Emergent Standard Model with Torsion from Noncommutative Geometry: A Complete Derivation from Spectral Triples

We present a complete derivation of the Standard Model coupled to gravity with torsion from the principles of noncommutative spectral geometry. The framework naturally unifies all fundamental forces and matter fields within a single geometricstructure based on a spectral triple. Key results include: identification of torsion as the covariant derivative of Yang–Mills field strength; dynamical generation of the noncommutativity scale ΛNC ∼ 1016 GeV; explanation of fermion mass hierarchy via renormalization group fixed points and a θ-field; geometric origins for dark matter and dark energy; resolution of the cosmological constant problem through multiple suppression mechanisms; and a novel baryogenesis mechanism via θ-fieldphase transitions. The theory predicts a stochastic gravitational wave backgroundat f ∼ 0.01 Hz with ΩGW ∼ 10−9, testable by upcoming space-based interferometers. Additionally, this background provides a physical mechanism for spontaneous wavefunction collapse, addressing the quantum measurement problem. All predictions are testable across energy scales from table-top experiments to cosmology.