A Geometric Framework for Emergent Intelligence
TCDE represents cognition as a continuous field Φ(x,t) evolving on a 6D Riemannian manifold with adaptive geometry. Unlike discrete AI systems, TCDE uses differential geometry to create truly continuous, self-organizing cognitive systems with emergent properties.
The fundamental equation governing TCDE dynamics:
∂Φ/∂t = D∇²_g Φ - α|Φ|²Φ + β𝒯_g(Φ) + γ𝒞_g(Φ) + η𝒜(Φ)
Where the metric tensor adapts to the field: g_ij(Φ) = g_ij⁰ + α|Φ|²δ_ij
This creates field-dependent geometry where curvature emerges from information density.
# Clone
git clone https://github.com/selectess/TCDE.git
cd TCDE
# Build (requires GCC/Clang, OpenSSL)
make clean && make
# Run demo
./bin/tcde_demo
# Run benchmarks
./bin/tcde_benchmark- GCC or Clang (C11 support)
- OpenSSL development libraries
- Make
| Capability | Description | Metric |
|---|---|---|
| Dimensional Expansion | Autonomous growth 6D → 11D+ | 150%+ expansion |
| Geometric Memory | Adaptive compression | 99.2% efficiency |
| Emergence Detection | Real-time spontaneous behavior | <1ms latency |
| Autopoiesis | Self-maintaining boundaries | 0.98+ health |
| Reflexivity | Φ(Φ(Φ)) consciousness measure | 0.76+ score |
| HIS Score | Holistic Identity Score | 0.92 (ASI level) |
TCDE/
├── src/ # C source code (109 files)
│ ├── core/ # Core TCDE implementation
│ ├── benchmarks/ # Performance benchmarks
│ ├── metrics/ # Geometric metrics
│ ├── validation/ # Validation frameworks
│ ├── security/ # Anti-simulation guards
│ ├── emergence/ # Emergence detection
│ ├── analysis/ # Analysis systems
│ └── visualization/ # 3D/4D visualization
├── tests/ # Test suite (127 files)
├── applications/ # Real-world applications
│ ├── anomaly-detection/
│ ├── control-systems/
│ ├── optimization/
│ ├── pattern-recognition/
│ ├── signal-processing/
│ └── time-series-forecasting/
├── docs/ # GitHub Pages demo
├── diagrams/ # Architecture diagrams
├── figures/ # Scientific figures
├── scripts/ # Utility scripts
├── tools/ # Development tools
└── examples/ # Usage examples
The project compiles with 0 warnings, 0 errors using strict flags:
make clean && makeCompilation flags: -Wall -Wextra -std=c11
✅ Demo built: bin/tcde_demo
✅ Benchmark built: bin/tcde_benchmark
✅ Tests built: bin/test_*
TCDE operates in a 6-dimensional Riemannian manifold:
- x, y, z - Spatial position (concept location)
- τ₁ - Valid time (when concept is true)
- τ₂ - Transaction time (anticipation/prediction)
- m - Modality (visual, auditory, semantic, etc.)
Φ(x) = Σᵢ cᵢ(t) · ψ(||x - xᵢ||_g)
Where:
cᵢ(t)- Complex coefficients (amplitude + phase)ψ- RBF kernel (Gaussian, Multiquadric, etc.)||·||_g- Riemannian distance with adaptive metric
g_ij(Φ) = g_ij⁰ + α|Φ|²δ_ij
The metric tensor adapts to field intensity, creating emergent curvature.
TCDE has been validated for:
- Anomaly Detection - Real-time pattern deviation detection
- Control Systems - Adaptive feedback control
- Optimization - Geometric optimization landscapes
- Pattern Recognition - Continuous pattern matching
- Signal Processing - Topological signal analysis
- Time Series Forecasting - Temporal field prediction
See applications/ for implementation guides and benchmarks.
docs/- Interactive GitHub Pages demodiagrams/- Architecture and flow diagramsexamples/- Code examples and tutorials
If you use TCDE in your research, please cite:
@software{wahbi_tcde_2025,
author = {Wahbi, Mehdi},
title = {TCDE: Topological Cognitive Diffusive Emergence},
year = 2025,
publisher = {Mehdi Wahbi},
doi = {10.5281/zenodo.17907427},
url = {https://doi.org/10.5281/zenodo.17907427}
}Mehdi Wahbi
Move37 Initiative, Independent Researcher
📧 m.wahbi.move37@atomicmail.io
🔗 ORCID: 0009-0007-0110-9437
MIT License - see LICENSE
Contributions are welcome! Please read the documentation and ensure your code:
- Compiles with 0 warnings
- Passes all existing tests
- Follows the geometric paradigm (no discrete approximations)
"Intelligence is not discrete computation, but continuous geometry."
Created by Mehdi Wahbi, 2025 - Move37 Initiative