Canonical form conjecture for binary Δ-matroids under handle slides

Let $D$ be a binary $\Delta$-matroid. A handle slide is the operation that replaces $D$ by $D_{ab}$ for distinct elements $a,b$ of its ground set, as defined by the feasible-set transformation in the source. Let $D_{i,j,k,l}$ be the direct sum of $D_{i,j,k}$ with $l$ copies of $(\{e\},\{\{e\}\})$, where $D_{i,j,k}$ is the direct sum of $i$ copies of $(\{e\},\{\emptyset\})$, $j$ copies of $(\{e,f\},\{\emptyset,\{e,f\}\})$, and $k$ copies of $(\{e\},\{\emptyset,\{e\}\})$. For a binary $\Delta$-matroid, call it even when all feasible sets have the same parity of cardinality, and write $w$ for the difference between the sizes of a largest and a smallest feasible set.

Canonical form conjecture. For each binary $\Delta$-matroid $D$, there is a sequence of handle slides taking $D$ to some $D_{i,j,k,l}$ where $i$ is the size of the ground set minus the size of a largest feasible set, $l$ is the size of a smallest feasible set, and $2j+k$ is the difference in the sizes of a largest and a smallest feasible set. Moreover, $k=0$ if and only if $D$ is even, and if $D$ is odd then every value of $j$ from $0$ to $\floor*{\frac{w}{2}}$ can be attained.

This conjecture proposes a canonical classification of binary $\Delta$-matroids under handle slides, with the parameters constrained by the extremal feasible-set sizes and parity. The supplied text does not state whether the conjecture has been proved or disproved.