World Extractable Value

                    ┌─────────────────────────┐
                    │     WORLD W₁ (Nash)     │
                    │     Cost = C_Nash       │
                    └───────────┬─────────────┘
                                │
                          ┌─────▼─────┐
                          │  MARKOV   │
                          │  BLANKET  │
                          │  (Event)  │
                          └─────┬─────┘
                                │
                    ┌───────────▼─────────────┐
                    │    WORLD W₂ (Optimal)   │
                    │     Cost = C_Opt        │
                    └─────────────────────────┘

    WEV = C_Nash - C_Opt = C_Opt × (PoA - 1)

Components

1. Price of Anarchy (Roughgarden)

For d-regular Ramanujan expanders:

PoA = 1 + 1/gap = 1 + 1/(d - 2√(d-1))

d=4: PoA = 1 + 1/0.536 ≈ 2.87

2. Free Energy (Friston)

F = E_q[log q(x) - log p(x,y)]
  = Prediction_Error + Model_Complexity
  
F ≈ 1/gap + 0.1 ≈ 1.96

3. Markov Blanket

The boundary between self and world:

• Sensory states: Observations from world
• Active states: Actions on world
• Internal states: Agent's model

4. Action Direction

GF(3) Triads

ramanujan-expander (-1) ⊗ world-extractable-value (0) ⊗ influence-propagation (+1) = 0 ✓
three-match (-1) ⊗ world-extractable-value (0) ⊗ gay-mcp (+1) = 0 ✓
sheaf-cohomology (-1) ⊗ world-extractable-value (0) ⊗ open-games (+1) = 0 ✓

Implementation

Babashka

(defn compute-wev [seed spectral-data]
  (let [poa (:price_of_anarchy spectral-data)
        gap (:spectral_gap spectral-data)
        wev (- poa 1)
        free-energy (+ (/ 1 gap) 0.1)
        action (if (> (/ 1 gap) 0.5)
                 :perceptual_inference
                 :active_inference)]
    {:wev wev
     :free_energy free-energy
     :action_direction action
     :pct_extractable (* 100 (/ wev poa))}))

Julia

function world_extractable_value(d::Int, n::Int)
    gap = d - 2√(d-1)
    poa = 1 + 1/gap
    wev = poa - 1
    mixing_time = log(n) / gap
    
    (wev=wev, poa=poa, gap=gap, mixing=mixing_time)
end

DuckDB Schema

CREATE TABLE world_extractable_value (
  wev_id VARCHAR PRIMARY KEY,
  seed_hex VARCHAR,
  world_from VARCHAR,
  world_to VARCHAR,
  price_of_anarchy FLOAT,
  free_energy FLOAT,
  wev FLOAT,
  prediction_error FLOAT,
  action_direction VARCHAR,
  markov_blanket_size INT,
  extracted_at TIMESTAMP
);

-- Query extractable value
SELECT 
  wev_id,
  wev,
  ROUND(wev / price_of_anarchy * 100, 1) as pct_extractable,
  action_direction
FROM world_extractable_value
ORDER BY extracted_at DESC;

Alterpolitics Interpretation

Alterpolitics = alternative coordination mechanisms that reduce PoA:

The goal: extract value by moving toward coordination.

Commands

just wev-history      # Query WEV log
just wev-summary      # Aggregate stats
just wev-compare      # Nash vs Optimal
just triad-anarchy    # Full anarchy triad

Integration

Pre-Interaction Hook

WEV is computed on every interaction via .ruler/hooks/pre-interaction.bb:

7. ALWAYS compute World Extractable Value
   └─ wev = compute-world-extractable-value(seed, spectral)

Glass Bead Game

World-hopping extracts value via Badiou triangle:

d(W₁, W₃) ≤ d(W₁, W₂) + d(W₂, W₃)

WEV(hop) = Σ d(Wᵢ, Wᵢ₊₁) × extraction_rate

Paradigm Multiverse Finance Integration

Dave White's Multiverse Finance (May 2025) provides the financial mechanism:

Verses as Worlds

A verse is a parallel universe corresponding to a probability event:

• Complement: V and not-V partition the outcome space
• Union: V1 OR V2 forms new verse
• Intersection: V1 AND V2 forms child verse

Ownership Operations

Multiverse Map

Map[verse_id, owner_address] -> balance

Splitting: parent.balance -= x; for child in partition: child.balance += x
Combining: for child in partition: child.balance -= x; parent.balance += x

Key Insight

Assets in the same verse can be borrowed/lent freely because if one disappears (verse resolves false), all disappear simultaneously. No liquidation risk within a verse.

WEV extraction = pull_up after favorable verse resolution.

References

1. Roughgarden, T. (2002) -- "How Bad is Selfish Routing?"
2. Friston, K. (2010) -- "The Free-Energy Principle"
3. Roughgarden, T. (2015) -- "Intrinsic Robustness of the Price of Anarchy"
4. Powers, W. (1973) -- "Behavior: The Control of Perception"
5. White, D. / Paradigm (2025) -- "Multiverse Finance" https://paradigm.xyz/2025/05/multiverse-finance

See Also

• ramanujan-expander - Spectral gap
• open-games - Nash equilibrium
• glass-bead-game - World-hopping
• influence-propagation - Network effects