Conjecture on clique counts forcing long cycles in bipartite graphs

Let $G$ be a connected bipartite graph with bipartition $(X,Y)$. Suppose

$$|X|=n\le |Y|=b,$$

let $h=\left\lfloor\frac{n-k}{2}\right\rfloor$, and assume that $\delta(G)\ge r\ge 1$, where $n\ge 2k+2r$ and $k\in\mathbb{Z}$. For positive integers $s$ and $t$, write $N(K_{s,t},G)$ for the number of copies of $K_{s,t}$ in $G$. Clique-count long-cycle conjecture. If

$$N(K_{s,t},G)>\begin{cases}\max\{f_{s,t}(b,n,n-k,r),f_{s,s}(b,n,n-k,h)\},&s=t,\\[2pt]\max\{f_{s,t}(b,n,n-k,r)+f_{t,s}(b,n,n-k,r),\f_{s,t}(b,n,n-k,h)+f_{t,s}(b,n,n-k,h)\},&s\ne t,\end{cases}$$

then $G$ contains a cycle of length $2n-2k$. This conjecture proposes a clique-count extremal condition for forcing a cycle of the specified length in a not necessarily balanced bipartite graph; the supplied excerpt gives no resolution or further context for the functions $f_{s,t}$, so the claim remains open here.