Li's contraction interlacing conjecture for matroid Chow polynomials

Let $\mathcal{L}$ be a geometric lattice, let $a$ be an atom of $\mathcal{L}$, and let $\underline{\mathrm{H}}_{[a,\widehat{1}]}$ and $\mathrm{H}_{[a,\widehat{1}]}$ denote the augmented and ordinary Chow polynomials of the upper interval $[a,\widehat{1}]$, with $\underline{\mathrm{H}}_{\mathcal{L}}$ and $\mathrm{H}_{\mathcal{L}}$ the corresponding polynomials of $\mathcal{L}$. Li's conjecture. The augmented and ordinary Chow polynomials of the upper interval interlace those of $\mathcal{L}$:

$$\underline{\mathrm{H}}_{[a,\widehat{1}]}\preceq\underline{\mathrm{H}}_{\mathcal{L}},\qquad \mathrm{H}_{[a,\widehat{1}]}\preceq\mathrm{H}_{\mathcal{L}}.$$

Equivalently, for any simple matroid $\mathrm{M}$ on ground set $E$ and any $i\in E$, contraction satisfies $\underline{\mathrm{H}}_{\mathrm{M}/i}\preceq\underline{\mathrm{H}}_{\mathrm{M}}$ and $\mathrm{H}_{\mathrm{M}/i}\preceq\mathrm{H}_{\mathrm{M}}$. The source describes this as a strengthening of the Chow-polynomial real-rootedness conjecture and gives no resolution.