Force Unification as Dimensional Projection: Gravity as the Single Fundamental Interaction in the Extended Randall-Sundrum Geometry

The Standard Model describes four fundamental interactions. This paper proposes that these are not four independent interactions but a single interaction — the gravitational coupling of the Randall-Sundrum bulk geometry — projected through different dimensional environments. Newton’s gravitational potential changes character at each dimensional step: linear in D = 2, logarithmic in D = 3, inverse-square in D = 4, Yukawa-screened in D = 4 with mass corrections. Each known force has the potential character of Newton’s law at exactly the dimensional step corresponding to its observed behavior. The force hierarchy is reinterpreted as a depth hierarchy. Three quantitative checks support the identification: the Regge slope from D = 2 string tension (0.5% agreement), the proton mass as ~5 string-tension units (2.2%), and the proton charge radius as the D = 2 → D = 3 dimensional boundary at 1/Λ_QCD = 0.91 fm versus observed 0.88 fm (3%). The dark matter signal arises from a dimensional mismatch between the gravitational interaction’s 1D read and the higher-dimensional addresses of ordinary matter: the shadow rule, which operates per-constituent and predicts 83.4% dark matter from cosmological hydrogen and helium abundances alone [15]. No new particles, fields, or coupling constants are introduced.