In this talk, we will explore the current status of precision determinations of the strong coupling and the top-quark mass. We will illustrate how high-precision top-quark data from the Large Hadron Collider (LHC) facilitates a simultaneous extraction of proton parton distribution functions (PDFs), the strong coupling, and heavy-quark masses at next-to-next-to-leading order (NNLO) accuracy in quantum chromodynamics (QCD). Special emphasis will be placed on the correlations with PDFs, particularly the gluon PDF, which shows strong consistency with previous results but with significantly reduced uncertainties. Additionally, we will discuss the implications of these findings for the Higgs cross section at the LHC and the stability of the electroweak vacuum.