The theory of negative mass instability (NMI) in proton synchrotrons has been regarded as established for about thirty years, but both accurate calculations and solid beam observations for real cases have been difficult and practically non-existent. The wider availability of so-called computing farms has made credible macroparticle simulations practical for routine use. The comparison of a macroparticle model with the existing theory indicates interesting discrepancies, although the theoretical threshold is confirmed. That comparison and code validation for the model are discussed in the context of useful specific cases. The importance of perturbations other than statistical fluctuation as the seed of instability is considered.