D = 11 and the Standard Model: Masses, Couplings, and the Cosmological Constant from a Single Geometry

We present an extended Randall-Sundrum (ERS) framework in which a hub-and-spoke geometry with D = 11 spacetime dimensions, N = 7 compact dimensions, and warp depth kL = 37 determines the Standard Model parameters with zero fitted inputs beyond the electron mass. The three parameters are not independent: N = D − 4 and kL is self-selected through the fine structure constant formula 1/α = 4kL − D + 1/ (dN) = 137. 036 (2 ppm accuracy). From this geometry we derive all twelve fermion masses (0. 83% average error), the Higgs boson mass (0. 27%), the Higgs vacuum expectation value (0. 25%), the strong coupling constant (1. 1%), the Weinberg angle (0. 07%), the Koide angle (0. 02%), the Cabibbo angle (0. 93%), the cosmological constant (0. 06%), the semi-empirical mass formula coefficients (0. 1–3%), the dark matter fraction (1. 7%), and θQCD = 0 from Z₂ spectral pairing (solving the strong CP problem without axions). The fermion mass spectrum arises from Bessel function eigenmodes on the compact geometry, with the Bessel order for each charge sector determined by ν = floor (3Q²). Generational mass ratios follow from Bessel zero ratios; absolute scales follow from amplitude ratios that reproduce the SU (3) Casimir C₂ = 4/3 without input. The Z₂ orbifold solves the strong CP problem without axions and explains maximal parity violation geometrically. The framework makes falsifiable predictions: no dark matter particle, exactly massless neutrinos (testable by KATRIN), proton stability, dark energy equation of state w = −0. 81 (consistent with DESI 2024), and specific relations between the Higgs quartic coupling and the nuclear surface tension through common dependence on the transverse dimension count D − 3 = 8.