theorem equal_weight_entry_improves_K {J : ℕ} (hJ : 1 ≤ J) {ρ : ℝ} (hρ : ρ < 1) :
curvatureK J ρ < curvatureK (J + 1) ρ := by
simp only [curvatureK]
have hJpos : (0:ℝ) < ↑J := by exact_mod_cast (show 0 < J by omega)
rw [div_lt_div_iff₀ hJpos (by push_cast; linarith)]
push_cast; nlinarith## Entry with General Weights