One Membrane, Everything: Dark Matter as Geometric Artifact and the Comprehensive Brane Framework

We present a physical framework built on a single idea: dark matter is not a new particle. It is the gravitational signature of ordinary matter extending into a dimension we cannot directly observe. If the universe is a membrane—a three-dimensional surface embedded in a five-dimensional space with the warped geometry of Randall and Sundrum1—then every particle is an excitation of that membrane, and every particle’s wavefunction extends to some degree into the transverse direction. The portion of each particle that extends beyond the reach of our electromagnetic instruments is invisible to telescopes but still gravitates. That invisible portion is what we have been calling dark matter for ninety years. This identification, combined with the established Gherghetta–Pomarol fermion localization mechanism2, produces a zero-parameter prediction: the cosmic baryon-to-total-mass ratio Ωb/Ωm = 15.8%. The observed value from the Planck satellite3 is 15.7 ± 0.3%. The same geometry that produces this ratio also yields the radial acceleration relation scale g† ≈ 1.2 × 10⁻¹⁰ m/s² from brane stiffness, the strong CP solution (θeff = 0 from orbifold symmetry), the cosmological constant as residual elastic strain, a mechanism for early dark energy that addresses the Hubble tension, three fermion generations from topological vortex stability, and the electroweak hierarchy from the warp factor—all from one Lagrangian with no new matter particles, no supersymmetry, no axions, and one additional broken symmetry on the brane. This paper presents the framework from its physical intuition through its mathematical foundations to its quantitative predictions, written to be readable by a non-specialist while retaining the technical substance required for evaluation by physicists.