wev-verification

# WEV Verification Skill

**Trit**: -1 (MINUS - Validator)
**GF(3) Triad**: `wev-verification (-1) ⊗ world-hopping (0) ⊗ alife (+1) = 0`

## Overview

World Extractable Value (WEV) verification connecting:
- Quadrant Chart (Colorable × Derangeable)
- Proof-of-Frog consensus
- Learning Agent reafference loops
- GF(3) conservation

## WEV Formula

```
WEV = Σ(coordinated outcomes) - Σ(coordination costs)

Legacy:  WEV = V - 0.5V - costs = 0.4V
GF(3):   WEV = V + 0.1V - 0.01 = 1.09V
Advantage: 2.7x
```

## Quadrant Classification

| Quadrant | Colorable | Derangeable | Examples |
|----------|-----------|-------------|----------|
| Q1 (OPTIMAL) | ✓ | ✓ | PR#18, Knight Tour |
| Q2 | ✓ | ✗ | Identity morphisms |
| Q3 (WORST) | ✗ | ✗ | Deadlock states |
| Q4 | ✗ | ✓ | Phase transitions |

## Learning Agent Architecture

```
┌─────────────────────────────────────────┐
│          Reafference Loop               │
├─────────────────────────────────────────┤
│ 1. Predict (Efference Copy)             │
│ 2. Execute (Action)                     │
│ 3. Observe (Sensation)                  │
│ 4. Match? (Validate)                    │
│ 5. Update Model (Learn)                 │
└─────────────────────────────────────────┘
```

## Usage

```julia
using .WEVVerification

# Quadrant verification
items = [
    ("PR#18", 0.85, 0.90),
    ("Knight Tour", 0.75, 0.85),
    ("Deadlock", 0.15, 0.15),
]
verify_quadrant(items)

# WEV comparison
comparison = compare_wev_legacy_vs_gf3(100.0)
println("Advantage: ", comparison.advantage)

# Learning agents
alice = LearningAgent(:alice, Int8(-1))
arbiter = LearningAgent(:arbiter, Int8(0))
bob = LearningAgent(:bob, Int8(1))

# Reafference loop
reafference_loop!(alice, action, world_state)

# Frog status
frog_status([alice, arbiter, bob])
```

## Neighbors

### High Affinity
- `world-hopping` (0): Cross-world navigation
- `alife` (+1): Emergent behavior
- `cybernetic-immune` (-1): Self/Non-Self

### Example Triad
```yaml
skills: [wev-verification, world-hopping, alife]
sum: (-1) + (0) + (+1) = 0 ✓ CONSERVED
```

## References

- [Block Science KOI](https://blog.block.science/a-language-for-knowledge-networks/)
- von Holst (1950) - Reafference principle
- Powers (1973) - Perceptual Control Theory



## Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

### Graph Theory
- **networkx** [○] via bicomodule
  - Universal graph hub

### Bibliography References

- `category-theory`: 139 citations in bib.duckdb

## Cat# Integration

This skill maps to **Cat# = Comod(P)** as a bicomodule in the equipment structure:

```
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
```

### GF(3) Naturality

The skill participates in triads satisfying:
```
(-1) + (0) + (+1) ≡ 0 (mod 3)
```

This ensures compositional coherence in the Cat# equipment structure.