theorem powerMean_zero {J : ℕ} (_hJ : 0 < J) {ρ : ℝ} (hρ : ρ ≠ 0) :
powerMean J ρ hρ (symmetricPoint J 0) = 0 := by
simp only [powerMean, symmetricPoint, zero_rpow hρ, Finset.sum_const_zero,
mul_zero, zero_rpow (one_div_ne_zero hρ)]Emergence results from Paper 1, Sections 3-5: