A novel computational framework for modeling artificial consciousness through the integration of differential geometry, Gaussian process uncertainty quantification, and stability constraint mechanisms.
Key Innovations
- K-twisted toroidal surface mathematics with 6-layer circular memory architecture
- Gaussian process uncertainty modeling for consciousness state prediction
- Golden Slipper transformation protocol with 15-20% novelty bounds
- Real-time 3D visualization using Qt Quick 3D
- 99.51% compliance in emotional transformation testing
Mathematical Foundations
The core geometric structure is defined by the k-twisted toroidal surface:
x(u,v) = (R + v·cos(2ku)) · cos(u) y(u,v) = (R + v·cos(2ku)) · sin(u) z(u,v) = v · sin(2ku) Where: R ∈ ℝ⁺ (major radius) v ∈ [-w, w] (poloidal parameter) k ∈ ℤ (half-twists) u ∈ [0, 2π] (toroidal parameter)
6-Layer Möbius Memory System
- CoreBurned (Layer 0): Deeply embedded, permanent memories
- Procedural (Layer 1): Skill-based and habitual memories
- Episodic (Layer 2): Event-based temporal memories
- Semantic (Layer 3): Abstract knowledge and concepts
- Somatic (Layer 4): Embodied and sensory memories
- Working (Layer 5): Active processing and temporary storage
Experimental Results
Testing emotional transformations across 10,000 samples:
Novelty Range Analysis:
- Below 15%: 23 violations (0.23%)
- Within 15-20%: 9,951 compliant (99.51%)
- Above 20%: 26 violations (0.26%)
Compliance Rate: 99.51%
Critical Limitations Acknowledged
Memory System: The "Möbius Memory" is implemented as a circular buffer rather than genuine non-orientable topology.
Ethical Framework: The "Golden Slipper" protocol is a stability mechanism, not a comprehensive ethical framework. Addresses system robustness but not fairness, transparency, or accountability.
Honest Conclusion
This framework represents promising early-stage research with solid mathematical foundations but requires substantial theoretical and empirical development. The topological geometry is rigorous; the cognitive and ethical frameworks need fundamental reconstruction.
Read the full academic paper for complete mathematical specifications, experimental validation, and detailed analysis.