theorem diversityBonus_pos {J ρ τ r : ℝ} (hJ : 1 < J) (hρ : ρ < 1)
(hτ : 0 < τ) (hr : r < 1) :
0 < diversityBonus J ρ τ r := by
simp only [diversityBonus]
exact mul_pos (mul_pos (curvatureKReal_pos hJ hρ) (sq_pos_of_pos hτ)) (by linarith)Firm Failure Resilience: Optimal Failure Rate for Long-Run Diversity