Spacetime Memristive Universe Model: Covariant Tensor Framework, Dynamical Origin of Light Speed Invariance, Emergence of Time Arrow and Full-sample Numerical Simulation of Galaxy Rotation Curves

Starting from the fundamental physical premise that spacetime is a causal respon sive medium for energy-momentum distribution, this paper presents a self-consistent mathematical derivation of spacetime memristivity, thus avoiding the logical flaw of taking ”intrinsic memristivity of spacetime” as an a priori assumption. On this basis, we construct an axiomatic theoretical framework consisting of 8 core theorems and 7 characteristic corollaries, and for the first time give the simplest Lorentz-covariant fourth-order tensor memory kernel form that satisfies the constraints of symmetry, causality and local limit. We prove that the scalar trace of metric perturbation strictly satisfies the definition of memristive systems, while the full tensor response constitutes its covariant generalization; therefore, spacetime memristivity holds rigorously in the scalar projection and manifests as its covariant extension at the tensor level. Within this framework, we further provide a closed dynamical derivation for the universal invariance of the speed of light, rigorously binding the speed of light to the causal support boundary of the spacetime memristive kernel, the characteristic surface velocity of transverse massless modes, and the electromagnetic propagation velocity. Meanwhile, by constructing a memory monotonic quantity, we self-consistently explain the origin of the unidirectionality of the cosmic time axis in the macroscopic coarse grained limit, interpreting the time arrow as a statistically unidirectional cumulative process of spacetime memristive writing. Through the self-consistent parameter constraints inside the model and external ob servational boundaries, we derive a minimum stable core scale of spacetime memristive polarization on the order of 3 nm and a critical threshold of memory writing on the order of 1.2 × 1019 GeV, and clarify their physical origins, dimensional structures and applicable boundaries. Based on 175 disk galaxy samples in the SPARC database, we complete a full-sample numerical simulation. Under the condition of adopting globally fixed parameters and introducing no additional free parameters for individual galax ies, we achieve a rotation curve fitting accuracy comparable to the ΛCDM dark halo 1model and superior in the low surface brightness galaxy subsample; the complete fitting results and numerical codes are given in the appendices. In addition, we supplement the proof framework for the existence and uniqueness of solutions to the field equations, as well as the analysis framework for the asymptotic stability of locally stable solutions, and explicitly present the applicable assumptions, regularity requirements and boundary conditions for all derivations. In general, the spacetime memristive universe model proposed in this paper provides a computable, falsifiable and parameter-compressible effective path for the unification of relativity and quantum theory; within the constraints considered in this paper, the model conclusions are consistent with existing observational boundaries.