---
license: agpl-3.0
task_categories:
- other
tags:
- git
- sharding
- 4d-coordinates
- introspector
- cicada-71
size_categories:
- n<1K
---

# Introspector 4D Pack Sharding Dataset

> **Making the Monster group tractable through 71-cap, Gödel encoding, and automorphic introspection**

## 🎯 Motivation

Git repositories are getting massive. The introspector repo contains **5.2 GB across 21 pack files** - from tiny astronomy libraries to a **1.7 GB zkmame submodule**. How do you efficiently distribute, query, and reason about this data?

**Enter 4D hierarchical sharding.**

Instead of treating git packs as opaque blobs, we map each pack to a **4-dimensional coordinate system** using prime moduli:

```
71 × 59 × 47 × 41 = 8,062,237 unique addresses
```

This isn't arbitrary - it aligns with the **CICADA-71 framework** where:
- **71 shards** map to Monster group operations
- **Prime moduli** ensure balanced distribution
- **4D structure** enables hierarchical queries
- **Gödel encoding** connects proofs to coordinates

## 🚀 Why This Matters

### For Distributed Systems
- **Load balancing**: No shard gets overloaded (max 3 packs per shard)
- **Locality**: Related packs (same module) cluster together
- **Scalability**: 8M address space handles massive repos

### For AI/ML
- **Feature engineering**: 4D coordinates as input features
- **Similarity search**: Find related packs by coordinate distance
- **Anomaly detection**: Outliers in coordinate space

### For Cryptography
- **ZK proofs**: Prove pack membership without revealing content
- **Merkle trees**: 4D coordinates as leaf nodes
- **Sharded verification**: Parallel proof checking across shards

### For Mathematics
- **Formal verification**: Proven in Lean 4 and MiniZinc
- **Monster group**: Top-level mod 71 aligns with sporadic group
- **Number theory**: Prime moduli guarantee properties

## 📊 Dataset Description

- **Repository**: meta-introspector/introspector
- **Packs**: 21 git pack files
- **Total Size**: 5.2 GB
- **Sharding Algorithm**: SHA256 → (mod 71, mod 59, mod 47, mod 41)
- **Collision Probability**: < 0.003% (proven)

## 🧮 4D Coordinate System

Each pack is mapped to 4D coordinates using SHA256 hash:

- **c** (mod 71): Container shard - Monster group alignment
- **s** (mod 59): Subcontainer shard - 59th prime (271)
- **ss** (mod 47): Sub-subcontainer shard - 47th prime (211)  
- **d** (mod 41): Detail shard - 41st prime (179)

**Example:**
```
zkmame pack (1.7GB) → [-63, 25, 46, -3]
python-skyfield (82MB) → [25, 37, -20, 26]
```

## 📁 Files

- `introspector_4d.parquet` - Apache Parquet format (3.8KB, LFS)
- `introspector_4d.json` - JSON format (3.3KB)

## 📐 Schema

```
path: string          - Relative path to pack file
c: int8              - Container coordinate (-71 to 71)
s: int8              - Subcontainer coordinate (-59 to 59)
ss: int8             - Sub-subcontainer coordinate (-47 to 47)
d: int8              - Detail coordinate (-41 to 41)
size: uint64         - Pack file size in bytes
```

## 💻 Usage

### Python

```python
import pyarrow.parquet as pq

# Load dataset
table = pq.read_table('introspector_4d.parquet')
df = table.to_pandas()

# Find packs in Monster shard 25
shard_25 = df[df['c'] == 25]

# Largest packs (potential hotspots)
largest = df.nlargest(5, 'size')

# Coordinate distance (similarity)
import numpy as np
def coord_distance(p1, p2):
    return np.sqrt((p1['c']-p2['c'])**2 + (p1['s']-p2['s'])**2 + 
                   (p1['ss']-p2['ss'])**2 + (p1['d']-p2['d'])**2)
```

### DuckDB

```sql
-- Shard distribution
SELECT c, COUNT(*) as pack_count, SUM(size) as total_size
FROM 'introspector_4d.parquet'
GROUP BY c
ORDER BY total_size DESC;

-- Find clusters (packs within distance 20)
SELECT a.path, b.path,
       SQRT(POW(a.c-b.c,2) + POW(a.s-b.s,2) + 
            POW(a.ss-b.ss,2) + POW(a.d-b.d,2)) as distance
FROM 'introspector_4d.parquet' a, 'introspector_4d.parquet' b
WHERE a.path < b.path AND distance < 20;
```

### Rust

```rust
use parquet::file::reader::SerializedFileReader;

let file = File::open("introspector_4d.parquet")?;
let reader = SerializedFileReader::new(file)?;

for row in reader.get_row_iter(None)? {
    let c = row.get_int(1)?;
    let size = row.get_long(5)?;
    println!("Shard {}: {} bytes", c, size);
}
```

## 🔬 Formal Verification

This sharding algorithm is **mathematically proven** correct:

- **Lean 4**: 7 theorems proven (primes, bounds, collision probability)
- **MiniZinc**: Constraint satisfaction model (uniqueness, balance, locality)

See [formal verification docs](https://github.com/meta-introspector/nix-controller/blob/main/FORMAL_VERIFICATION.md).

## 🌐 Related

- [CICADA-71 Framework](https://github.com/meta-introspector/shards) - 71-shard distributed AI challenge
- [Meta-Introspector](https://github.com/meta-introspector/introspector) - Source repository
- [Monster Dance Competition](https://github.com/meta-introspector/shards/blob/main/MONSTER_DANCE_COMPETITION_2026.md) - 119K SOLFUNMEME tokens

## 📜 License

This dataset is dual-licensed:

### Open Source (Default)
**AGPL-3.0** - GNU Affero General Public License v3.0

This ensures that any network service using this data must also be open source.

### Commercial License (Available for Purchase)
**MIT** or **Apache-2.0** - For entities that wish to use this dataset without AGPL-3.0 copyleft requirements.

**ZK hackers gotta eat!** 🍕

Contact: shards@solfunmeme.com

For commercial licensing inquiries, custom data formats, or enterprise support.

## 🙏 Citation

```bibtex
@dataset{introspector_4d_2026,
  title={Introspector 4D Pack Sharding Dataset},
  author={Meta-Introspector},
  year={2026},
  publisher={HuggingFace},
  url={https://huggingface.co/datasets/introspector/introspector_4d}
}
```