Aptos Orderless WEV Skill

Trit: +1 (PLUS) - Generative parallel execution

World Extractable Value via Aptos orderless transactions with Strong Parallelism Invariance (SPI) guarantees and GF(3) conservation.

Core Concept

WEV (World Extractable Value) exploits knowledge differentials between domains in orderless execution systems. Unlike MEV (order-dependent extraction), WEV leverages parallel execution invariance.

┌─────────────────────────────────────────────────────────────────────┐
│  MEV vs WEV                                                         │
├─────────────────────────────────────────────────────────────────────┤
│  MEV: Extract value from transaction ORDERING                      │
│       Sequencer sees tx₁ before tx₂ → front-run                    │
│       Order matters, position is power                             │
│                                                                     │
│  WEV: Extract value from KNOWLEDGE DIFFERENTIALS                   │
│       World A knows X, World B knows Y                              │
│       Orderless execution → position irrelevant                     │
│       Knowledge asymmetry is power                                  │
└─────────────────────────────────────────────────────────────────────┘

Aptos Orderless Transactions (AIP-123)

From Aptos Documentation:

• Purpose: Execute transactions out of order for multi-machine signing
• Replay Protection: Uses replayProtectionNonce (random u64)
• Max Expiration: 60 seconds
• Block-STM: Parallel execution engine

// Orderless transaction structure
interface OrderlessTransaction {
  replayProtectionNonce: bigint;  // Random u64 for replay protection
  payload: TransactionPayloadPayload;  // AIP-129 payload
  expirationTimestamp: number;  // Max 60 seconds
}

GF(3) Conservation as Orderless Guarantee

For any valid WEV transaction triplet, the sum of trits must be zero:

PLUS  (+1): Generators (A, B, C, D, E, W, X, Y, Z)
ERGODIC(0): Coordinators (F, G, H, I, J, K, L, M)
MINUS (-1): Validators (N, O, P, Q, R, S, T, U, V)

Sum: 9(+1) + 8(0) + 9(-1) = 0 ✓

WEV Triplet Structure

(defn wev-triplet [from-world to-world mediator]
  (let [trits [(world-trit from-world)   ; PLUS (+1) sender
               (world-trit mediator)      ; ERGODIC (0) coordinator
               (world-trit to-world)]]    ; MINUS (-1) validator
    (assert (zero? (mod (reduce + trits) 3))
            "GF(3) conservation violated!")
    {:transactions [from-world mediator to-world]
     :orderless true
     :conserved true}))

Strong Parallelism Invariance (SPI)

SPI Theorem: For any deterministic generator G with seed s,
             ∀ permutation π of indices I:
             G(s, I) ≡ G(s, π(I)) (modulo ordering)

Verification:

• ordered == reversed == shuffled
• parallel == sequential
• GF(3) sum preserved across all orderings

Open Games Formalization

Orderless Game as Open Game

data OrderlessGame s t a b = OrderlessGame
  { play    :: s -> a                    -- Forward: knowledge state → action
  , coplay  :: s -> b -> t               -- Backward: observation → utility
  , nonce   :: Word64                    -- Replay protection
  , triplet :: (World, World, World)     -- GF(3)-balanced worlds
  }

-- Composition is order-invariant
instance Category OrderlessGame where
  (.) g h = OrderlessGame
    { play = play g . play h
    , coplay = \s b -> coplay h s (coplay g (play h s) b)
    , nonce = xor (nonce g) (nonce h)  -- Combined nonce
    , triplet = mergeTriplets (triplet g) (triplet h)
    }

Epistemic Arbitrage as Nash Equilibrium

-- Knowledge differential game
epistemicArbitrage :: OpenGame KnowledgeState KnowledgeState Action Utility
epistemicArbitrage = OpenGame
  { play = \k -> 
      let diff = knowledgeDifferential k
      in if profitable diff then ExtractWEV else Wait
  , coplay = \k a -> 
      case a of
        ExtractWEV -> k { value = value k + wevProfit }
        Wait -> k
  , equilibrium = \k -> 
      -- Nash: extract iff differential profitable
      profitable (knowledgeDifferential k) == (play k == ExtractWEV)
  }

Triangle Arbitrage Across Worlds

World_PLUS ←──────────→ World_ERGODIC
     (+1)    knowledge      (0)
      ▲         flow         ▲
       \                    /
        \   GF(3) = 0      /
         \                /
          ▼              ▼
           World_MINUS
              (-1)

Mediator Selection Logic

(defn find-mediator [worlds from-world to-world]
  (let [from-trit (get-in worlds [from-world :trit])
        to-trit (get-in worlds [to-world :trit])
        sum-mod3 (mod (+ from-trit to-trit) 3)
        needed-trit (case sum-mod3
                      0  0    ; need 0 to make sum 0
                      1 -1    ; need -1: (1 + (-1) = 0)
                      2  1)]  ; need +1: (2 + 1 = 3 ≡ 0)
    (first (filter #(= needed-trit (get-in worlds [% :trit]))
                   (keys worlds)))))

Babashka Implementation

wev_orderless.bb

#!/usr/bin/env bb
;; World Extractable Value via orderless Aptos transactions

(require '[babashka.cli :as cli])

(def WORLDS
  {:a {:trit +1 :wallet "0x...a"}
   :b {:trit +1 :wallet "0x...b"}
   :f {:trit  0 :wallet "0x...f"}  ; mediator
   :n {:trit -1 :wallet "0x...n"}
   :p {:trit -1 :wallet "0x...p"}})

(defn knowledge-differential [from-world to-world]
  ;; Compute knowledge asymmetry between worlds
  (let [k1 (io/file (str "/tmp/" (name from-world) "_knowledge"))
        k2 (io/file (str "/tmp/" (name to-world) "_knowledge"))]
    (cond
      (and (.exists k1) (not (.exists k2))) :from-advantage
      (and (.exists k2) (not (.exists k1))) :to-advantage
      :else :equilibrium)))

(defn wev-triplet [from to]
  (let [mediator (find-mediator WORLDS from to)
        trits [(get-in WORLDS [from :trit])
               (get-in WORLDS [mediator :trit])
               (get-in WORLDS [to :trit])]]
    (assert (zero? (mod (reduce + trits) 3)))
    {:from from :mediator mediator :to to
     :orderless true
     :nonce (rand-int Integer/MAX_VALUE)}))

(defn extract-wev [from to]
  (let [triplet (wev-triplet from to)
        diff (knowledge-differential from to)]
    (when (not= diff :equilibrium)
      (println "WEV opportunity:" diff)
      (println "Triplet:" triplet)
      triplet)))

;; CLI
(def cli-opts
  {:scan    {:fn (fn [_] (scan-opportunities WORLDS))}
   :triplet {:fn (fn [{:keys [from to]}] 
                   (wev-triplet (keyword from) (keyword to)))}
   :extract {:fn (fn [{:keys [from to]}]
                   (extract-wev (keyword from) (keyword to)))}})

(cli/dispatch cli-opts *command-line-args*)

ACSet Schema

@present SchOrderlessWEV(FreeSchema) begin
    # Worlds
    World::Ob
    Transaction::Ob
    Triplet::Ob
    
    # World structure
    Trit::AttrType
    Wallet::AttrType
    Knowledge::AttrType
    
    world_trit::Attr(World, Trit)
    world_wallet::Attr(World, Wallet)
    world_knowledge::Attr(World, Knowledge)
    
    # Triplet structure (GF(3)-balanced)
    plus_world::Hom(Triplet, World)
    ergodic_world::Hom(Triplet, World)
    minus_world::Hom(Triplet, World)
    
    # Transaction
    Nonce::AttrType
    tx_nonce::Attr(Transaction, Nonce)
    tx_triplet::Hom(Transaction, Triplet)
    
    # Constraint: sum of trits = 0 (mod 3)
    # Enforced at construction time
end

GF(3) Triads

aptos-orderless-wev (+1) ⊗ boneh-roughgarden-wev (0) ⊗ solver-fee (-1) = 0 ✓
aptos-orderless-wev (+1) ⊗ open-games (0) ⊗ intent-sink (-1) = 0 ✓
aptos-orderless-wev (+1) ⊗ gay-mcp (0) ⊗ protocol-evolution-markets (-1) = 0 ✓

Integration

Skill	Connection	Direction
open-games	OrderlessGame as Para morphism	→
boneh-roughgarden-wev	Shared WEV mechanism	↔
spi-parallel-verify	Verification of order-invariance	←
gay-mcp	Seed generation for nonces	←
epistemic-arbitrage	Knowledge differential exploitation	→

CLI Commands

# Scan for WEV opportunities
bb scripts/wev_orderless.bb scan

# Build GF(3)-balanced triplet
bb scripts/wev_orderless.bb triplet --from a --to p

# Extract WEV (if differential exists)
bb scripts/wev_orderless.bb extract --from a --to p

# Verify SPI
just spi-verify triplet.json

References

1. AIP-123: Orderless Transactions
2. AIP-129: Transaction Payload Payload
3. Block-STM: Aptos parallel execution engine
4. Ghani, Hedges et al.: Compositional Game Theory
5. Gay.jl: SplitMix64 for deterministic nonces

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Skill Name: aptos-orderless-wev Type: Parallel Execution / Game Theory Trit: +1 (PLUS) Key Property: GF(3)-conserved orderless triplets with SPI guarantees