Conjectured minimum degree threshold for Hamilton $ell$-cycles

For $k\ge3$, $1\le\ell<k/2$, and $k-\ell\le d\le k-1$, let $h_d^\ell(k)$ be the limiting normalized minimum $d$-degree threshold for Hamilton $\ell$-cycles. Let $t(k,d,\ell)$ be the corresponding limiting threshold for an almost perfect tiling by copies of $Y_{k,2\ell}$, where $Y_{k,2\ell}$ consists of two $k$-edges intersecting in exactly $2\ell$ vertices. The Hamilton-cycle threshold conjecture. For all such $k,\ell,d$,

$$h_d^\ell(k)=t(k,d,\ell)=1-\left(1-\frac{1}{2(k-\ell)}\right)^{k-d}.$$

The equality is motivated by the space-barrier construction and known evidence, but the source presents it as conjectural; the general statement remains open.