universal-captp-derivation

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](../../lib/culture_alter.rb) - Stigmergic evolution
• [lib/color_capability.rb](../../lib/color_capability.rb) - CapTP goblin swarm
• [lib/interactome_open_games.rb](../../lib/interactome_open_games.rb) - Expert triads
• [scripts/culture_games.rb](../../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

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 6. Layering

Concepts: layered data, metadata, provenance, units

GF(3) Balanced Triad

universal-captp-derivation (+) + SDF.Ch6 (+) + [balancer] (+) = 0

Skill Trit: 1 (PLUS - generation)

Secondary Chapters

• Ch10: Adventure Game Example
• Ch1: Flexibility through Abstraction

Connection Pattern

Layering adds metadata. This skill tracks provenance or annotations.

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.