Geometric Derivation of Fermion Mass Hierarchies: From Twistor Cycles to Exponential Mass Relations

We present a first-principles derivation of the exponential mass relations for Standard Modelfermions within a unified geometric-algebraic framework. Fermions are identified as coherent statesin a twisted twistor bundle with Cartan connection, where three generations emerge from orthogonalcomplex structures I, J, K in the internal twistor space T . The theory yields the mass formulam(n)f = m(f )0 exp[−κf β(f )χn ] as an exact solution to the fermion state equations. The parametersβ(f )X are computed as period integrals over twistor cycles Γ(f )X , while κf arises from the normalizedvolume of the fermion’s support in T . For leptons we obtain κlep = 0.10, βlepI = 82.7, βlepJ = 29.3,βlepK = 1.0, reproducing me/mμ = 0.0048 and mμ/mτ = 0.059 exactly. Quark masses are fitted with κ(quark) = 0.15 and different β values, reflecting color confinement as a topological constraint onadmissible sections. The results constitute a geometrically grounded, parameter-sparse explanation of fermion mass hierarchies