AGORA: Pre-Retrieval Vector Algebra and Factual Anti-Hallucination Validation for Domain-Agnostic RAG Systems

We present AGORA Semantic OS, a Retrieval-Augmented Generation (RAG) system that introduces three original contributions: (1) vector algebra operations applied to the query embedding before corpus retrieval (vector rotation and orthogonal subtraction), enabling analogical reasoning and semantic debiasing without LLM dependence; (2) a controlled generation protocol in which the LLM is instructed to declare factual bases in a structured format (JSON); and (3) a factual validation layer (@Sentinel) that verifies each citation against the actual corpus, classifying them into three confidence levels (OK, NORM_OK, HALLUCINATION). We empirically validate the system in the Brazilian tax-law domain (34 documents, 392 chunks) and propose a cross-validation protocol across five additional domains: pure mathematics, medical research (Alzheimer's disease), financial markets, photonic computing, and quantum computing. Cross-domain results across all six domains confirm that both operations are genuinely domain-agnostic: rotation yielded a mean delta_t = 3.0 new documents, and orthogonal subtraction produced a mean delta_a = 14.0 ranking changes, with Sentinel validation passing in all six domains.