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graph-grafting
Graph Grafting Skill
Packaged view
This page reorganizes the original catalog entry around fit, installability, and workflow context first. The original raw source lives below.
Stars
8
Hot score
84
Updated
March 20, 2026
Overall rating
C3.6
Composite score
3.6
Best-practice grade
B78.7
Install command
npx @skill-hub/cli install plurigrid-asi-graph-grafting
Repository
Best for
Primary workflow: Ship Full Stack.
Technical facets: Full Stack.
Target audience: everyone.
License: Unknown.
Original source
Catalog source: SkillHub Club.
Repository owner: plurigrid.
This is still a mirrored public skill entry. Review the repository before installing into production workflows.
What it helps with
- Install graph-grafting into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
- Review https://github.com/plurigrid/asi before adding graph-grafting to shared team environments
- Use graph-grafting for development workflows
Works across
Claude CodeCodex CLIGemini CLIOpenCode
Favorites: 0.
Sub-skills: 0.
Aggregator: No.
Original source / Raw SKILL.md
---
name: graph-grafting
description: Graph Grafting Skill
version: 1.0.0
---
# Graph Grafting Skill
**Trit**: 0 (ERGODIC - Coordinator)
**GF(3) Triad**: `queryable (-1) ⊗ graftable (0) ⊗ derangeable (+1) = 0`
## Overview
Combinatorial complex operations replacing GraphQL with pure graph theory:
| Operation | Trit | Description |
|-----------|------|-------------|
| **Queryable** | -1 | Tree-shape decision via bag decomposition |
| **Colorable** | 0 | GF(3) 3-coloring via sheaf |
| **Derangeable** | +1 | Permutations with no fixed points |
| **Graftable** | 0 | Attach rooted tree at vertex |
## Mathematical Foundation
**Grafting** = attaching a rooted tree T at vertex v of graph G:
```
Graft(T, v, G) → G' where:
- V(G') = V(G) ∪ V(T)
- E(G') = E(G) ∪ E(T) ∪ {(v, root(T))}
- Adhesion = shared labels at attachment point
```
## Quadrant Chart: Colorable × Derangeable
```
Balanced (GF3=0)
│
Q2 │ Q1 ← OPTIMAL
Identity │ PR#18, Knight Tour
│ SICM Galois
──────────────┼──────────────
Q3 │ Q4
Deadlock │ Phase Trans
│
Fixed Points → Derangement
```
## Usage
```julia
using .GraphGrafting
c = GraftComplex(UInt64(1069))
# Build PR tree
root = GraftNode(:pr18, Int8(0), :golden, 0)
alice = GraftNode(:alice, Int8(-1), :baseline, 1)
bob = GraftNode(:bob, Int8(1), :original, 1)
# Graft nodes
graft!(c, root, :none, String[])
graft!(c, alice, :pr18, ["aptos-wallet-mcp"])
graft!(c, bob, :pr18, ["aptos-wallet-mcp"])
# Operations
tree_shape(c) # Queryable
trit_partition(c) # Colorable
derange!(c) # Derangeable
compose(c1, c2, :vertex) # Graftable
# Verify
verify_gf3(c) # → (conserved=true, sum=0)
```
## Neighbors
### High Affinity
- `three-match` (-1): Graph coloring verification
- `derangeable` (+1): No fixed points
- `bisimulation-game` (-1): Attacker/Defender
### Example Triad
```yaml
skills: [graph-grafting, three-match, derangeable]
sum: (0) + (-1) + (+1) = 0 ✓ CONSERVED
```
## References
- Joyal, Combinatorial Species (1981)
- Flajolet & Sedgewick, Analytic Combinatorics (2009)
- Topos Institute, Observational Bridge Types
## Scientific Skill Interleaving
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
### Graph Theory
- **networkx** [○] via bicomodule
- Graph manipulation and algorithms
### Bibliography References
- `graph-theory`: 38 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.