From asi
Compares databases like DuckDB and LanceDB using ACSet morphisms across dimensions like storage hierarchy, density/sparsity, versioning, and traversal patterns. For algebraic data structure analysis.
npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
**Trit**: 0 (ERGODIC - Coordinator)
ColoringFunctor.jlColoringFunctor.orgComparisonUtils.jlComparisonUtils.orgDuckDBACSet.jlDuckDBACSet.orgGeometricMorphism.jlGeometricMorphism.orgGhristCoverage.jlGhristCoverage.orgIrreversibleMorphisms.jlIrreversibleMorphisms.orgLanceDBACSet.jlLanceDBACSet.orgSideBySideComparison.jlSideBySideComparison.orggeodesics/ColoringFunctor.geodesic.jlgeodesics/ComparisonUtils.geodesic.jlgeodesics/DuckDBACSet.geodesic.jlgeodesics/GeometricMorphism.geodesic.jlGuides architecture decisions for PostgreSQL, DuckDB, Parquet, PGVector, Neo4j across OLTP, OLAP, vector search, graph workloads including schema design, query optimization, and performance tuning.
Provides DuckDB temporal versioning for interaction history with time-travel queries, frozen snapshots, causality tracking via vector clocks, and immutable audit logs.
Provides expert guidance for LadybugDB, an embedded property graph database using openCypher, covering schema design, Cypher queries, lbug CLI, Python/Node.js/Java/Rust/Go/Swift integrations, graph algorithms, HNSW vector search, and data import/export.
Share bugs, ideas, or general feedback.
Trit: 0 (ERGODIC - Coordinator) Color: #26D826 (Green) Domain: Compositional algorithm/data analysis via algebraic databases
In self-hosted Lisps, the boundary between data structures and algorithms dissolves:
Compare data structures and their properties (density/sparsity, dynamic/static, versioning strategies) using the richness afforded by ACSets. Uses Gay.jl-aided superrandom walks for deterministic exploration of comparison dimensions.
schema-validation (-1) ⊗ compositional-acset-comparison (0) ⊗ gay-mcp (+1) = 0 ✓ [Property Analysis]
three-match (-1) ⊗ compositional-acset-comparison (0) ⊗ koopman-generator (+1) = 0 ✓ [Dynamic Traversal]
temporal-coalgebra (-1) ⊗ compositional-acset-comparison (0) ⊗ oapply-colimit (+1) = 0 ✓ [Versioning]
polyglot-spi (-1) ⊗ compositional-acset-comparison (0) ⊗ gay-mcp (+1) = 0 ✓ [Homoiconic Interop]
Each dimension is explored via φ-angle (137.508°) golden spiral for maximal dispersion:
| Step | Dimension | Hex Color | Hue |
|---|---|---|---|
| 1 | Storage Hierarchy | #EE2B2B | 0° |
| 2 | Density/Sparsity | #2BEE64 | 137.51° |
| 3 | Dynamic/Static | #9D2BEE | 275.02° |
| 4 | Versioning Strategy | #EED52B | 52.52° |
| 5 | Traversal Patterns | #2BCDEE | 190.03° |
| 6 | Index Structures | #EE2B94 | 327.54° |
| 7 | Compression | #5BEE2B | 105.05° |
| 8 | Query Model | #332BEE | 242.55° |
| 9 | Embedding Support | #EE6C2B | 20.06° |
| 10 | Interoperability | #2BEEA5 | 157.57° |
| 11 | Concurrency | #DE2BEE | 295.08° |
| 12 | Memory Model | #C5EE2B | 72.59° |
DuckDB LanceDB
────── ───────
Table Database
└─RowGroup (122K rows) └─Table
└─Column └─Manifest (version)
└─Segment └─Fragment
└─Block └─Column
└─VectorColumn
ACSet Morphism Depth:
| Property | DuckDB | LanceDB |
|---|---|---|
| Default | Dense columnar | Dense Arrow arrays |
| Sparse Support | Via NULL bitmask | Via Arrow validity bitmask |
| Vector Sparsity | N/A | Sparse via IVF partitioning |
| Storage Efficiency | ALP, ZSTD compression | Lance columnar format |
| ACSet Rep | DenseFinColumn | DenseFinColumn with VectorColumn extension |
Density Formula:
density(acset, obj) = nparts(acset, obj) / theoretical_max(acset, obj)
# DuckDB Segment: ~2048 rows per vector batch
# LanceDB Fragment: variable, optimized for vector search
| Property | DuckDB | LanceDB |
|---|---|---|
| Schema Evolution | ALTER TABLE | Manifest versioning |
| Row Updates | In-place (TRANSIENT→PERSISTENT) | Append + compaction |
| Index Updates | Dynamic B-Tree/ART | Rebuild IVF partitions |
| ACSet Mutation | set_subpart!, rem_part! | Append-only, version chains |
State Machine:
DuckDB Segment: TRANSIENT ⟷ PERSISTENT (bidirectional)
LanceDB Manifest: V1 → V2 → V3 → ... (append-only chain)
Critical Update (December 15, 2025): Lance SDK adopts SemVer 1.0.0
| Component | Versioning | Strategy |
|---|---|---|
| Lance SDK | SemVer 1.0.0 | MAJOR.MINOR.PATCH |
| Lance File Format | 2.1 | Binary compatibility, independent |
| Lance Table Format | Feature flags | Full backward compat, no linear versions |
| Lance Namespace Spec | Per-operation | Iceberg REST Catalog style |
Key Insight: Breaking SDK changes will NOT invalidate existing Lance data.
# ACSet representation of versioning strategies
@present SchVersioning(FreeSchema) begin
SDKVersion::Ob # SemVer (1.0.0)
FileFormat::Ob # Binary compat (2.1)
TableFormat::Ob # Feature flags
NamespaceSpec::Ob # Per-operation
# Morphisms: SDK ≠ Format
sdk_file::Hom(SDKVersion, FileFormat) # Many-to-one
file_table::Hom(FileFormat, TableFormat) # Independent
table_ns::Hom(TableFormat, NamespaceSpec) # Independent
end
DuckDB Versioning:
VERSION AT| Pattern | DuckDB | LanceDB |
|---|---|---|
| Sequential Scan | RowGroup→Column→Segment | Fragment→Column |
| Index Scan | ART/B-Tree navigation | IVF partition probe |
| Vector Search | N/A (extension) | Centroid→Partition→Rows |
| Time Travel | FOR SYSTEM_TIME AS OF | checkout(version) |
ACSet Incident Queries:
# DuckDB: Find all segments in a column
incident(duckdb_acset, col_id, :column)
# LanceDB: Find all centroids for an index
incident(lancedb_acset, idx_id, :partition_index) |>
flatmap(p -> incident(lancedb_acset, p, :centroid_partition))
| Index Type | DuckDB | LanceDB |
|---|---|---|
| Primary | None (heap) | None (Lance format) |
| Secondary | ART (Radix Tree) | Scalar indexes |
| Vector | Extension (vss) | IVF_PQ, IVF_HNSW_SQ, IVF_HNSW_PQ |
| Full-Text | Extension (fts) | N/A |
ACSet Index Representation:
# LanceDB vector index hierarchy
VectorIndex → Partition → Centroid
↓
index_column → VectorColumn → Column
| Algorithm | DuckDB | LanceDB |
|---|---|---|
| Numeric | ALP (Adaptive Lossless) | Arrow encoding |
| String | Dictionary, FSST | Dictionary |
| General | ZSTD, LZ4 | ZSTD |
| Vector | N/A | PQ (Product Quantization) |
| Aspect | DuckDB | LanceDB |
|---|---|---|
| Language | SQL | Python/Rust API + SQL filter |
| Optimization | Volcano/push-based | Vector-first + filter |
| Execution | Vectorized (2048 batch) | Arrow RecordBatch |
| Parallelism | Morsel-driven | Partition-parallel |
| Feature | DuckDB | LanceDB |
|---|---|---|
| Native | No | Yes (FixedSizeList) |
| Generation | UDF/Extension | EmbeddingFunction registry |
| Storage | ARRAY type | VectorColumn |
| Search | Extension (vss) | Native (IVF, HNSW) |
| Format | DuckDB | LanceDB |
|---|---|---|
| Arrow | Full support | Native (Lance = Arrow extension) |
| Parquet | Read/Write | Read (convert to Lance) |
| CSV/JSON | Read/Write | Via Arrow |
| ACSets | Via Tables.jl | Via Arrow → Tables.jl |
Cross-Language (from ACSets Intertypes):
# Generate interoperable types
generate_module(DuckDBACSet, [PydanticTarget, JacksonTarget])
generate_module(LanceDBACSet, [PydanticTarget, JacksonTarget])
| Aspect | DuckDB | LanceDB |
|---|---|---|
| Model | MVCC | Optimistic (manifest-based) |
| Writers | Single (or WAL) | Single (append) |
| Readers | Unlimited concurrent | Unlimited concurrent |
| Isolation | Snapshot | Version snapshot |
| Aspect | DuckDB | LanceDB |
|---|---|---|
| Buffer Pool | BufferManager | Memory-mapped Arrow |
| Eviction | LRU | OS page cache |
| Allocation | Unified allocator | Arrow allocator |
| Out-of-Core | Automatic spill | Lazy loading |
Using GF(3) conservation for balanced parallel analysis:
Stream 1 (Blue, -1): Validation/Constraints
#31945E → #B3DA86 → #8810F2 → #2F5194 → #2452AA → #245FB4
Stream 2 (Green, 0): Coordination/Transport
#6D59D2 → #9E2981 → #72E24F → #31C5B4 → #C04DDD → #1C8EEE
Stream 3 (Red, +1): Generation/Composition
#E22FA7 → #E812C8 → #6F68E6 → #25D840 → #DA387F → #A82358
Data structures map to crystal symmetry:
| Crystal Family | Symmetry | DuckDB Analog | LanceDB Analog |
|---|---|---|---|
| Cubic (#9E94DD) | Order 48 | RowGroup uniformity | Fragment uniformity |
| Hexagonal (#65F475) | Order 24 | Column types | Vector dimensions |
| Tetragonal (#E764F1) | Order 16 | Segment blocking | Partition structure |
| Orthorhombic (#2ADC56) | Order 8 | Type system | Index types |
| Monoclinic (#CD7B61) | Order 4 | Compression | Quantization |
| Triclinic (#E4338F) | Order 2 | Raw storage | Raw Arrow |
Powers PCT cascade for harmonious comparison:
Level 5 (Program): "Compare DuckDB vs LanceDB"
↓ sets reference for
Level 4 (Transition): Dimension sequence [30° steps]
↓ sets reference for
Level 3 (Configuration): Property relationships
↓ sets reference for
Level 2 (Sensation): Individual metrics
↓ sets reference for
Level 1 (Intensity): Numeric values
Colors: #B322C0 → #D5268C → #DC3946 → #DF884A → #E0D551 → #A3E04E
At τ=0.5 (ordered phase, τ < τ_c=0.893):
Interpretation: Both DuckDB and LanceDB are in "ordered phase" - mature, production-ready systems with well-defined structures.
using ACSets, Catlab
# Load both schemas
include("DuckDBACSet.jl")
include("LanceDBACSet.jl")
# Compare morphism structures
compare_schemas(SchDuckDB, SchLanceDB)
# Analyze density
density_analysis = map([SchDuckDB, SchLanceDB]) do sch
Dict(ob => sparsity_metric(sch, ob) for ob in obs(sch))
end
# Traverse with Gay.jl colors
for (i, dimension) in enumerate(DIMENSIONS)
color = gay_color_at(1000000, i)
analyze_dimension(dimension, color)
end
| File | Purpose | Gay.jl Seed |
|---|---|---|
DuckDBACSet.jl | Schema for DuckDB storage layer | 1000000 |
LanceDBACSet.jl | Schema for LanceDB vector store | 1000000 |
IrreversibleMorphisms.jl | Analysis of lossy morphisms | 2000000 |
SideBySideComparison.jl | Visual comparison tables | 3000000 |
ComparisonUtils.jl | 12-dimension comparison utilities | 1000000 |
GhristCoverage.jl | Persistent homology coverage analysis | 4000000 |
ColoringFunctor.jl | Schema coloring + GF(3) verification | 4000000 |
GeometricMorphism.jl | Presheaf topos translation analysis | 4000000 |
Based on de Silva & Ghrist "Coverage in Sensor Networks via Persistent Homology":
AM Radio Coverage Analogy:
Betti Numbers for Schemas:
Persistent Holes (never die):
parent_manifest: Temporal irreversibility (version chain)source_column: Semantic irreversibility (embedding loss)For presheaf topoi PSh(SchDuckDB) and PSh(SchLanceDB):
Essential Image (lossless translation):
Partial Coverage (lossy translation):
Dead Zones (no translation):
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
general: 734 citations in bib.duckdbThis 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
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.