The Dark Sector as a Geometric Residue: LKP Stability and the e−4kL Suppression of Dark Energy

We provide a unified geometric origin for Dark Matter and Dark Energy within a 5Dwarped AdS5 manifold. By utilizing the stabilized warp factor kL = 38.44, we demonstratethat the observed Dark Energy density is not a fine tuned parameter but a residual vacuumenergy density suppressed by the fourth power of the geometry (e−4kL). This yields apredicted Cosmological Constant of 1.67 × 10−67 in reduced Planck units, aligning withobservational data. Furthermore, we identify Dark Matter as the Lightest Kaluza-KleinParticle (LKP) resulting from the S1/Z2 orbifolding of the gauge sector. We predict astable Dark Matter candidate with a mass of 1219.67 GeV, providing a clear target fornext-generation detection experiments.