Sierksma's Dutch cheese conjecture over valued fields

Let $K$ be a valued field and let $X\subset K^d$ satisfy

$$|X|=(r-1)(d+1)+1.$$

Sierksma's Dutch cheese conjecture. There are at least $((r-1)!)^d$ partitions of $X$ into parts whose convex hulls intersect. The conjecture extends the Dutch cheese conjecture from real convexity to valued fields; the source presents this as an expected analogue and does not indicate a resolution.