Phase Transition & Acid-Base Equilibrium Model] Dynamic Phase Transition Model of Outcome Creation under Human-AI Co-Creation — Critical Boundary Formalization of Depth of Thought (D_k) via Acid-Base Equilibrium Buffer Curves —

Abstract

Abstract This paper introduces an acid-base equilibrium (titration curve) model from biochemistry as an analogy and dynamic mathematical framework to explain the non-linear jump phenomenon in outcome creation during interaction with Generative AI. Traditional project management and business performance metrics have relied on gentle S-curves (logistic curves) or linear approximations. However, under a Generative AI co-creation environment, when the Depth of Thought (D_k = O_k \times A_k \times U_k)—the multiplicative product of Observation (O), Altruistic Perspective (A), and Utility Understanding (U)—reaches a critical threshold (equivalence point), outcome creation capacity exhibits a nearly vertical, explosive surge. This paper formalizes this phenomenon using a Henderson-Hasselbalch-type response function and integrates it with the cumulative outcome function S_n = \sum (a D_k^2 + b D_k + c), mathematically establishing the mechanisms of cognitive synchronization and phase transition between humans and AI.