Light vectors and scalar interactions near heterotic K3 gauge enhancement

We prove a uniform comparison for a four-scalar tree amplitude near gauge enhancement in a smooth SO(32) heterotic K3 compactification. A rank-six stable-bundle family approaches the direct sum of two isomorphic stable rank-three bundles. Two harmonic deformation amplitudes a,b give three squared Higgs masses proportional to b², a² and a²+b². For two specified massless bundle scalars, the complete leading Yang–Mills amplitude, including all internal vector and scalar Kaluza–Klein modes, approaches an explicit light-vector exchange formula. The absolute error is quadratic in the deformation amplitudes, uniformly as b/a tends to zero, below the heavier Higgs masses and away from the light poles. Harmonic orthogonality controls the actual cubic vertices, while an exact scalar contact–exchange cancellation removes inverse-mass losses. The same estimates give inverse-square growth of the sectional curvature of the harmonic bundle-moduli metric on a selected plane, with uniform relative error. We also obtain a ratio-uniform relative bound for the first-order coupled vector equation and a fixed-ray coefficient with a Pauli selection rule. At the next tree order we control quadratic potential mixing with K3 metric deformations and compute the universal graviton exchange. The complete coefficient at that order and a finite-string-scale remainder remain open.