The Law of the Dark A Unification Attempt via a Fifth Scale Dimension and Vacuum Relativity (General Mechanics Framework)

[Abstract] General Mechanics (GM) is a 5-dimensional geometric framework built on one central hypothesis, originated by Mike One: the renormalization-group scale µ—a formal book- keeping device in standard quantum field theory—is a real coordinate S on a fifth geometric dimension. In this geometry the vacuum is not uniform. Its effective curvature Λeff(x,S) varies with both position and scale. Matter produces positive curvature at every scale layer; the vacuum medium substrate, Darkness, produces negative curvature. This opposition is the geometric foundation of the entire framework. The gradient of vacuum curvature along S gives rise to the Law of the Dark: a universal tendency for vacuum curvature to steepen at smaller S and flatten at larger S, with matter locally relaxing the surrounding negative curvature. This single geometric law accounts, without new particles, for: (1) galaxy rotation anomalies, (2) cosmic acceleration, (3) the hierarchy and scale-running of all four Standard Model forces, (4) the cosmological constant problem, and (5) cyclical cosmology. I verified the framework against 11 independent public datasets. The vacuum response coefficient is s = 0.30±0.05, consistent across all probes. Five core claims are formally verified via three independent SymPy symbolic computation paths (13/13 checks passed). No new particles, no free parameters beyond the scale potential V(S). All pipeline code is fully reproducible in a single Google Colab notebook: https://colab.research.google. com/drive/1r3kLeVe9JeTxTaQyslUtl7ACL7LVYfBf