Split link detection for sl(P) link homology in characteristic P

If $P$ is a prime number, we show that reduced $\mathfrak{s}\mathfrak{l}(P)$ link homology with coefficients in $\mathbf{Z}\mathrm{/}P$ detects split links. The argument uses Dowlin’s spectral sequence and sutured Floer homology with twisted coefficients. When $P=2$, we recover Lipshitz-Sarkar’s split link detection result for Khovanov homology with $\mathbf{Z}\mathrm{/}2$ coefficients.