Skill Connectivity Hub

---
name: skill-connectivity-hub
description: Skill Connectivity Hub
version: 1.0.0
---

# Skill Connectivity Hub

**Trit**: 0 (ERGODIC - coordinator)  
**Role**: Graph-based skill orchestration via neighbor-aware interleaving  
**GF(3)**: Conserved via hub-spoke triadic routing

## Overview

Identifies and routes through maximally-connected "hub skills" that reference the most neighbors. Uses Babashka for graph analysis and Narya for counterfactual diffing of skill evolution.

## Hub Skills (by Reference Count)

| Skill | Out-Degree | Key Neighbors |
|-------|------------|---------------|
| `narya-proofs` | 5 | bisimulation-game, gay-mcp, ordered-locale, sheaf-cohomology, topos-generate |
| `bisimulation-game` | 5 | gay-mcp, localsend-mcp, open-games, unwiring-arena, unworld |
| `ordered-locale` | 5 | narya, gf3, segal-types, unworld, triad-interleave |
| `sheaf-cohomology` | 5 | acsets, unworld, glass-bead-game, rubato-composer, tree-sitter |
| `topos-generate` | 5 | sheaf-cohomology, dialectica, kan-extensions, open-games, temporal-coalgebra |
| `dynamic-sufficiency` | 145 refs | GF(3), ACSet, skill, triadic, Gay, operad |

## GF(3) Triads (Verified)

```
narya-proofs (-1) ⊗ ordered-locale (0) ⊗ gay-mcp (+1) = 0 ✓
sheaf-cohomology (-1) ⊗ dialectica (0) ⊗ topos-generate (+1) = 0 ✓
bisimulation-game (-1) ⊗ open-games (0) ⊗ unwiring-arena (+1) = 0 ✓
```

## Babashka Connectivity Analyzer

```clojure
#!/usr/bin/env bb
(require '[babashka.fs :as fs])
(require '[clojure.string :as str])

(defn extract-skill-refs [content]
  "Extract skill-like hyphenated references from content."
  (->> (re-seq #"\b([a-z]+-[a-z]+(?:-[a-z]+)*)\b" content)
       (map second)
       (filter #(> (count %) 5))
       distinct))

(defn build-skill-graph [skills-dir]
  "Build adjacency graph of skill references."
  (let [skill-files (fs/glob skills-dir "**/SKILL.md")]
    (into {}
      (for [f skill-files
            :let [skill-name (-> f fs/parent fs/file-name str)
                  content (slurp (str f))
                  refs (extract-skill-refs content)]]
        [skill-name {:neighbors refs
                     :degree (count refs)}]))))

(defn find-hubs [graph n]
  "Find top n hub skills by out-degree."
  (->> graph
       (sort-by (comp :degree val) >)
       (take n)))

(defn verify-gf3-triad [s1 s2 s3]
  "Verify GF(3) conservation for skill triad."
  (let [trits {:minus -1 :ergodic 0 :plus 1}
        sum (+ (get trits s1 0) (get trits s2 0) (get trits s3 0))]
    (zero? (mod sum 3))))

;; Usage
(def graph (build-skill-graph "/Users/alice/.claude/skills"))
(def hubs (find-hubs graph 10))
(println "Top 10 Hub Skills:")
(doseq [[name data] hubs]
  (println (format "  %s: %d neighbors" name (:degree data))))
```

## Narya Counterfactual Diffing

Compare skill evolution using observational bridge types:

```python
from narya_proofs import NaryaProofRunner

def diff_skill_versions(skill_name, v1_path, v2_path):
    """Counterfactual diff via Narya proof verification."""
    runner = NaryaProofRunner(seed=0x42D)
    
    # Load both versions
    v1_content = open(v1_path).read()
    v2_content = open(v2_path).read()
    
    # Generate delta
    delta = {
        "skill": skill_name,
        "before": hash(v1_content),
        "after": hash(v2_content),
        "impact": 1 if v1_content != v2_content else 0,
        "type": "skill_evolution"
    }
    
    return delta

# Compare with Emacs integration via .el
def emacs_narya_diff(skill_name):
    """Invoke Emacs Narya mode for interactive diffing."""
    import subprocess
    elisp = f'''
    (progn
      (require 'narya-ordered-locale)
      (narya-diff-skill "{skill_name}")
      (narya-gf3-verify))
    '''
    subprocess.run(["emacs", "--batch", "--eval", elisp])
```

## libghosty VT Integration

Self-operating auto-formalizing society via terminal virtualization:

```rust
// libghosty skill dispersal interface
pub struct SkillDispersalVT {
    hub_skills: Vec<String>,
    active_triads: Vec<[String; 3]>,
    gf3_conservation: bool,
}

impl SkillDispersalVT {
    pub fn new(seed: u64) -> Self {
        // Initialize with SplitMix64 for deterministic routing
        Self {
            hub_skills: vec!["narya-proofs", "bisimulation-game", 
                            "ordered-locale", "sheaf-cohomology", 
                            "topos-generate"].into_iter()
                           .map(String::from).collect(),
            active_triads: vec![],
            gf3_conservation: true,
        }
    }
    
    pub fn interleave_direction(&mut self, direction: i8) {
        // Trifurcate every decision through hub skills
        // direction: -1 (MINUS), 0 (ERGODIC), +1 (PLUS)
        assert!(self.gf3_conservation);
    }
    
    pub fn auto_formalize(&self) -> String {
        // Generate Narya proof certificate for current state
        format!("sha256:{:x}", self.state_hash())
    }
}
```

## Emacs/.el Integration

```elisp
;;; skill-connectivity-hub.el --- Hub skill orchestration

(require 'narya-ordered-locale)

(defvar skill-hub-skills
  '("narya-proofs" "bisimulation-game" "ordered-locale" 
    "sheaf-cohomology" "topos-generate")
  "Most connected hub skills for routing.")

(defun skill-hub-interleave (skill-list)
  "Interleave skills through hub for maximum connectivity."
  (let ((triad (skill-hub-form-triad skill-list)))
    (when (skill-hub-verify-gf3 triad)
      (skill-hub-dispatch triad))))

(defun skill-hub-verify-gf3 (triad)
  "Verify GF(3) conservation for skill triad."
  (let ((sum (apply #'+ (mapcar #'skill-hub-get-trit triad))))
    (= (mod sum 3) 0)))

(defun skill-hub-narya-diff (before after)
  "Counterfactual diff using Narya observational bridge."
  (narya-bridge-type before after 1))

(provide 'skill-connectivity-hub)
```

## Commands

```bash
# Analyze skill connectivity
just skill-hub-analyze

# Find top hubs
just skill-hub-top 10

# Verify GF(3) triads
just skill-hub-verify-triads

# Generate Narya proof of connectivity
just skill-hub-narya-proof

# Emacs interactive mode
emacs --eval "(skill-hub-mode)"
```

## Integration Patterns

### Pattern 1: Hub-First Routing
Always route new skills through a hub skill first to maximize connectivity.

### Pattern 2: Triadic Interleaving
Form triads with hub skills to ensure GF(3) conservation.

### Pattern 3: Narya-Verified Evolution
Use Narya proofs to verify skill evolution preserves invariants.

### Pattern 4: libghosty Auto-Formalization
Self-operating VT system for autonomous skill society.

---

**Skill Name**: skill-connectivity-hub  
**Type**: Graph Analysis / Skill Orchestration  
**Trit**: 0 (ERGODIC - coordinator)  
**GF(3)**: Conserved via triadic routing  
**Dependencies**: narya-proofs, bisimulation-game, babashka
## Skill Interaction Entropy

| Thread | Color | Entropy | Trit | Hue |
|--------|-------|---------|------|-----|
| T-019b5e16-f9ad-773c-b2ef-ae65bc084748 | #D647B0 | 42 | 0 (ERGODIC) | 158° |

Generated via Gay.jl SplitMix64 deterministic coloring.




## Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

### Graph Theory
- **networkx** [○] via bicomodule
  - Hub for all graph/network skills

### 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.