wev-verification

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

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

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

References

• Block Science KOI
• 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

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 10. Adventure Game Example

Concepts: autonomous agent, game, synthesis

GF(3) Balanced Triad

wev-verification (−) + SDF.Ch10 (+) + [balancer] (○) = 0

Skill Trit: -1 (MINUS - verification)

Secondary Chapters

• Ch4: Pattern Matching
• Ch2: Domain-Specific Languages

Connection Pattern

Adventure games synthesize techniques. This skill integrates multiple patterns.

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.