AI Safety
C4-SECURE protocol with Modal Firewall. 100% detection of Agents of Chaos failure modes.
- 27-state monitoring
- Φ-attractor convergence
- 6-layer security
C4 Universe · formal theory
Complete Cognitive Coordinate System Z₃³ · 27 states
Theorem-backed map of cognition — Time × Scale × Agency. Geometry is a navigation grammar, not a consciousness oracle.
Agda proofs
Einstein ≤6 steps
ID=3 validation
T: Time
S: Scale
A: Agency
Paths by role
Applications Six Domains, One Framework
Optimization
FRA routing for NP-hard problems. +10.3% improvement on TSP/SAT/CSP.
- 7D fingerprinting
- Adaptive routing
- 0.39% median gap on TSP
Therapy
TOTE cycles for cognitive navigation. Depression: F⟨Past,Concrete,Self⟩ → Φ
- State tracking
- Hamming distance paths
- Clinical validation
Scientific Discovery
CDI algorithm for breakthrough insights. Einstein Test: 4/6 steps validated.
- Destructive insights
- Domain transfer
- Algorithmic creativity
Cross-Domain Intelligence
Isomorphism Scanner. Type I & II structural mappings across 6+ domains.
- Geometry ↔ Physics
- Algorithms ↔ Cognition
- 32 systems mapped
Formal Proofs
20+ theorems from Agent of Order Research Zero holes, --safe --without-K.
- Theorem 17: Compassion convergence
- Theorem 11: ≤6 steps
- Tested in multi-agent C4-SECURE protocol
Hugging Face
Production Classifier
BERT-C4: 12 LoRA adapters on mDeBERTa-v3-base. 93.5% accuracy on 27 cognitive states. Deployed and ready for inference.
HangJang/c4-cognitive-adapters
View on Hugging Face →
Mathematical Structure
ℤ₃³ = 27 states forming complete cognitive space. Each state F⟨T,S,A⟩ represents a unique mode of thinking.
Formal Verification
Validated in Agent of Order research. Multi-agent safety protocol with 100% AoC detection. Zero false negatives in 16-agent chaos testing.
The Einstein Test
C4 derives Special Relativity in 4 steps and General Relativity in 6 steps from 1902 data. Algorithmic scientific discovery.
Universal Pattern
FRA (Fingerprint-Route-Adapt) found in 32+ systems across 6 domains: from immune systems to financial markets.
🔵 Formal Theorems
20+ theorems proven in Agda. Click to explore dependencies and proofs.
THEOREM 1
✓ Proven
Existence of C4 Structure
Z₃³ forms a complete cognitive coordinate system with 27 unique states.
Agda
Base Axiom
THEOREM 2
✓ Proven
Minimality of Z₃³
No smaller structure (Z₂³ or Z₃²) captures all required cognitive properties.
Agda
← Theorem 1
THEOREM 11
✓ Proven
Six Steps Convergence
Any cognitive state reachable from any other in ≤6 steps through Φ-attractor.
Agda
Hamming Distance
THEOREM 17
✓ Proven
FRA Universality
FRA pattern emerges in any system with ≥3 scales and adaptation mechanism.
Category Theory
THEOREM 37
In progress
UCOS Completeness
4-layer UCOS architecture is sufficient for general cognitive computation.
Categorical
In Progress
Theorem Dependency Graph
1
Base
→
2-10
Structure
→
11
≤6 Steps
→
37
Completeness
📐 Hamming Distance Explorer
Visualize the metric space of C4. Click on any state to see distances to others. The "6 steps" theorem becomes visible: any state reachable in ≤3 Hamming distance units.
Loading interactive visualization...
🔵 Metric Properties
Hamming Distance Definition
For states
s₁ = (T₁, D₁, I₁)
and
s₂ = (T₂, D₂, I₂):
d(s₁, s₂) = |T₁-T₂|ₘₒ𝒹₃ + |D₁-D₂|ₘₒ𝒹₃ + |I₁-I₂|ₘₒ𝒹₃
Distance Color Coding
d = 0
Same state (identity)
d = 1
One dimension changes (adjacent)
d = 2
Two dimensions change
d = 3
Complete transformation (opposite)
🔗 Connection to Theorem 11
Maximum Hamming distance in Z₃³ is 3. Therefore, any state reachable in ≤6 steps through intermediate states — confirming the theorem experimentally.