Fermion Mass Hierarchy from Topological KO⁻² Torsion: Algebraic Origin, Near-Flat Directions, and UV Stabilization

We analyze fermion mass hierarchy generation through the topological KO⁻² torsion of the condensed variationalframework. Three results are reported. (1) Algebraic origin: The 3-cycle KO⁻² twist diagonalizes in theeigenbasis of T+T†, whose spectrum 2, −1, −1 creates a natural 1+2 splitting. Off-diagonal cubic couplingsbetween the degenerate −1 modes break the residual degeneracy, producing non-trivial generational ratios. (2) Near-flat directions and CKM mixing: A Hessian analysis identifies a near-flat direction in the SD landscapecorresponding to the generation rotation generator, proving that tree-level VCKM = I is a structural theorem;non-trivial CKM mixing requires loop-level electroweak radiative corrections. Differential Casimir sliding of theup and down sectors provides a geometric origin for CP violation. (3) UV stabilization: The effective potentialfrom the Seeley–DeWitt expansion yields a potential well whose minimum determines the absolute Yukawa scale.