The Associator Attention Block: Bridging the Non-Associative Gap in Large Language Models

Current Large Language Models (LLMs) rely on standard matrix multiplication, an inher-ently associative operation ((AB)C = A(BC)). This algebraic constraint limits their capacityfor agency, restricting them to deterministic, linear information processing (System 1 thinking).We propose a novel architectural primitive: the Associator Attention Block. By embed-ding the latent space into the non-associative algebra of Octonions (O), this block introducesGeometric Torsion as a measure of causal ambiguity. We define a Fano Gate mechanismthat detects high-torsion states and triggers a Geometric Stop, forcing the model to resolvenon-associative conflicts. We derive the scaling laws for this mechanism and predict a super-exponential suppression of hallucination rates in the Strong Buffer regime.