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The LHCb collaboration has recently observed three narrow pentaquark states--- the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ ---that are located close tothe $\bar{D} \Sigma_c$ and $\bar{D}^* \Sigma_c$ thresholds. Among the so-farproposed theoretical interpretations for these pentaquarks, the molecularhypothesis seems to be the preferred one. Nevertheless, in the molecularpicture the spins of the $P_c(4440)$ and $P_c(4457)$ have not beenunambiguously determined yet. In this letter we point out that heavyantiquark-diquark symmetry induces a model-independent relation between thespin-splitting in the masses of the $P_c(4440)$ and $P_c(4457)$ $\bar{D}^*\Sigma_c$ pentaquarks and the corresponding splitting for the $0^+$ and $1^+$$\Xi_{cc} \Sigma_c$ triply charmed dibaryons. This is particularly relevantowing to a recent lattice QCD prediction of the $1^+$ triply charmed dibaryon,which suggests that a calculation of the mass of its $0^+$ partner might bewithin reach. This in turn would reveal the spins of the $P_c(4440)$ and$P_c(4457)$ pentaquarks, providing a highly nontrivial test of heavy-quarksymmetry and the molecular nature of the pentaquarks. Furthermore, themolecular interpretation of the hidden-charm pentaquarks implies the existenceof a total of ten triply charmed dibaryons as $\Xi_{cc}^{(*)} \Sigma_c^{(*)}$molecules, which, if confirmed in the lattice, will largely expand ourunderstanding of the non-perturbative strong interaction in the heavy-quarksector.

Model independent determination of the spins of the $P_{c}$(4440) and $P_{c}$(4457) from the spectroscopy of the triply charmed dibaryons