  We consider a gas of bosons interacting through a three-body hard-core
potential in the thermodynamic limit. We derive an upper bound on the ground
state energy of the system at the leading order using a Jastrow factor. Our
result matches the lower bound proven by Nam-Ricaud-Triay and therefore
resolves the leading order. Moreover, a straightforward adaptation of our proof
can be used for systems interacting via combined two-body and three-body
interactions to generalise Theorem 1.2. from arXiv:2402.05646 to hard-core
potentials.
