✨ A mathematical primitive for the next generation of AI and Cryptography.
This framework provides highly optimized Python implementations of the E8 Lattice (8D) and the Leech Lattice (24D), designed for high-density data quantization and post-quantum cryptographic research.
In the race toward AGI and ultra-secure communication, the "structure" of data is as important as the data itself. Standard AI embeddings are continuous and unstructured. This framework transforms that "noise" into a highly symmetrical, discrete lattice structure.
- AI: Map 24D transformer embeddings to Leech Lattice centroids for 70%+ storage efficiency.
- Crypto: Use E8-structured noise for Learning With Errors (LWE) primitives.
- Storage: Turn vectors into "addresses" for O(1) semantic retrieval.
- Lattice Engine: Pure Python/NumPy implementation of E8 and Leech lattices.
- Fast Decoders: Snaps any arbitrary vector to the nearest lattice point using the Conway-Sloane algorithm.
- Golay Core: Full implementation of the [24, 12, 8] Extended Binary Golay Code.
- LEM (Lattice Embedding Mapping): Prototype for quantizing AI embeddings.
- Crypto Suite: Structured error generation for lattice-based key exchange.
| Metric | Raw (FP32) | Leech Lattice | Improvement |
|---|---|---|---|
| Storage (1000 Vectors) | 96 KB | 26 KB | ~3.7x Compression |
| Retrieval Speed | Linear/KD-Tree | Lattice Hash | O(1) Potential |
| Semantic Preservation | Partial | High Density | Minimal Distortion |
from core.lattices import LeechLattice
import numpy as np
# Initialize the 24D Leech Lattice
leech = LeechLattice()
# Snap a random 'thought vector' to the nearest lattice point
thought_vector = np.random.randn(24)
lattice_address = leech.quantify(thought_vector)
print(f"Original: {thought_vector[:3]}...")
print(f"Lattice Address: {lattice_address[:3]}...")- Phase 1: Math & Research (E8 Basis, Golay Code)
- Phase 2: Core Engine (Leech Generator, Conway-Sloane Decoder)
- Phase 3: Domain Applications (AI LEM, E8-LWE Crypto)
- Phase 4: Optimization & Documentation
- Phase 5: Production Deployment (NumPy -> Numba/C++ Port)
Built by Idan Koda Weezy ✨ for the Lanry Weezy Empire.