Local weak-measure bounds and sharp tails for a homogeneous de Branges kernel

On a fixed homogeneous de Branges space with spectral measure ν(dx) = (1/2)|x|-1/2 dx, we compare the reproducing kernels obtained by changing the spectral norm to hν, where 0 < c ≤ h ≤ C < ∞. For every complex compact set, the kernel error is bounded by QM,c,C(D_R(hν,ν) + R⁻¹). Here D_R tests bounded Lipschitz functions supported in [−2R,2R]. A second-order identity for the positive Gram operator pairs the two residuals and yields the stated tail order. Perturbations supported in [3R,4R] show that the independent R⁻¹ remainder is sharp. An exact dilation identity gives a quantitative scaling estimate for the prescribed family of spaces.