Overview GTMØ (Geometry Topology Mathematics Øndefiniteness) is a mathematical framework that formalizes the indefinable aspects of language and meaning through geometric and topological structures. This repository contains the Python implementation of GTMØ theory, which bridges mathematics, linguistics, and cognitive science.

🌟 Key Features

AlienatedNumbers: Mathematical objects capturing indefinite aspects through geometric configuration 9-Dimensional Topological Space: Complete architecture for meaning representation Adaptive Observation System: Multiple geometric lenses for semantic interpretation SANB-5 Logic: 5-valued logic system (O, Z, Ø, ∞, Ψ) for handling topological paradoxes Topological Knowledge Attractors: Dynamic classification in phase space

🚀 Quick Start pythonfrom gtmo_core_v1 import UnifiedGTMOSystem, Configuration, AlienatedNumber

Create GTMØ system

system = UnifiedGTMOSystem()

Demonstrate lens-based observation

system.demonstrate_lens_based_alienation()

Create AlienatedNumber - a hybrid of definable and indefinable

alien_num = AlienatedNumber( definable="bitcoin_2030", configuration=Configuration(position=[0.5, 0.3, 0.7]), emergence_strength=0.85 ) 🧠 Core Concepts

1. Phase Space Topology (3D)

Determinacy: Geometric certainty (0→1) Stability: Topological invariance (0→1) Entropy: Configurational chaos (0→1)

2. Topological Knowledge Types

Ψᴷ - Knowledge Particle (topologically stable) Ψʰ - Knowledge Shadow (boundary regions) Ψᴺ - Emergent (topological transitions) Ø - Singularity (undefined topology)

3. Geometric Observation Lenses

Concatenation Lens (distance-based) Causal Lens (orientation-based) Topological Lens (loop detection) Quantum Lens (superposition states)

📊 Example: Word Trajectory in Configuration Space python# Track how "virus" moves through topological space over time word_trajectory = [ (1900, [0.2, 0.8, 0.1]), # Low determinacy, high stability (1950, [0.8, 0.9, 0.2]), # Medical definition solidifies (1990, [0.6, 0.5, 0.7]), # "Computer virus" emerges (2020, [0.7, 0.3, 0.9]) # COVID + memes = chaos ] 🔬 Mathematical Applications

Topological Semantics: Mapping meaning through geometric structures Configuration Dynamics: Tracking semantic evolution in phase space Emergence Geometry: Formalizing how new meanings arise from configuration limits Cognitive Topology: Modeling knowledge as topological attractors

📚 Documentation For detailed mathematical foundations and topological theory, see:

Matematyka Języka i Znaczeń - Complete GTMØ theory (Polish) Academic papers in /docs directory

🤝 Contributing Contributions are welcome! Areas of interest:

Additional topological operators Phase space visualization improvements Geometric meaning algorithms Mathematical proofs and extensions

📖 Citation If you use GTMØ in your research, please cite: bibtex@article{skuza2025gtmo, title={GTMØ: Geometry Topology Mathematics Øndefiniteness}, author={Skuza, Grzegorz}, year={2025}, journal={arXiv preprint} } 📄 License This project is licensed under the MIT License - see the LICENSE file for details.

"At the intersection of geometry and meaning, where topology meets indefiniteness, new mathematical structures emerge" - GTMØ principle