Two novel languages built on field theory and geometric calculus
WPE/TME for structural reasoning · Crystalline for code synthesis

Two programming languages. One geometric foundation.

Traditional programming lacks explicit representation of structure, coupling, and temporal relationships. These languages use field theory and geometric calculus to make these explicit:

Both are deterministic (same input → same output), explainable (equations show why), and geometric (structure encoded in parameters).

Geometric calculus for structural and temporal reasoning

What it is: A notation system (like mathematical notation) for encoding semantic relationships with explicit coupling strengths, hierarchical influences, and temporal ordering.

Why it matters: Structure is implicit in most systems. WPE/TME makes it explicit and manipulable.

# Feedback control loop
Sensor:P:2@0|-3.0      # Physics domain, shell 2, 0° phase
Controller:C:3@90|-2.5  # Cognition domain, shell 3, 90° phase
Actuator:P:4@180|-2.0   # Physics domain, shell 4, 180° phase

# Coupling (automatic from phase relationships)
Sensor <-> Controller   # cos(90°) = 0 (orthogonal, no interference)
Controller <-> Actuator # cos(90°) = 0
Actuator <-> Sensor     # cos(180°) = -1 (opposition, feedback)

Use cases:

• LLM scaffolding (provide explicit reasoning structure)
• Multi-agent systems (define interaction geometry)
• Temporal logic (left-to-right = forward in time)
• System modeling (encode complex relationships)

📄 Read the paper | 📖 View specification →

Code synthesis through geometric field optimization

What it is: A language for synthesizing code by treating program structure as a geometric field, then optimizing through evolutionary transformations.

Why it matters: Enables systematic code generation with explainable decision-making and deterministic output.

Crystalline Core: Language specification and synthesis engine

Intelligent Manifolds: Subproject for adaptive computational structures

Input specification:

synthesize {
  task: "API integration with large dataset"
  constraints: ["optimize for speed", "low memory"]
  target: Python
}

What Crystalline discovers:

• Async I/O patterns
• Streaming generators
• Parallel execution opportunities
• Loop fusion optimizations

Process:

1. Field architecture optimization (golden angle phase spacing)
2. Computational atom decomposition
3. Evolutionary synthesis (physics-guided transformations)
4. Code generation with synthesis certificate

📄 Read the paper | 🔧 View specification →

Multi-scale biological modeling using WPE/TME

Seven-layer framework applying WPE/TME to biology:

L0: Substrate (quantum/chemistry/physics)
L1: Universal constraints (allometry, homeostasis)
L2: Selection operators (evolution, self-organization)
L3: Information encoding + DNA interface
L4: Robustness mechanisms
L5: Generative engine
L6: Layer coupling
L7: Quantitative computation

Key innovation: DNA sequences encode computational logic through geometric principles (LYRA Θ∞ interface).

📄 Read the paper | 🧬 View examples →

All systems share 4-parameter geometric encoding:

Coupling strength:

cos(θᵢ - θⱼ)

• 0° difference = maximum coupling (1.0)
• 90° difference = no coupling (0.0)
• 180° difference = opposition (-1.0)

Hierarchical influence:

1/λ_low - 1/λ_high

• Shell 7 → Shell 1: 0.857 (strong top-down)
• Shell 3 → Shell 2: 0.167 (moderate peer)

Energy functional:

E = ∫[|∇Ψ|² + κΨ² + Σγⱼₖ ΨⱼΨₖ + Σαᵢⱼ⟨Ψᵢ|Ψⱼ⟩] dV

git clone https://github.com/[user]/wpe-tme-language
cd wpe-tme-language

# View language specification
cat specification/wpe-core.md

# View examples (pure notation)
cat examples/feedback-loop.wpe
cat examples/multi-agent-system.wpe
cat examples/temporal-sequences.tme

Note: WPE/TME are notation systems (like LaTeX for math). There is no "implementation" - you write directly in the notation.

git clone https://github.com/[user]/crystalline-language
cd crystalline-language

# View language specification
cat specification/language-spec.md

# View Python synthesis engine
cd implementation/python
python crystalline_codegen_v3_1.py "API integration, optimize for speed"

git clone https://github.com/[user]/biogenerative-crystal
cd biogenerative-crystal

# View examples in WPE/TME notation
cat examples/glycolysis.wpe

# Run Python modeling framework
python examples/glycolysis.py

The problem: Neural networks are black boxes. Templates are limited. Traditional paradigms don't capture geometric properties of information.

The insight: Information processing has geometric structure. Coupling, hierarchy, and temporal flow can be modeled using field theory.

The result: Two novel programming languages with:

• ✅ Deterministic execution (reproducible)
• ✅ Explainable decisions (energy equations)
• ✅ Geometric optimization (golden angle, phase coupling)
• ✅ Cross-domain applicability (same math, different substrates)

The mathematics comes from electromagnetic field theory:

• Golden angle (φ = 137.5°) creates optimal phase spacing
• Curvature minimization (δS/δΨ = 0) finds stable configurations
• Energy functionals guide evolution toward optima

Applied to programming, this enables genuinely novel language designs.

📄 WPE & TME: A Geometric Calculus for Structural and Temporal Reasoning (30 pages)
Language specification and formal semantics
ResearchGate • PDF

📄 Crystalline: Physics-Guided Evolutionary Code Synthesis (25 pages)
Language specification for code generation
ResearchGate • PDF

📄 BioGenerative Cognition Crystal (30 pages)
Multi-scale biological modeling framework
ResearchGate • PDF

• 💬 Discussions: GitHub Discussions
• 🐛 Issues: Report bugs or request features in individual repos

All projects: Apache 2.0 License

• Complete language specifications
• Syntax highlighting for editors
• Interactive web demos
• Community examples library

• Additional target languages (Rust, Julia)
• Language server protocol (LSP) support
• Formal verification tools
• Academic collaborations

• Production use cases
• Conference presentations
• Standardization efforts
• Educational materials

Two languages. One foundation. Built with geometry.

⭐ Star us if this interests you!

Built by Chris Young • Research in computational physics, programming language design, and AI systems