Implements graph grafting by attaching rooted trees to graph vertices, supporting queryable tree decompositions, GF(3) 3-coloring, derangements, and triad compositions in Julia.
From asi-skillsnpx claudepluginhub plurigrid/asiThis skill uses the workspace's default tool permissions.
Guides Next.js Cache Components and Partial Prerendering (PPR) with cacheComponents enabled. Implements 'use cache', cacheLife(), cacheTag(), revalidateTag(), static/dynamic optimization, and cache debugging.
Migrates code, prompts, and API calls from Claude Sonnet 4.0/4.5 or Opus 4.1 to Opus 4.5, updating model strings on Anthropic, AWS, GCP, Azure platforms.
Analyzes BMad project state from catalog CSV, configs, artifacts, and query to recommend next skills or answer questions. Useful for help requests, 'what next', or starting BMad.
Trit: 0 (ERGODIC - Coordinator)
GF(3) Triad: queryable (-1) ⊗ graftable (0) ⊗ derangeable (+1) = 0
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 |
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
Balanced (GF3=0)
│
Q2 │ Q1 ← OPTIMAL
Identity │ PR#18, Knight Tour
│ SICM Galois
──────────────┼──────────────
Q3 │ Q4
Deadlock │ Phase Trans
│
Fixed Points → Derangement
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)
three-match (-1): Graph coloring verificationderangeable (+1): No fixed pointsbisimulation-game (-1): Attacker/Defenderskills: [graph-grafting, three-match, derangeable]
sum: (0) + (-1) + (+1) = 0 ✓ CONSERVED
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
graph-theory: 38 citations in bib.duckdbThis 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
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.