The scalability of Large Language Models (LLMs) is fundamentally constrained by the O (N²) time and memory complexity of standard Transformer attention mechanisms, which force discrete token sequences into continuous Euclidean spaces. This technical documentation introduces the Geometric Attention Mechanism (GeoLLM), a production-grade architecture built on discrete p-adic topology and the SL (3, Z) algebraic group. By replacing the dense O (N²) attention matrix with a topological geometric inner product governed by the Tribonacci constant, the framework natively compresses token history into a geometrically stable state. This paradigm shift yields exact context retrieval with O (N log N) time complexity and flat O (N) memory scaling, entirely eliminating the VRAM explosion associated with long-context windows. • Hardware-level parallelization and vectorization. • Gradient stability and numerical precision protocols. • Memory-efficient Streaming and Sparse Geometric Attention. • Elimination of standard KV-cache bottlenecks. Access Note: This document contains proprietary production-level architectural designs and is published under a restricted CC BY-NC 4. 0 license. Access to the full manuscript is granted upon request for purposes of enterprise integration, commercial licensing, and strategic API deployments.
Dávid Navrátil (Wed,) studied this question.