This paper systematically presents the core logical framework and the first formalizable dynamic computing system of Zhao Futao's Axiom of Matter Memory, and clarifies the theoretical positioning, hierarchical structure and open cooperation path of the axiom. Taking "memory as an inherent attribute of matter with mass-energy" as the core premise, the axiom constructs a pyramid system of "underlying axiom-middle mechanism-upper interpretation", and for the first time proposes the B-Style Velocity Evolution Equation (Memory Velocity Evolution Equation) as the dynamic foundation, which realizes the transformation of the abstract axiom from philosophical speculation to a computable framework with formulas, parameters and experimental interfaces. The framework abandons redundant physical presuppositions, has the characteristics of universality, expandability and endogenous time arrow, and can provide new interpretive perspectives and quantitative methods for interdisciplinary research fields such as quantum physics, biophysics and astrophysics. At the same time, this paper clarifies the open principle of the theoretical framework, and puts forward specific paths for individual research and institutional cooperation, aiming to build an interdisciplinary academic ecosystem with the core axiom and jointly promote the empirical verification and application expansion of the matter memory theory.