theorem correlation_le_one {r : ℝ} {J : ℕ} (hJ : 2 ≤ J) (hr : 0 ≤ r) :
compoundSymmetryCorr r J ≤ 1 := by
have h := gap_from_one hJ hr
have hJ_pos : (0 : ℝ) < ↑J := by linarith [hJ_sub_one_pos hJ]
have hden := den_pos hJ hr
linarith [div_nonneg (mul_nonneg (le_of_lt hJ_pos) hr) (le_of_lt hden)]Correlation Convergence at the Regime Boundary