Chain theorem conjecture for highly connected matroids and $t$-spikes

Let $t$ be a positive integer. A matroid is $(2t-1)$-connected if it has the stated matroid connectivity property, and a $t$-spike is a matroid with the $(t,2t)$-property. Consider matroids with no circuits or cocircuits of size $2t-1$.

Chain theorem conjecture. There exists a function $f(t)$ such that if $M$ is a $(2t-1)$-connected matroid with no circuits or cocircuits of size $2t-1$ and

$$|E(M)| \ge f(t),$$

then either there exists a $t$-element set $X \subseteq E(M)$ such that either $M/X$ or $M \backslash X$ is $(t+1)$-connected, or $M$ is a $t$-spike.

This conjecture proposes that sufficiently large highly connected matroids either admit a connectivity-preserving deletion or contraction of a $t$-element set, or belong to the structured exceptional class of $t$-spikes. The source does not indicate that it has been resolved.