plurigrid Universal CapTP Derivation Skill
Traces capability derivation chains through 3×3 expert poset with GF(3) conservation.
Core Principle
A capability IS the (seed, index) tuple. Expertise IS the trit alignment.
3×3 Expert Poset Structure
| Layer | Validator (-1) | Coordinator (0) | Generator (+1) | Domain |
|---|---|---|---|---|
| 1 | Jules Hedges | John Baez | Fabrizio Genovese | categorical-games |
| 2 | David Egolf | Mike Shulman | sarahzrf | sheaf-theory |
| 3 | Betweenness | Mantissa | ModalNoah | neural-categorical |
Derivation Chains
capability(-1) → vat(0) → invoke(+1) [spawn-lifecycle]
membrane(-1) → netlayer(0) → lambda(+1) [invoke-path]
handoff(-1) → syrup(0) → sturdy_ref(+1) [transfer-path]
revoke(-1) → promise(0) → goblin(+1) [revoke-path]
Superposition States
Each capability exists in superposition across expert domains:
- generator-dominant: Red channel highest (trit=+1)
- coordinator-dominant: Green channel highest (trit=0)
- validator-dominant: Blue channel highest (trit=-1)
- superposed: Balanced RGB
GF(3) Conservation
Term Σ + Expert Σ ≡ 0 (mod 3)
Current state: COHERENT (residue = 0)
Commands
# Trace derivation chains
python3 -c "import duckdb; c=duckdb.connect('culture_evolution.duckdb'); print(c.execute('SELECT * FROM derivation_chains').df())"
# View expert triads
python3 -c "import duckdb; c=duckdb.connect('culture_evolution.duckdb'); print(c.execute('SELECT * FROM expert_triads').df())"
# Query NOW superposition
python3 -c "import duckdb; c=duckdb.connect('culture_evolution.duckdb'); print(c.execute('SELECT * FROM now_superposition').df())"
# Universal skill derivation
python3 -c "import duckdb; c=duckdb.connect('culture_evolution.duckdb'); print(c.execute('SELECT * FROM universal_skill_derivation LIMIT 20').df())"
Integration Points
| Database | Table/View | Purpose |
|---|---|---|
| culture_evolution.duckdb | derivation_chains | CapTP flow traces |
| culture_evolution.duckdb | expert_triads | 3×3 expert poset |
| culture_evolution.duckdb | capability_poset | Lattice structure |
| culture_evolution.duckdb | now_superposition | Current state |
| culture_evolution.duckdb | universal_skill_derivation | Full matrix |
| gh_interactome.duckdb | captp_third_party_contributions | Contributor mapping |
Key Files
- lib/culture_alter.rb - Stigmergic evolution
- lib/color_capability.rb - CapTP goblin swarm
- lib/interactome_open_games.rb - Expert triads
- scripts/culture_games.rb - Culture × Open Games
Trit Assignments
| Trit | Role | Color Channel | Experts |
|---|---|---|---|
| -1 | Validator | Blue | Hedges, Egolf, Betweenness |
| 0 | Coordinator | Green | Baez, Shulman, Mantissa |
| +1 | Generator | Red | Genovese, sarahzrf, ModalNoah |
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.