wev-tesseract

# 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

```clojure
(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):

```clojure
(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

```clojure
(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:

```clojure
(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

```bash
# 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

```bash
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/wev_26_worlds.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

## 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.