  The ab-initio understanding of hadronic three-body systems above threshold,
such as exotic resonances or the baryon spectrum, requires the mapping of the
finite-volume eigenvalue spectrum, produced in lattice QCD calculations, to the
infinite volume. We present the first application of such a formalism to a
physical system in form of three interacting positively charged pions. The
results for the ground state energies agree with the available lattice QCD
results by the NPLQCD collaboration at unphysical pion masses. Extrapolations
to physical pion masses are performed using input from effective field theory.
The excited energy spectrum is predicted. This demonstrates the feasibility to
determine three-body amplitudes above threshold from lattice QCD, including
resonance properties of axial mesons, exotics, and excited baryons.
