Klee–Novik's balanced lower bound conjecture

Let $\Delta$ be a balanced normal pseudomanifold of dimension $d-1\geq 3$. Klee–Novik's balanced lower bound conjecture.

$$2h_2(\Delta)-(d-1)h_1(\Delta)\geq 4\binom{d}{2}\bigl(\beta_1(\Delta;\mathbf{k})-\beta_0(\Delta;\mathbf{k})\bigr).$$

This extends the balanced Lower Bound Theorem by including Betti-number terms; the supplied text records only partial results, so the conjecture remains open.