  Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules: \[ \sum_n
(-1)^{2S_n} g_n = 0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^2 =0; \qquad \sum_n
(-1)^{2S_n} g_n \; m_n^4=0. \] These three sum rules are intimately related to
both the Lorentz invariance and the finiteness of the zero-point stress-energy
tensor. Further afield, these three constraints are also intimately related to
the existence of finite QFTs ultimately based on fermi--bose cancellations.
(Supersymmetry is neither necessary nor sufficient for the existence of these
finite QFTs; though softly but explicitly broken supersymmetry or mis-aligned
supersymmetry can be used as a book-keeping device to keep the calculations
manageable.) In the current article I shall instead take these three Pauli sum
rules as given, assume their exact non-perturbative validity, contrast them
with the observed standard model particle physics spectrum, and use them to
extract as much model-independent information as possible regarding beyond
standard model (BSM) physics.
