Effective Parallelism Skill

GF(3)-balanced parallel agent orchestration with operad composition and prediction market allocation.

Core Pattern: Triadic Agent Dispatch

┌─────────────────────────────────────────────────────────┐
│  MINUS (⊖)        ERGODIC (⊙)        PLUS (⊕)         │
│  trit = -1        trit = 0           trit = +1         │
│  ────────────────────────────────────────────────────  │
│  Backfill         Verify             Live              │
│  Cool hue         Neutral            Warm hue          │
│  ACP protocol     DuckDB             MCP protocol      │
│  gravity operad   thread operad      little_disks      │
└─────────────────────────────────────────────────────────┘
         Sum mod 3 = 0  →  GF(3) CONSERVED ✓

7-Operad Batch Template

For 7 parallel agents, use these operads (sum = 0 mod 3):

Operad	Trit	Role
little_disks	+1	Forward exploration
cubes	-1	Grid traversal
cactus	-1	Tree decomposition
thread	0	Sequential anchor
gravity	-1	Attraction dynamics
modular	+1	Composable units
swiss_cheese	+1	Boundary handling

Sum: +1 -1 -1 +0 -1 +1 +1 = 0 ✓

Usage Patterns

Pattern 1: Random Walk with Replacement Check

from concurrent.futures import ThreadPoolExecutor, as_completed

def parallel_skill_walk(skills: list, n_agents: int = 3):
    """Dispatch n_agents over skills with GF(3) balance."""
    trits = [-1, 0, +1][:n_agents]  # Ensure balance
    
    with ThreadPoolExecutor(max_workers=n_agents) as executor:
        futures = {
            executor.submit(agent_task, skills, trit): trit
            for trit in trits
        }
        for future in as_completed(futures):
            yield future.result()

Pattern 2: Prediction Market Allocation

def allocate_by_probability(contracts: list, budget: float):
    """Allocate budget proportional to contract probabilities."""
    total_p = sum(c.current_price for c in contracts)
    return {
        c.id: budget * (c.current_price / total_p)
        for c in contracts
    }

Pattern 3: 23³ Orthogonal Grid Walk

DIM = 23  # Prime for collision avoidance

def hash_to_cell(name: str) -> tuple:
    """Map skill name to 23³ grid cell."""
    x = hash(name + "x") % DIM
    y = hash(name + "y") % DIM
    z = hash(name + "z") % DIM
    return (x, y, z)

DuckDB Integration

Query Nov2025 tables for synergy-informed dispatch:

-- Top ego nodes for agent assignment
SELECT ego, COUNT(*) as n_alters, AVG(synergy_score) as avg_synergy
FROM gaymc_diffusion
GROUP BY ego ORDER BY n_alters DESC LIMIT 15;

-- Temporal evolution for scheduling
SELECT month_bin, n_threads, mean_hue FROM gay_equiv_temporal
ORDER BY month_bin DESC;

-- Verification status
SELECT verification_status, hue_entropy_normalized
FROM gay_solomonoff_verification LIMIT 1;

Skill Dispatch Rules

1. Always check GF(3) sum before spawning agents
2. Use ThreadPoolExecutor with max_workers = 3, 7, or 12 (balanced batches)
3. Assign protocols by trit: MCP (+1), DuckDB (0), ACP (-1)
4. Color-code agents from Gay.jl seed 42069 palette
5. Track boredom: If agent revisits 3+ times, expand skill pool

Gay.jl Palette (seed 42069)

COLORS = ["#28C3BF", "#DDB562", "#AC2A5A", "#A55936", "#5A8C3E", "#7B68EE", "#FF6B6B"]

Verification Command

# Check GF(3) balance of any trit list
python3 -c "print(sum([-1, 0, +1, +1, -1, +1, -1]) % 3)"  # Should be 0

---

End-of-Skill Interface

Related Skills

• tripartite-decompositions

  - GF(3) structured decompositions

• parallel-fanout

  - Maximum synergistic parallelism

• triad-interleave

  - Interleave three color streams

• spi-parallel-verify

  - Strong Parallelism Invariance verification

• entropy-sequencer

  - Interaction interleaving for max info gain

---

Autopoietic Marginalia

The interaction IS the skill improving itself.

Every use of this skill is an opportunity for worlding:

• MEMORY (-1): Record what was learned
• REMEMBERING (0): Connect patterns to other skills
• WORLDING (+1): Evolve the skill based on use

Add Interaction Exemplars here as the skill is used.