theorem knockout_total_failure {ρ : ℝ} (hρ : ρ ≤ 0) {m : ℕ} (hm : 0 < m) :
knockoutRetained J ρ m = 0 := by
simp only [knockoutRetained]
simp [show ¬(ρ > 0) by linarith, show ¬(m = 0) by omega]Further properties of CES curvature (Paper 1, Section 9):