| # Barycentric Simplicial Hashing (BSH) 🔺 |
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| **A Four-State Topological Hash Competitive with Industry-Standard Product Quantization at Half the Memory.** |
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| **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 |
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| 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. |
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| 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. |
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| ### 📊 Core Benchmark (Out-of-Sample) |
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| | 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 | — | |
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| *Tested on completely independent distributions (never seen during index construction) using ARM Cortex-X3.* |
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| ## 🔒 Intellectual Property & Commercial Licensing |
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| This repository contains the **official research paper** outlining the mathematical algorithms and pseudocode for BSH. |
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| 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. |
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| ### 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. |
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| **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. |
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| 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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