theorem marginalCurvatureLoss_eq {J ρ : ℝ} (hJ : 1 < J) :
curvatureKReal J ρ - curvatureKReal (J - 1) ρ = marginalCurvatureLoss J ρ := by
simp only [curvatureKReal, marginalCurvatureLoss]
have hJpos : 0 < J := by linarith
have hJm1pos : 0 < J - 1 := by linarith
rw [div_sub_div _ _ (ne_of_gt hJpos) (ne_of_gt hJm1pos)]
congr 1
ringFirm Failure Resilience: Optimal Failure Rate for Long-Run Diversity