Hölder regularity on all bounded horizons

For each exponent below the stable height exponent, choose a sufficiently high moment. Horizon modifications agree with the common continuous reconstruction by indistinguishability. A countable intersection then covers every real horizon.

theorem BGW.StableTrees.ae_heightLoc_locallyHolder {θ : ℝ} (hθ : 1 < θ ∧ θ ≤ 2) {γ : ℝ} (hγ0 : 0 < γ) (hγ : γ < 1 - 1 / θ) : ∀ᵐ (f : Skorokhod.DLoc) ∂↑(stableLocalLaw θ), ∀ (T : NNReal), ∃ (C : ℝ), ∀ (s t : NNReal), s ≤ T → t ≤ T → |heightLoc θ f s - heightLoc θ f t| ≤ C * |↑s - ↑t| ^ γ

Almost surely the continuous height is locally γ-Hölder for every γ < 1 - 1/θ.