The series-parallel characterization of equality in the f-vector conjecture

Let $L$ be a tropical linear space, and call it series-parallel when it arises from a matroidal decomposition whose facets are polytopes of series-parallel matroids. For a $d$-dimensional tropical linear space in $n$-space, let $i$ be a face dimension. The series-parallel equality conjecture. Equality in the f-vector bound

$$\binom{n-2i}{d-i}\binom{n-i-1}{i-1}$$

is achieved precisely by series-parallel tropical linear spaces. The paper proves that constructible tropical linear spaces achieve the f-vector bound, but the claimed characterization of all equality cases remains open.