Non-perturbative insights into the spectral properties of QCD at finite temperature

In quantum field theories at finite temperature spectral functions describe how particle systems behave in the presence of a thermal medium. Although data from lattice simulations can in principle be used to determine spectral function characteristics, existing methods rely on the extraction of these quantities from temporal correlators, which requires one to circumvent an ill-posed inverse problem. In these proceedings we report on a recent approach that instead utilises the non-perturbative constraints imposed by field locality to extract spectral function information directly from spatial correlators. In particular, we focus on the application of this approach to lattice QCD data of the spatial pseudo-scalar meson correlator in the temperature range $220-960 \, \text{MeV}$, and outline why this data supports the conclusion that there exists a distinct pion state above the chiral pseudo-critical temperature $T_{\!\text{pc}}$.