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

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

Key Files

• [lib/culturealter.rb](../../lib/culturealter.rb) - Stigmergic evolution
• [lib/colorcapability.rb](../../lib/colorcapability.rb) - CapTP goblin swarm
• [lib/interactomeopengames.rb](../../lib/interactomeopengames.rb) - Expert triads
• [scripts/culturegames.rb](../../scripts/culturegames.rb) - Culture × Open Games

Trit Assignments

ACP atlas

Part of: acp-commons.