  Viewing the BRAID invariant as a generator of link Floer homology we
generalise work of Baldwin-Vela-Vick to obtain rank bounds on the next to top
grading of knot Floer homology. These allow us to classify links with knot
Floer homology of rank at most eight, and prove a variant of a classification
of links with Khovanov homology of low rank due to Xie-Zhang. In another
direction we use a variant of Ozsv\'ath-Szab\'o classification of $E_2$
collapsed $\mathbb{Z} \oplus\mathbb{Z}$ filtered chain complexes to show that
knot Floer homology detects $T(2,8)$ and $T(2,10)$. Combining these techniques
with the spectral sequences of Batson-Seed, Dowlin, and Lee we can show that
Khovanov homology likewise detects $T(2,8)$ and $T(2,10)$.
