Preprint Draft v3.0] Kajino Multiplicative Language Model (KM-LLM): Deterministic Governance and Phase Equilibrium Model via Tensor Multiplication, Decay Dynamics, and the Zero-Logic Principle

Abstract This paper presents the "Kajino Multiplicative Language Model (KM-LLM)," a novel computational architecture designed to overcome the fundamental flaws of current Large Language Models (LLMs)—specifically, their reliance on vector addition (\boldsymbol{v}_A + \boldsymbol{v}_B), which leads to contextual collapse, hallucinations, and ideological polarization. KM-LLM shifts the core computational paradigm from additive vector spaces to multiplicative tensor products (\boldsymbol{v}_A \otimes \boldsymbol{v}_B), introducing absolute core-theme invariance (1^n = 1) and an automatic zero-logic circuit breaker (1 \times 1 \times 0 = 0). Furthermore, this paper formalizes the "Societal Dynamics Model" (\text{Society} = \text{Right} \times \text{Left}) to demonstrate the mathematical decay dynamics triggered by values below 1. We prove that while additive models erroneously permit incomplete compromises or unilateral bias, KM-LLM enforces absolute parity (1 \times 1 = 1) and synergistic expansion (> 1) as mandatory mathematical conditions for system stability and societal sustainability.