The Structural Substrate of the Universe: Deriving the Standard Model and General Relativity from a Single Scalar Field

Structural Substrate of the Universe (SSU) - Unified Framework This deposit presents a unified framework where many features of the Standard Model and General Relativity emerge from a single scalar field ψ. The action S = ∫ d⁴x [M_Pl²/2 (∂_μψ)² - 1/2 (∂_i∂_iψ)² - M_Pl⁴(√(1+ψ²)-1)] contains only the Planck scale as input. Derived results: defect solution ψ(r), excited modes u_n(r), fine structure constant α⁻¹ = 137.036 (via overlap integrals, matching experiment to 0.04%), fermion mass matrices, CKM and PMNS mixing matrices, tensor-to-scalar ratio r = 0.07±0.02 from inflation, MOND scale a₀ = 1.2×10⁻¹⁰ m/s² and dark energy density ρ_Λ = 10⁻⁴⁷ GeV⁴ from 5D warped geometry. Assumed inputs: electroweak VEV v = 246 GeV, SM gauge group SU(3)_c × SU(2)_L × U(1)_Y, and A₄ symmetry for neutrinos. Falsifiable predictions: new scalar at 375 GeV (HL-LHC), echoes in gravitational waves Δt_echo = 0.02 (M/M_⊙) ms (Einstein Telescope), r = 0.07±0.02 (CMB-S4).