$π$-RAG: Oblivious Retrieval via Semantic Quantization and Transcendental Addressing for Large Language Models

This paper introduces $π$-RAG, a novel architecture for oblivious retrieval that decouples Large Language Models (LLMs) from sensitive data storage without sacrificing semantic understanding. Traditional Retrieval-Augmented Generation (RAG) architectures expose raw vector embeddings to potential inversion attacks and nondeterministic retrieval failures. To address this, we utilize the digits of $π$ as a source of transcendental entropy, creating an immutable indirection layer between the LLM and private records. The value $π$ provides immutability, is uneditable and math governs it. The architecture also introduces a Semantic Quantization Layer. This layer projects user inputs onto a pre-computed manifold of Canonical Intent Centroids. RAG performs vector cosine similarity but here it maps the centroids to deterministic offsets via cryptographic salt. The resulting $π$-key is a pointer to standardized payload from the actual datastore. By replacing direct access to the datastore via LLM with this transcendental layer, $π$-RAG mathematically guarantees that the inference remains oblivious to the data. This architecture unifies deterministic randomness, auditability, and differential privacy, demonstrating high efficacy for high-compliance sectors such as finance and healthcare.