Towards classification of 5d SCFTs: Single gauge node

We propose a number of apparently equivalent criteria necessary for the consistency 5d SCFT in its Coulomb phase and use these to classify SCFTs arising from gauge theory with simple group. These include convergence 5-sphere partition function; positivity particle masses monopole string tensions; positive definiteness metric some region branch. find that large rank classical groups classes emerge where bounds on matter content Chern-Simons level grow linearly rank. For less than or equal 8, our classification leads additional cases which do not fit analysis. also allowed all exceptional groups.