This paper proposes a density-dependent effective dark matter framework. The vacuum is regarded as the sole dynamical ground state, and visible matter and dark matter effects are two manifestations of the same physical field under different density environments. The physical picture of this framework is inspired by the structure of Euler's identity e^i+1=0, where 0 symbolizes the vacuum ground state, 1 symbolizes the high-density visible matter manifestation, and e^i symbolizes the low-density dark matter manifestation — but the rigorous derivation comes from D₈ vacuum geometry and density-dependent restoring force. We construct two progressive sub-models: V1 (Phase Field Model) attributes dark matter effects to the spatially varying phase of the visible matter field, = ₕ₈ₒ e^i (r) ; V2 (Modified Gravity Model) directly modifies gravity in low-density regions, requiring no dark matter particles. Both models share the unified geometric exponent = (/8) 0. 382683, fully consistent with the core parameters of Mem-force Theory. SPARC galaxy sample fits show that both models have better goodness-of-fit than MOND and (V1: ²/dof=1. 08, V2: ²/dof=1. 10, MOND: 1. 18,: 1. 27). The paper presents the mathematical framework, fitting results, comparisons with mainstream theories, falsification conditions, and next-step verification plans.
Ma et al. (Sun,) studied this question.
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