DuckLake Random Walk

Ergodic random walk exploration of DuckDB/DuckLake schemas with concurrent Society-of-Mind walkers. Implements PageRank-style teleportation for irreducibility and GF(3)-balanced walker coordination.

Triadic Structure

Stream	Trit	Role	Implementation
MINUS (-1)	Validator	Constraint verification, DuckLake semantics	duckdb-validator.sql
ERGODIC (0)	Coordinator	Random walk orchestration	ducklake-walk.clj
PLUS (+1)	Generator	Concurrent walker execution	mensi_walker.py

Conservation: Σ trits = -1 + 0 + 1 = 0 (mod 3) ✓

Lojban Gismu Mapping

Gismu	Meaning	Component
pensi	think	PensiWalker - individual cognition
jimpe	understand	Jimpe - shared understanding
djuno	know	Djuno - knowledge units
mensi	sibling	Walker siblings in society
gunma	group	GunmaSociety - collective

Algorithm: Ergodic Random Walk

The walk follows a Markov chain with teleportation (PageRank-style):

P(teleport) = 0.15  # Random restart for ergodicity
P(follow_edge) = 0.85 × (has_neighbors ? 1 : 0)
P(forced_teleport) = 1 - P(teleport) - P(follow_edge)

Guarantees:

• Irreducibility: All tables reachable via teleportation
• Aperiodicity: Random restarts break cycles
• Ergodicity: Unique stationary distribution exists

Usage

Babashka Ergodic Walker (ERGODIC stream)

# Demo mode with in-memory schema
bb ducklake-walk.clj

# With existing DuckDB file
bb ducklake-walk.clj /path/to/lakehouse.duckdb

Python Society-of-Mind (PLUS stream)

# Run concurrent walkers
python mensi_walker.py

# Interactive REPL
python jimpe_repl.py

DuckLake Validation (MINUS stream)

LOAD ducklake;
ATTACH 'ducklake:metadata.duckdb' AS lake (DATA_PATH './data');

-- Create walk history table
CREATE TABLE lake.main.walk_history (
    step_id INTEGER,
    from_state VARCHAR,
    to_state VARCHAR,
    trit INTEGER,
    walk_time TIMESTAMPTZ
);

-- Verify GF(3) conservation
SELECT SUM(trit) % 3 AS conservation FROM lake.main.walk_history;
-- Should return 0

Output Metrics

Metric	Target	Description
Coverage	>80%	Unique tables visited / total tables
Entropy	~ln(N)	Shannon entropy of visit distribution
Edge ratio	~38%	FK-following vs teleportation
GF(3) sum	0 mod 3	Conservation across all trits

Integration Points

• duckdb-timetravel: Snapshot versioning for walk history
• random-walk-fusion: Seed chaining for deterministic walks
• gay-mcp: Color assignment for walker visualization
• acsets: Algebraic database schema navigation

Files

skills/ducklake-walk/
├── SKILL.md                 # This file
├── ducklake-walk.clj        # Babashka ergodic walker
├── mensi_walker.py          # Python concurrent walkers
├── jimpe_repl.py            # Interactive REPL
└── demo_interleaving.py     # Thread visualization

Example Output

=== DuckLake Random Walk ===
GF(3) Color: ERGODIC (0) - Neutral Coordinator
Tables found: 8
Random restart probability: 0.15
Starting at: ducklake.products

Step   0: ducklake.products        (rows: 4) -> ducklake.categories [edge]
Step   1: ducklake.categories      (rows: 4) -> ducklake.products [edge]
Step   2: ducklake.products        (rows: 4) -> ducklake.users [teleport]
...

=== Ergodicity Analysis ===
Coverage: 100.0%
Edge transitions: 38.0%
Teleportations: 62.0%
Entropy: 1.994 / 2.079 (max)
Ergodic: YES

GF(3) Walker Roles

class GF3Trit(IntEnum):
    MINUS = -1     # Validator (cold hue 270°)
    ERGODIC = 0    # Coordinator (neutral hue 180°)
    PLUS = 1       # Generator (warm hue 30°)

# Role-specific behavior weights
PLUS:    explore=0.7, validate=0.1, synthesize=0.2
MINUS:   explore=0.2, validate=0.6, synthesize=0.2
ERGODIC: explore=0.3, validate=0.2, synthesize=0.5

Related Skills

• duckdb-timetravel (trit: 0) - Temporal versioning
• duckdb-ies (trit: +1) - Interactome analytics
• random-walk-fusion (trit: +1) - Skill graph navigation
• acsets (trit: 0) - Algebraic databases

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

• graph-theory: 38 citations in bib.duckdb

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.

Forward Reference

• unified-reafference (canonical cross-agent DuckDB schema)