  Recent studies indicate that the ground state of a QCD four bottom quark
system may form a resonance in the range $\sim 18 -19$ GeV, near the
di-$\Upsilon$ threshold, which may be observable at the LHC in the four lepton
final state. These studies also predict a variety of possible resonances
associated with the various excited states and allow for a number of possible
spin and $CP$ quantum numbers. Of course, even if a resonance is observed in
four leptons in the predicted mass range, it will be prudent to experimentally
confirm its four bottom quark QCD nature or whether it is perhaps something
more exotic. We initiate an investigation in this direction by exploring the
ability of the \emph{normalized} fully differential decay width for decays to
four leptons to probe the underlying nature of a putative resonance including
$CP$ and tensor properties. We assume the first observed state is a spin-0
boson decaying to at least one on-shell $\Upsilon$, but allow for decays to
four leptons through $\Upsilon\Upsilon,\,\Upsilon\gamma$, and $\Upsilon Z$
vector boson pairs. We consider a range of resonance masses around the
di-$\Upsilon$ threshold and find excellent prospects at the LHC for
establishing its $CP$ and tensor properties, perhaps not long after a discovery
depending on (unknown) production cross sections and the exact resonance mass.
