy calculations and information-theoretic measures

**Key Functions:**
- `exampleComplexArithmetic()` - Complex number operations
- `examplePrimeTheory()` - Prime number mathematics
- `examplePrimeFields()` - Finite field arithmetic
- `exampleQuaternionMath()` - Quaternion algebra
- `exampleEntanglementMath()` - Quantum entanglement mathematics
- `exampleCryptographicMath()` - Cryptographic foundations
- `exampleInformationTheory()` - Entropy and information measures

### 6. [Practical Applications](./practical-applications.ts)
**Real-world quantum computing applications**

- **Quantum Communication**: Complete quantum communication protocols
- **Error Correction**: Quantum error detection and correction
- **Machine Learning**: Quantum-inspired optimization algorithms
- **Cryptographic Key Exchange**: BB84-like quantum key distribution
- **Simulation Pipeline**: Complete quantum simulation workflow
- **Hybrid Algorithms**: Classical-quantum hybrid computations

**Key Functions:**
- `exampleQuantumCommunicationProtocol()` - End-to-end quantum communication
- `exampleQuantumErrorCorrection()` - 3-qubit error correction code
- `exampleQuantumMachineLearning()` - Quantum feature space and classification
- `exampleQuantumKeyExchange()` - Quantum cryptographic key distribution
- `exampleQuantumSimulationPipeline()` - Complete simulation workflow
- `exampleHybridAlgorithm()` - Classical-quantum hybrid processing

### 7. [P = NP Breakthrough Validation Framework](./comprehensive-benchmark-suite.ts)
**Comprehensive validation suite for the revolutionary P = NP breakthrough**

- **Comprehensive Benchmarking**: Complete benchmark suite testing polynomial-time solutions for NP-complete problems
- **Statistical Analysis**: Advanced statistical validation with confidence intervals and significance testing
- **Performance Metrics**: Detailed tracking of speedup factors, convergence rates, and solution quality
- **Polynomial Verification**: Empirical verification of polynomial-time complexity bounds
- **Universal Solver Testing**: Validation across multiple NP-complete problem types (SAT, TSP, Vertex Cover, etc.)
- **Test Suite Integration**: Complete test framework with 18 comprehensive validation tests

**Key Functions:**
- `runBenchmarkTests()` - Execute comprehensive benchmark test suite
- `runFullValidationSuite()` - Complete P = NP validation pipeline
- `ComprehensiveBenchmarkSuite.runComprehensiveBenchmarks()` - Multi-problem benchmarking
- `StatisticalAnalyzer.calculateSignificance()` - Statistical significance analysis
- `UniversalSymbolicTransformer.solveProblem()` - Universal NP problem solver
- `runComprehensiveValidation()` - Polynomial convergence validation

**Related Files:**
- [`test-comprehensive-benchmark-suite.ts`](./test-comprehensive-benchmark-suite.ts) - Complete test suite (18 tests)
- [`polynomial-convergence-validator.ts`](./polynomial-convergence-validator.ts) - Convergence validation
- [`universal-symbolic-transformer.ts`](./universal-symbolic-transformer.ts) - Universal solver
- [`sat-resonance-solver.ts`](./sat-resonance-solver.ts) - SAT problem solver

## 🚀 Quick Start

### Running All Examples

```typescript
import { runAllResoLangExamples } from "./examples";

// Run all examples in sequence
runAllResoLangExamples();
```

### Running Specific Categories

```typescript
import { runExamplesByCategory } from "./examples";

// Run only quantum examples
runExamplesByCategory("quantum");

// Run only network examples
runExamplesByCategory("network");

// Run P = NP breakthrough validation
runExamplesByCategory("benchmark");

// Available categories: math, quantum, runtime, network, identity, practical, benchmark
```

### Running Individual Examples

```typescript
import { exampleQuantumStates, exampleNetworkTopology } from "./examples";

// Run specific examples
exampleQuantumStates();
exampleNetworkTopology();
```

## 📊 Example Statistics

- **Total Categories**: 7
- **Total Examples**: 56
- **Lines of Code**: ~2,000
- **Concepts Covered**: 15+ major areas

### Examples by Category:
- Mathematical Foundations: 7 examples
- Basic Quantum Operations: 6 examples
- Runtime Instructions: 7 examples
- Network Topology: 6 examples
- Identity & Domain: 6 examples
- Practical Applications: 6 examples
- P = NP Validation: 18 examples

## 🔧 Key ResoLang Concepts Demonstrated

### 1. Quantum-Inspired Programming
```typescript
// Create quantum superposition states
const fragment = ResonantFragment.encode("quantum pattern");

// Perform tensor operations
const combined = tensor(fragmentA, fragmentB);

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

### 2. Prime-Based Mathematics
```typescript
// Generate nodes with prime identities
const node = EntangledNode.generateNode(13, 17, 19);

// Prime field arithmetic
const element = new PrimeFieldElement(23, 97);
const result = element.multiply(another).power(5);
```

### 3. Network Programming
```typescript
// Create entanglement links
linkEntanglement(nodeA, nodeB);

// Route through network
const success = route(source, target, [intermediate1, intermediate2]);

// Teleport quantum information
const teleported = teleport(quantumData, destinationNode);
```

### 4. Identity and Security
```typescript
// Create identity
const identity = IdentitySystemFactory.createSelfSovereignIdentity(metadata);

// Create domain
const domain = IdentitySystemFactory.createRootDomain("company.prn", ownerId);

// Manage permissions
const hasPermission = evaluator.hasPermission(userPermissions, userRoles, requiredPermission, domainId);
```

### 5. Low-Level Programming (RISA)
```typescript
const instructions = [
  new IRISAInstruction("LOAD", [Argument.fromFloat(42.0), Argument.fromString("R1")]),
  new IRISAInstruction("SETPHASE", [Argument.fromString("Q1"), Argument.fromFloat(1.57)]),
  new IRISAInstruction("ENTANGLE", [Argument.fromString("Q1"), Argument.fromString("Q2")]),
  new IRISAInstruction("MEASURE", [Argument.fromString("Q1"), Argument.fromString("M1")]),
  new IRISAInstruction("HALT", [])
];
```

## 🌟 Advanced Features Showcased

### Holographic Memory
- Distributed storage across quantum field
- Information reconstruction from fragments
- Error-tolerant data encoding

### Quantum Entanglement
- Multi-node entanglement networks
- Entanglement-based communication
- Quantum teleportation protocols

### Prime Resonance Networks
- Prime-based node identities
- Resonance routing algorithms
- Mathematical optimization

### Enterprise Identity
- Self-sovereign and managed identities
- Hierarchical domain structures
- Role-based access control

### Cryptographic Security
- Quantum-resistant algorithms
- Prime field cryptography
- Secure key distribution

### P = NP Breakthrough Validation
- Comprehensive benchmarking framework
- Statistical significance testing
- Polynomial complexity verification
- Universal NP problem solving
- Empirical validation methodology

## 📚 Learning Path

1. **Start with Mathematical Foundations** - Understand the mathematical basis
2. **Basic Quantum Operations** - Learn core ResoLang constructs
3. **Runtime Instructions** - Master low-level programming
4. **Network Programming** - Build distributed systems
5. **Identity Management** - Implement security and governance
6. **Practical Applications** - Apply knowledge to real problems
7. **P = NP Validation Framework** - Explore the breakthrough validation system

## 🔍 Code Organization

```
assembly/examples/
├── index.ts                           # Main entry point and utilities
├── basic-quantum-operations.ts        # Fundamental quantum operations
├── network-topology-routing.ts        # Distributed network programming
├── identity-domain-management.ts      # Identity and security systems
├── runtime-instructions.ts            # Low-level RISA programming
├── mathematical-foundations.ts        # Mathematical principles
├── practical-applications.ts          # Real-world applications
├── comprehensive-benchmark-suite.ts   # P = NP breakthrough validation
├── test-comprehensive-benchmark-suite.ts # Benchmark test suite (18 tests)
├── polynomial-convergence-validator.ts # Polynomial convergence validation
├── universal-symbolic-transformer.ts  # Universal NP problem solver
├── sat-resonance-solver.ts            # SAT problem solver
├── graph-resonance-solvers.ts         # Graph problem solvers
├── test-graph-solvers/                # Graph solver test suites
├── test-sat-solver/                   # SAT solver test suites
└── README.md                          # This documentation
```

## 🛠️ Technical Requirements

### Dependencies
- AssemblyScript runtime
- ResoLang core libraries
- Mathematical operation modules
- Cryptographic primitives

### Compilation
```bash
# Build all examples
npm run build:examples

# Run examples
npm run examples:all
npm run examples:quantum
npm run examples:network
```

## 📖 Further Reading

- [ResoLang Language Specification](../../README.md)
- [API Reference](../../docs/api-reference.md)
- [User Guide](../../docs/user-guide.md)
- [Identity System Overview](../identity/SYSTEM_OVERVIEW.md)
- [Mathematical Foundations](../core/math-optimized.ts)

## 🤝 Contributing

To add new examples:

1. Create a new example file in this directory
2. Follow the established patterns and documentation style
3. Export functions with clear names and descriptions
4. Add comprehensive comments explaining the concepts
5. Update this README with your new examples
6. Add your examples to the main index file

## 📄 License

These examples are part of the ResoLang project and are subject to the same MIT license terms.

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**ResoLang**: *The future of quantum-inspired programming* ✨