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

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 (v_A + 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 (v_A ⊗ v_B), introducing absolute core-theme invariance (1^n = 1) and an automatic zero-logic circuit breaker (1 × 1 × 0 = 0). Furthermore, this paper formalizes the "Societal Dynamics Model" (Society = Right × 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 × 1 = 1) and synergistic expansion (> 1) as mandatory mathematical conditions for system stability and societal sustainability.