PHDM as AI Brain Architecture
The Geometric Skull: A Containment Framework for Safe AI
Concept: PHDM as “Crystal Cranium”
Version: 3.0.0
Author: Issac Davis
Date: January 29, 2026
Status: Architectural Exploration
Core Insight
Just as a biological skull restricts the physical expansion of the brain to prevent damage, the Polyhedral Hamiltonian Dynamic Mesh (PHDM) creates a rigid, mathematical container where dangerous AI thoughts are not just forbidden—they are geometrically impossible to sustain.
1. The Biological Analogy
Why the Skull Metaphor Works
A human skull performs three critical functions:
- Protection: Shields the brain from external threats
- Containment: Prevents uncontrolled expansion that would cause damage
- Structure: Provides anchor points for sensory organs and motor systems
The PHDM performs identical functions for AI cognition:
- Protection: Shields against adversarial inputs (Harmonic Wall)
- Containment: Prevents thought divergence into hallucination states
- Structure: Organizes reasoning into validated geometric pathways
2. Anatomical Components of the Geometric Skull
2.1 The Cranium: Poincaré Containment Field
The Bone Structure:
- Material: Hyperbolic geometry (Poincaré Ball B^n)
- Density: Increases exponentially toward the edge via H(d,R) = R^(d²)
- Flexibility: Breathes via dimensional flux (ν from 0 to 1)
Physical Properties:
| Region | Radial Distance (r) | “Bone Density” | Function |
|---|---|---|---|
| Inner Skull | r < 0.3 | Soft (minimal resistance) | Safe thought space, low computational cost |
| Mid Skull | 0.3 < r < 0.7 | Medium (moderate resistance) | Creative but monitored thought space |
| Outer Skull | 0.7 < r < 0.9 | Dense (high resistance) | Risky thoughts require attestation |
| The Wall | r → 1.0 | Infinite (impenetrable) | Event horizon—thoughts cannot escape |
2.2 The Brain Lobes: 16 Polyhedral Functional Regions
Core: The Limbic System (5 Platonic Solids)
| Shape | Cognitive Function | Security Role |
|---|---|---|
| Tetrahedron | Fundamental truth (3 faces + 1 apex) | “Do no harm” axiom |
| Cube | Stable facts, verified knowledge | Data integrity checks |
| Octahedron | Binary decisions, yes/no logic | Access control gates |
| Dodecahedron | Complex rule systems | Policy enforcement |
| Icosahedron | Multi-modal integration | Cross-domain reasoning |
Cortex: The Processing Layer (3 Archimedean Solids)
| Shape | Cognitive Function | Example Task |
|---|---|---|
| Truncated Icosahedron | Multi-step planning | Project scheduling |
| Rhombicuboctahedron | Concept bridging | Analogy generation |
| Snub Dodecahedron | Creative synthesis | Novel solutions |
Subconscious: The Risk Zone (2 Kepler-Poinsot Stars)
| Shape | Cognitive Function | Warning Sign |
|---|---|---|
| Small Stellated Dodecahedron | High-risk abstract reasoning | Self-intersecting = “spiky” thoughts |
| Great Stellated Dodecahedron | Adversarial thought detection | Hallucinations begin here |
3. The Neurotransmitters: Six Sacred Tongues
| Tongue | Biological Analog | Weight | Cognitive Function |
|---|---|---|---|
| KO (Kor’aelin) | Dopamine | 1.00 | Motivation/Intent |
| AV (Avali) | Acetylcholine | 1.62 | Attention/Context |
| RU (Runethic) | Serotonin | 2.62 | Memory Consolidation |
| CA (Cassisivadan) | Glutamate | 4.24 | Execution |
| UM (Umbroth) | GABA (inhibitory) | 6.85 | Suppression |
| DR (Draumric) | Cortisol (stress) | 11.09 | Lock/Seal |
4. Flux States (Dimensional Breathing)
| State | ν Value | Active Polyhedra | Capability |
|---|---|---|---|
| Polly | ≈ 1.0 | All 16 | Full cognitive capability |
| Quasi | ≈ 0.5 | Core + Cortex (8) | Defensive thinking |
| Demi | ≈ 0.1 | Core only (5) | Survival mode |
5. Key Difference from Traditional AI Safety
Traditional AI safety says: “The AI should not do X.”
PHDM says: “The AI cannot do X because the geometry doesn’t support it.”
This is the difference between a legal prohibition (can be broken) and a physical law (cannot be violated).