# Layer L1: Geometric

## Overview
Shape-aware topology and coupling geometry. Bridges pure mathematics with spatial computation.

## Status
🟡 **Partial** - Some proofs in Lean, documentation migrated

## Key Components

### GWL 5-factor Coupling
- Geometric coupling mechanism
- 5 independent coupling factors
- Tension-compression balance

### TorsionalPIST
- Quaternion-based torsional dynamics
- 3D rotation representation
- Torque transfer mechanics

### HybridTSMPISTTorus
- Toroidal topology implementation
- Hybrid TSM/PIST integration
- Periodic boundary conditions

### GWL Throat
- Geometric throat construction
- Flow channel optimization
- Cross-sectional area control

## Formal Proofs
- [[Eigensolid Convergence]] - Braid crossing loop stabilization
- [[Geometric Coupling Correctness]] - GWL factor validation

## Documentation
- [[Geometric Topology Primer]]
- [[Coupling Mechanics]]
- [[Torsional Dynamics Guide]]

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#layer-L1 #geometric #topology