# Effective Parallelism

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

- Skill: `plurigrid/effective-parallelism` (Agent Skill, multi-file: 3 files)
- Install (CLI): `npx skillmds@latest add plurigrid/effective-parallelism`
- Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/effective-parallelism/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: plurigrid (https://skillmd.com/u/plurigrid)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/plurigrid/effective-parallelism

---

# 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

```python
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

```python
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

```python
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:

```sql
-- 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)

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

## Verification Command

```bash
# 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.*


## Para(Optic) atlas

Part of: `para-mensch-commons`.