theorem premium_factor_eq_K_scaled (hJ : 2 ≤ J) {ρ : ℝ} (hρ : ρ ≠ 0) :
(1 - ρ) / ρ = curvatureK J ρ * ↑J / ((↑J - 1) * ρ) := by
simp only [curvatureK]
have hJne : (↑J : ℝ) ≠ 0 := Nat.cast_ne_zero.mpr (by omega)
have hJm1_ne : (↑J : ℝ) - 1 ≠ 0 := by
have : (1 : ℝ) < ↑J := by exact_mod_cast (by omega : 1 < J)
linarith
field_simp## Network Scaling Results