The Duality Framework: A Mathematical Inversion Approach to Dark Matter Composition

Five decades of direct detection experiments have failed to identify dark matter particles, suggesting a fundamental flaw in the particle paradigm. This paper proposes that dark matter is not a new particle to be discovered, but the mathematical dual of ordinary matter under a systematic symmetry transformation. We introduce the Duality Inversion Operator 𝒟̂ that maps the Standard Model to a "dark sector" by inverting coupling constants, exchanging gauge group factors (SU(3)C↔SU(2)L ), and transforming the Higgs VEV as v→v~=Λ2/v . This framework naturally explains why dark matter interacts only gravitationally, predicts the observed dark-to-baryonic ratio ΩD/ΩB≈5 , and derives the characteristic acceleration scale a0≈1.2×10−10 m/s² without free parameters. The theory makes distinctive predictions: continued null results in direct detection, self-interacting dark matter with σ/m∼0.1−1 cm²/g, and modified galactic dynamics at low accelerations without modifying gravity.