The decomposition theorem for projective maps of rigid spaces

Let $K/\mathbf{Q}_p$ be a finite extension, and let $f:X\to Y$ be a projective map of rigid spaces over $K$ with $Y$ qcqs. Let $\mathrm{IC}_{X,\mathbf{Q}_\ell}$ be the intersection complex, and for a Zariski-locally closed immersion $j:U\to Y$ let $j_{!*}\mathscr{L}$ denote the intermediate extension of a $\mathbf{Q}_\ell$-local system $\mathscr{L}$ on $U$. Decomposition theorem conjecture. The complex $Rf_*\mathrm{IC}_{X,\mathbf{Q}_\ell}$ is a direct sum of shifts of perverse sheaves of the form $j_{!*}\mathscr{L}$. This would be the rigid-analytic analogue of the decomposition theorem for projective maps in complex geometry. The paper explains that the theorem cannot hold for arbitrary proper maps, but presents this projective version as plausible; no resolution is supplied.