Mem-Force Theory Research Notes (Comprehensive Version)

This note integrates the core content of the series of works on Mem-Force Theory, including the establishment of the theoretical framework, observational verification at galaxy scales, cross-scale connections to the QCD mass gap, strong-field gravity predictions, and experimental test schemes. The core hypothesis of Mem-Force Theory is: gravity is not the essence of spacetime geometry, but a restoring force exerted by the vacuum on matter perturbations. The strength of this restoring force depends on the local matter density ρ, following a power law μ(ρ) = μ₀(ρ/ρ₀)ᵅ, where α ≈ 0.38 is a universal critical index. Starting from the fitting of galaxy rotation curves, this note shows how α = 0.38 is linked to the density dependence of gluon condensates through QCD sum rules, thereby deriving the theoretical value α = 3/8. Furthermore, this index is extended to black hole horizon corrections, gravitational wave polarization modes, cosmological dark energy evolution, and laboratory fifth-force detection, forming a cross-scale unified framework covering 36 orders of magnitude from 10⁻¹⁵ m to 10²¹ m. All core predictions are connected to current/next-generation experimental facilities (SKA, EHT, LISA, LIGO, LHC, etc.) and can be tested within the next 5-20 years. This note aims to provide a complete, self-consistent, and testable literature record for Mem-Force Theory.