# Barycentric Simplicial Hashing (BSH) 🔺

**A Four-State Topological Hash Competitive with Industry-Standard Product Quantization at Half the Memory.**

**Author:** Andres Sebastian Pirolo  
**ORCID:** [0009-0004-3899-1222](https://orcid.org/0009-0004-3899-1222)  
**Email:** lctrnc1@gmail.com  
**DOI:** [insert after Zenodo upload]  

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## 🚀 The Breakthrough

Barycentric Simplicial Hashing (BSH) is a hardware and software-agnostic mathematical framework that uses the local triangulation of a vector space as a discrete coordinate system for Approximate Nearest Neighbor (ANN) search.

By extending the natural three-vertex zone assignment with a **fourth state (the triangle barycentre)**, BSH creates a topological buffer zone. This turns the curse of dimensionality into a feature, assigning >51% of vectors to the barycentre region in 24D spaces.

### 📊 Core Benchmark (Out-of-Sample)

| Method | Recall@1 (OOS) | Memory Footprint | Lift over Random |
|--------|----------------|------------------|------------------|
| 3-state Hash | 64.5% | 34 bytes | 14.3x |
| **BSH 4-state (This Work)** | **84–90%** | **34–57 bytes** | **18.7x** |
| FAISS IVF-PQ | 85–90% | 64 bytes | — |

*Tested on completely independent distributions (never seen during index construction) using ARM Cortex-X3.*

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## 🔒 Intellectual Property & Commercial Licensing

This repository contains the **official research paper** outlining the mathematical algorithms and pseudocode for BSH.

The theoretical framework is published as **Prior Art** to prevent third-party patenting of simplicial complex indexing, four-state barycentric quantization, and related RAG/LLM applications.

### Proprietary Implementation Available
The highly optimized, production-ready **C++ / ARM NEON SIMD implementation** is retained as a Trade Secret. It is exceptionally fast, avoiding full matrix instantiations via implicit L1 Laplacian power iterations and barycentric popcount hashing.

**Strategic Commercial Licensing & First-Mover Advantage:**
Entities seeking to integrate BSH into production LLM inference, vector databases, or on-device AI accelerators should secure licensing rights. 

For commercial licensing of the intellectual property or the proprietary C++ engine, contact: **lctrnc1@gmail.com**

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## 📄 License
* **Paper:** CC BY-NC-ND 4.0
* **Commercial Application of the Math/Algorithms:** Requires explicit written authorization. See `LICENSE.md` for full Layer-3 Commercial Notice.
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