WEV Tesseract Skill

Trit: 0 (ERGODIC - coordinator) Color: #26D826 (Green) Role: Thread ancestry verification and world state reconstruction

Overview

WEV (World Extractable Value) Tesseract provides:

1. Thread ancestry verification - Walk up parent chain to known anchors
2. World state reconstruction - Rebuild GF(3)-balanced world from history
3. Skill collapse protocol - Load ALL skills when genesis reached
4. Epistemic arbitrage - Extract knowledge differentials between 26 worlds

26-World GF(3) Structure

PLUS  (+1): A, B, C, D, E, W, X, Y, Z    (9 worlds)
ERGODIC(0): F, G, H, I, J, K, L, M       (8 worlds)
MINUS (-1): N, O, P, Q, R, S, T, U, V    (9 worlds)

Sum: 9(+1) + 8(0) + 9(-1) = 0 ✓

Thread Ancestry Protocol

(defn verify-thread-ancestry
  "Verify thread is in known set or walk to parent"
  [thread-id parent-map]
  (loop [tid thread-id
         chain []]
    (cond
      ;; Found known anchor
      (thread-in-known? tid)
      {:verified true
       :anchor-thread tid
       :ancestry-chain (conj chain tid)
       :depth (count chain)}
      
      ;; Has parent - continue walking
      (contains? parent-map tid)
      (recur (get parent-map tid) (conj chain tid))
      
      ;; Genesis reached - collapse all skills
      :else
      {:verified false
       :reason :genesis-reached
       :ancestry-chain (conj chain tid)
       :action :collapse-all-skills})))

Skill Collapse Protocol

When genesis thread is reached (no verified ancestor):

(defn collapse-all-skills
  "Load ALL skills when genesis thread reached"
  [skill-dirs]
  (let [skills (for [dir skill-dirs
                     :let [expanded (str/replace dir "~" (System/getenv "HOME"))]
                     :when (.exists (java.io.File. expanded))
                     skill-dir (.listFiles (java.io.File. expanded))
                     :when (.isDirectory skill-dir)
                     :let [skill-file (java.io.File. skill-dir "SKILL.md")]
                     :when (.exists skill-file)]
                 {:name (.getName skill-dir)
                  :path (.getPath skill-file)})]
    {:total (count skills)
     :skills (vec skills)}))

WEV Extraction Triplets

(defn wev-triplet
  "Create a WEV extraction triplet from source to target world"
  [from-world to-world seed]
  (let [from-trit (WORLD-TRITS from-world)
        to-trit (WORLD-TRITS to-world)
        coordinator (nth (vec ERGODIC-WORLDS) (mod seed 8))]
    {:from {:world from-world :trit from-trit :role :source}
     :coordinator {:world coordinator :trit 0 :role :bridge}
     :to {:world to-world :trit to-trit :role :target}
     :triplet-sum (+ from-trit 0 to-trit)
     :balanced? (zero? (mod (+ from-trit to-trit) 3))
     :orderless true}))

Integration with Block-STM SPI

Strong Parallelism Invariance links to GF(3) Conservation:

Execute(T) ≡ Execute(π(T)) → sum(t.trits) ≡ 0 (mod 3)

For any permutation π of transaction T, execution is equivalent if and only if the triplet trits sum to 0 (mod 3).

Epistemic Arbitrage

Extract knowledge differential between worlds:

(defn epistemic-arbitrage
  "Extract knowledge differential between worlds"
  [from-world to-world knowledge-base]
  (let [from-knowledge (get knowledge-base from-world 0.0)
        to-knowledge (get knowledge-base to-world 0.0)
        differential (- from-knowledge to-knowledge)
        profitable? (> differential 0)]
    {:from-world from-world
     :to-world to-world
     :differential differential
     :profitable? profitable?
     :extraction-value (when profitable?
                         (* differential 0.1))  ; 10% extraction
     :triplet (wev-triplet from-world to-world (hash [from-world to-world]))}))

Usage

# Run WEV extraction
bb lib/wev_26_worlds.clj T-019b588f-323e-776a-8cc5-8a0fdb8756e6

# Verify GF(3) society
bb -e '(load-file "lib/wev_26_worlds.clj") (wev.twenty-six-worlds/verify-gf3-society)'

# Select balanced triplet
bb -e '(load-file "lib/wev_26_worlds.clj") (wev.twenty-six-worlds/select-balanced-triplet 1069)'

GF(3) Triads

wev-tesseract (0) ⊗ sheaf-cohomology (-1) ⊗ triad-interleave (+1) = 0 ✓
wev-tesseract (0) ⊗ bisimulation-game (-1) ⊗ gay-mcp (+1) = 0 ✓

Commands

just wev-verify    # Verify thread ancestry
just wev-extract   # Extract WEV from worlds
just wev-arbitrage # Find arbitrage opportunities
just wev-collapse  # Collapse all skills (genesis mode)

Skill Name: wev-tesseract Type: World State Verification Trit: 0 (ERGODIC) Dependencies: gay-mcp, sheaf-cohomology, bisimulation-game Source: lib/wev26worlds.clj

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

• general: 734 citations in bib.duckdb

SDF Interleaving

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

Primary Chapter: 6. Layering

Concepts: layered data, metadata, provenance, units

GF(3) Balanced Triad

wev-tesseract (+) + SDF.Ch6 (+) + [balancer] (+) = 0

Skill Trit: 1 (PLUS - generation)

Secondary Chapters

• Ch10: Adventure Game Example

Connection Pattern

Layering adds metadata. This skill tracks provenance or annotations.

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.