Geometric Origin of Gauge Couplings and a Four-Force Unification Hypothesis in Memory Force Theory — A Falsifiable Path from D_8-Symmetric Vacuum to the Standard Model Gauge Group

Memory Force Theory has recently been proposed as a framework in which gravity arises as a density-dependent restoring force of the vacuum, with the universal exponent α = sin(π/8) originating from a D_8 octuple symmetry of the vacuum geometry. In this paper we extend that geometric picture to the gauge sector. We put forward the conjecture that the Standard Model gauge group SU(3)× SU(2)× U(1) emerges from the D_8 symmetry via subgroup layering, symmetry breaking and continuum limit: C_4 → U(1)_Y, C_2× C_2 → SU(2)_L, and a triple-fractal branch of D_8 → SU(3)_c. We further show that the energy-scale dependence of gauge couplings follows from the vacuum density scaling ρ(Q)∝ Q^4 combined with μ^2(ρ)∝ ρα, leading to a power-law running g^2(Q)∝ Q4α. At the electroweak scale m_Z a geometric resonance condition is hypothesized, which locks the strong coupling to the exact value α_s(m_Z) = 11/2sin^4π/8, in agreement with the current experimental value to within 0.05%. Additional falsifiable predictions include a ~ 0.5% shift of the M87* black hole shadow, a scalar polarization amplitude A_S/A_T~ 10⁻⁶–10⁻⁴ in gravitational waves, and a precise infrared exponent α = sin(π/8) in galaxy rotation curves. The framework is explicitly declared as conjectural, and five core open problems are listed together with a roadmap for further development. All main predictions are falsifiable within the coming 10–20 years.