Geometric Origin of Fermion Mass Hierarchies: Exact Exponential Relations from Torsion and Twistor Geometry

We derive exact exponential mass relations for all Standard Model fermions within a unified geometric-algebraic framework. Fermions are identified as topological defects in spacetime torsion, with three generations arising from orthogonal complex structures I, J, K in twistor space. The model yields mass formulae m(n)f = m(f )0 exp[−κf β(f )Xn ], where β(f )Xn are torsion-coupling constants and κfgeometric factors. For leptons we obtain κlep = 0.10, β(lep)I = 82.7, β(lep)J = 29.3, β(lep)K = 1.0,reproducing me/mμ = 0.0048 and mμ/mτ = 0.059 exactly. Quark masses are fitted with κquark = 0.15 and different β values, reflecting their colour charge and confinement. The results constitute a precise, geometrically grounded explanation of fermion mass hierarchies.