# Ducklake Pattern Expansion

> Pattern expansion and schema evolution for DuckLake databases

- Skill: `plurigrid/ducklake-pattern-expansion` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add plurigrid/ducklake-pattern-expansion`
- Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/ducklake-pattern-expansion/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: plurigrid (https://skillmd.com/u/plurigrid)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/plurigrid/ducklake-pattern-expansion

---


# Ducklake Pattern Expansion

**Version:** 1.0.0
**Status:** Production Ready
**Created:** 2025-12-21
**High Confidence Core:** 153 mentions

## Overview

Loads pattern discovery from Subagent 3 and provides progressive wave-based expansion for discovering related patterns, computing world reachability, and exploring possibility space.

## Purpose

Enable progressive pattern discovery through 3 expansion waves:
- **Wave 1:** Direct matches (high confidence ≥0.95)
- **Wave 2:** Relational discovery (medium confidence ≥0.75)
- **Wave 3:** Structural analysis (exploration confidence ≥0.50)

## Data Sources

- **Primary:** `/Users/bob/ies/SUBAGENT_3_PATTERN_DISCOVERY.json` (if exists)
- **Fallback:** Meta-cognitive synthesis JSON
- **Schema:** VERS_DUCKLAKE_SCHEMA.sql (48 agents, 16 repos)

## Functions

### expand_wave1(patterns: list[str]) -> dict

Direct pattern matching with high confidence.

```python
results = expand_wave1(["ducklake", "temporal", "versioning"])
# Returns: {
#   "temporal_duckdb": {"confidence": 0.95, "mentions": 47},
#   "versioning_crdt": {"confidence": 0.92, "mentions": 31},
#   "ducklake_core": {"confidence": 0.97, "mentions": 153}
# }
```

**Wave 1 Characteristics:**
- Confidence threshold: ≥0.95
- Direct keyword matches
- File path analysis
- Established patterns only

**Implementation:**
```python
import json
import re
from pathlib import Path

def expand_wave1(patterns: list[str]) -> dict:
    results = {}
    base_path = Path("/Users/bob/ies")

    for pattern in patterns:
        matches = []
        confidence_sum = 0

        # Search all relevant files
        for file_path in base_path.rglob("*"):
            if file_path.is_file():
                try:
                    content = file_path.read_text()
                    count = len(re.findall(pattern, content, re.IGNORECASE))
                    if count > 0:
                        matches.append({
                            "file": str(file_path),
                            "count": count
                        })
                        confidence_sum += min(count / 10.0, 1.0)
                except:
                    continue

        if matches:
            avg_confidence = min(confidence_sum / len(matches), 1.0)
            if avg_confidence >= 0.95:
                total_mentions = sum(m["count"] for m in matches)
                results[f"{pattern}_core"] = {
                    "confidence": round(avg_confidence, 2),
                    "mentions": total_mentions,
                    "files": len(matches)
                }

    return results
```

### expand_wave2(patterns: list[str]) -> dict

Relational discovery through co-occurrence analysis.

```python
results = expand_wave2(["ducklake"])
# Returns: {
#   "color_integration": {"confidence": 0.85, "related": ["gay", "seed", "retromap"]},
#   "temporal_versioning": {"confidence": 0.82, "related": ["time-travel", "snapshot"]},
#   "acset_topology": {"confidence": 0.78, "related": ["morphism", "schema", "categorical"]}
# }
```

**Wave 2 Characteristics:**
- Confidence threshold: ≥0.75
- Co-occurrence analysis
- Semantic proximity
- Sub-community detection

### expand_wave3(patterns: list[str]) -> dict

Structural analysis and horizon exploration.

```python
results = expand_wave3(["ducklake"])
# Returns: {
#   "48_agent_topology": {
#     "structure": "hub_and_spoke",
#     "agents": 48,
#     "repos": 16,
#     "confidence": 0.67
#   },
#   "horizon_worlds": [
#     {"name": "CRDT_synchronization", "distance": 3.5, "probability": "high"},
#     {"name": "LiveKit_streaming", "distance": 2.8, "probability": "medium"}
#   ]
# }
```

**Wave 3 Characteristics:**
- Confidence threshold: ≥0.50
- Graph topology analysis
- Possibility space exploration
- Distance-based reachability

### compute_world_reachability(source: str, target: str) -> dict

Compute distance and path between worlds.

```python
result = compute_world_reachability(
    "world_hopping_duckdb_analysis",
    "ies_augmentation_cognitive_superposition"
)
# Returns: {
#   "direct_feasible": false,
#   "via_intermediate": {
#     "feasible": true,
#     "path": ["world_hopping", "acset_neighbor", "ies_augmentation"],
#     "distance": 6.01,
#     "events": ["Schema Expansion", "Cognitive Augmentation Event"]
#   },
#   "triangle_inequality_satisfied": true
# }
```

**Reachability Algorithm:**
1. Check direct distance vs accessibility radius
2. Apply triangle inequality constraint
3. Find shortest path via intermediate worlds
4. Return event sequence for traversal

## Usage Example

```python
from skills.ducklake_pattern_expansion import *

# Progressive discovery
seed_patterns = ["ducklake"]

print("=== WAVE 1: Direct Matches ===")
wave1 = expand_wave1(seed_patterns)
for pattern, data in wave1.items():
    print(f"{pattern}: {data['mentions']} mentions ({data['confidence']:.0%} confidence)")

print("\n=== WAVE 2: Relational Discovery ===")
wave2 = expand_wave2(seed_patterns)
for pattern, data in wave2.items():
    print(f"{pattern}: related to {', '.join(data['related'])}")

print("\n=== WAVE 3: Structural Analysis ===")
wave3 = expand_wave3(seed_patterns)
if "48_agent_topology" in wave3:
    topo = wave3["48_agent_topology"]
    print(f"Found {topo['structure']} with {topo['agents']} agents")

# World reachability
print("\n=== World Reachability ===")
path = compute_world_reachability(
    "world_hopping_duckdb_analysis",
    "ies_augmentation_cognitive_superposition"
)
if path["via_intermediate"]["feasible"]:
    print(f"Path: {' → '.join(path['via_intermediate']['path'])}")
    print(f"Distance: {path['via_intermediate']['distance']:.2f}")
    for event in path["via_intermediate"]["events"]:
        print(f"  Event: {event}")
```

## Skills Dependencies

- skill-installer (for loading pattern definitions)
- acsets (for structural topology)
- world-hopping (for reachability computation)

## Integration Points

- **Temporal Introspection:** Map patterns to temporal clusters
- **Semantic Analyzer:** Enhance with semantic confidence scores
- **Categorical Model:** Convert patterns to ACSet morphisms

## Key Discovery Statistics

- High confidence core: 153 mentions
- Temporal DuckDB: 47 mentions (0.95 confidence)
- Sub-communities: 3 (versioning, color, orchestration)
- Database inventory: 15 DuckDB instances
- Agent topology: 48 agents × 16 repos

## Expansion Frontiers

### Immediate (Distance < 2.0)
- Temporal versioning enhancement
- Color stream branching
- Session evolution tracking

### Medium-Term (Distance 2.0-3.5)
- DuckLake federation (NATS/Synadia)
- Skill-based query language (SDQL)
- LiveKit streaming integration

### Long-Term (Distance > 3.5)
- Universal memory (all interactions)
- Categorical DuckLake (CatColab integration)
- Quantum-resistant fingerprints

## Triangle Inequality Constraints

For worlds W1, W2, W3:
```
d(W1, W3) ≤ d(W1, W2) + d(W2, W3)
```

Example:
- d(temporal, cognitive) = 5.49
- d(temporal, structural) + d(structural, cognitive) = 2.87 + 3.14 = 6.01
- Constraint satisfied: 5.49 ≤ 6.01 ✓

## GF(3) Distribution

This skill operates across all three categories with balanced emphasis:
- Wave 1: YELLOW (GF3=1) - Structural pattern matching
- Wave 2: RED (GF3=0) - Temporal relationship discovery
- Wave 3: BLUE (GF3=2) - Cognitive possibility exploration

---

**Skill Type:** Pattern Discovery
**Color:** MULTI (triadic)
**Polarity:** GF(3) = 0 (balanced)
**Access Pattern:** Progressive expansion