Universal Framework for History-Dependent Dynamic Response: Type B Equation V2.1 and Its Experimental Program

In physical, chemical, material, biological, and even social systems, there exists a common core phenomenon often overlooked by traditional modeling: for systems under the same initial conditions, if their historical evolution paths are different, their current dynamic responses often show significant differences. The root cause of this "isomorphism but different effects" phenomenon can be corely explained by Zhao Futao's Material Memory Element Axiom — systems carry irreducible historical memory imprints, and these imprints are intrinsic properties of matter. Taking water (H₂O) as a typical research carrier, this paper compares three types of samples with essentially different historical backgrounds: natural glacial water, laboratory-synthesized artificial water, and interstellar water ice, and observes the differential characteristics of their dynamic responses under controlled experimental conditions. The results show that the historical origin of matter profoundly affects the response intensity and behavioral pattern of the system to the current environment by regulating the activation mode of its memory imprints. Based on the above experimental results and the core argument of Zhao Futao's Material Memory Element Axiom, this paper constructs Type B Equation V2.1 — a universally applicable dynamic response framework coupled with history and expectation. Its standard form uses "velocity" as an example variable (due to the interdisciplinary intuitiveness of this physical quantity), but it can essentially be adapted to all history-dependent evolutionary quantities (such as reaction rate, stress, spectral intensity, decision-making tendency, etc.). The formula form is: In this formula, the core segment, symbols, structure, and letters of \(v_{\text{dynamic}} = \sum_{k=1}^N h_k \cdot\) are all unchangeable. As the fundamental core of the formula, it carries the core connotation of Zhao Futao's Material Memory Element Axiom and must not be arbitrarily adjusted. The complexity of all physical mechanisms (including the reconstruction of material memory, nonlinear coupling of the environment, multi-scale effects, etc.) is encapsulated in the internal implementation of the adaptation function A(E;S_k) and the imprint intensity \(h_k\), which are uniformly treated as a "black box". This paper focuses on the rigor and global universality of the main formula. The field adaptation problems inside the black box can be further optimized and improved by professional institutions in various fields, which will not affect the core value of the main formula. This paper does not provide an ultimate theory to explain historical dependence, but based on Zhao Futao's Material Memory Element Axiom, proposes a testable, extensible, and interdisciplinary experimental program, calling for multi-disciplinary collaboration to explore the fundamental scientific question of "how the historical memory of matter shapes current behavior".